Statistical physics of crime: A review
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paper_title: The Stability of Space-Time Clusters of Burglary

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This research, inspired by the precepts of optimal foraging theory, suggests that areas where domestic burglaries cluster shift over time, such that the location of clusters is not predictable over periods of three or more months. However, although clusters do not remain in the same location over time (i.e. are not stable over prolonged periods) they do tend to move in a 'slippery' manner, moving to nearby areas at successive points in time. The implications of the findings for hot-spotting and crime prevention are discussed.
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paper_title: Correlation of positive and negative reciprocity fails to confer an evolutionary advantage: Phase transitions to elementary strategies

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Economic experiments reveal that humans value cooperation and fairness. Punishing unfair behavior is therefore common, and according to the theory of strong reciprocity, it is also directly related to rewarding cooperative behavior. However, empirical data fail to confirm that positive and negative reciprocity are correlated. Inspired by this disagreement, we determine whether the combined application of reward and punishment is evolutionary advantageous. We study a spatial public goods game, where in addition to the three elementary strategies of defection, rewarding and punishment, a fourth strategy combining the later two competes for space. We find rich dynamical behavior that gives rise to intricate phase diagrams where continuous and discontinuous phase transitions occur in succession. Indirect territorial competition, spontaneous emergence of cyclic dominance, as well as divergent fluctuations of oscillations that terminate in an absorbing phase are observed. Yet despite the high complexity of solutions, the combined strategy can survive only in very narrow and unrealistic parameter regions. Elementary strategies, either in pure or mixed phases, are much more common and likely to prevail. Our results highlight the importance of patterns and structure in human cooperation, which should be considered in future experiments.
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paper_title: Cooperation and punishment in an adversarial game: how defectors pave the way to a peaceful society.

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The evolution of human cooperation has been the subject of much research, especially within the framework of evolutionary public goods games, where several mechanisms have been proposed to account for persistent cooperation. Yet, in addressing this issue, little attention has been given to games of a more adversarial nature, in which defecting players, rather than simply free riding, actively seek to harm others. Here, we develop an adversarial evolutionary game using the specific example of criminal activity, recasting the familiar public goods strategies of punishers, cooperators, and defectors in this light. We then introduce a strategy-the informant-with no clear analog in public goods games and show that individuals employing this strategy are a key to the emergence of systems where cooperation dominates. We also find that a defection-dominated regime may be transitioned to one that is cooperation-dominated by converting an optimal number of players into informants. We discuss these findings, the role of informants, and possible intervention strategies in extreme adversarial societies, such as those marred by wars and insurgencies.
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paper_title: Self-Exciting Point Process Modeling of Crime

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Highly clustered event sequences are observed in certain types of crime data, such as burglary and gang violence, due to crime-specific patterns of criminal behavior. Similar clustering patterns are observed by seismologists, as earthquakes are well known to increase the risk of subsequent earthquakes, or aftershocks, near the location of an initial event. Space–time clustering is modeled in seismology by self-exciting point processes and the focus of this article is to show that these methods are well suited for criminological applications. We first review self-exciting point processes in the context of seismology. Next, using residential burglary data provided by the Los Angeles Police Department, we illustrate the implementation of self-exciting point process models in the context of urban crime. For this purpose we use a fully nonparametric estimation methodology to gain insight into the form of the space–time triggering function and temporal trends in the background rate of burglary.
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paper_title: Incentives and opportunism: from the carrot to the stick

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Cooperation in public good games is greatly promoted by positive and negative incentives. In this paper, we use evolutionary game dynamics to study the evolution of opportunism (the readiness to be swayed by incentives) and the evolution of trust (the propensity to cooperate in the absence of information on the co-players). If both positive and negative incentives are available, evolution leads to a population where defectors are punished and players cooperate, except when they can get away with defection. Rewarding behaviour does not become fixed, but can play an essential role in catalysing the emergence of cooperation, especially if the information level is low.
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paper_title: Cleaning up drug hot spots in Oakland, California: The displacement and diffusion effects

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This paper examines the displacement and diffusion of a civil remedy program in Oakland, California. Coined the “SMART” (Specialized Multi-Agency Response Team) approach, the program uses municipal codes and drug nuisance abatement laws to control drug and disorder problems. The study finds that the SMART program not only decreases drug problems at the target sites, but also leads to a “net diffusion of benefits” in the areas surrounding targeted places.
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paper_title: Evolutionary advantages of adaptive rewarding

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Our well-being depends on both our personal success and the success of our society. The realization of this fact makes cooperation an essential trait. Experiments have shown that rewards can elevate our readiness to cooperate, but since giving a reward inevitably entails paying a cost for it, the emergence and stability of such behavior remains elusive. Here we show that allowing for the act of rewarding to self-organize in dependence on the success of cooperation creates several evolutionary advantages that instill new ways through which collaborative efforts are promoted. Ranging from indirect territorial battle to the spontaneous emergence and destruction of coexistence, phase diagrams and the underlying spatial patterns reveal fascinatingly rich social dynamics that explain why this costly behavior has evolved and persevered. Comparisons with adaptive punishment, however, uncover an Achilles heel of adaptive rewarding, coming from over-aggression, which in turn hinders optimal utilization of network reciprocity. This may explain why, despite its success, rewarding is not as firmly embedded into our societal organization as punishment.
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paper_title: Elements of Applied Bifurcation Theory

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1 Introduction to Dynamical Systems.- 2 Topological Equivalence, Bifurcations, and Structural Stability of Dynamical Systems.- 3 One-Parameter Bifurcations of Equilibria in Continuous-Time Dynamical Systems.- 4 One-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems.- 5 Bifurcations of Equilibria and Periodic Orbits in n-Dimensional Dynamical Systems.- 6 Bifurcations of Orbits Homoclinic and Heteroclinic to Hyperbolic Equilibria.- 7 Other One-Parameter Bifurcations in Continuous-Time Dynamical Systems.- 8 Two-Parameter Bifurcations of Equilibria in Continuous-Time Dynamical Systems.- 9 Two-Parameter Bifurcations of Fixed Points in Discrete-Time Dynamical Systems.- 10 Numerical Analysis of Bifurcations.- A Basic Notions from Algebra, Analysis, and Geometry.- A.1 Algebra.- A.1.1 Matrices.- A.1.2 Vector spaces and linear transformations.- A.1.3 Eigenvectors and eigenvalues.- A.1.4 Invariant subspaces, generalized eigenvectors, and Jordan normal form.- A.1.5 Fredholm Alternative Theorem.- A.1.6 Groups.- A.2 Analysis.- A.2.1 Implicit and Inverse Function Theorems.- A.2.2 Taylor expansion.- A.2.3 Metric, normed, and other spaces.- A.3 Geometry.- A.3.1 Sets.- A.3.2 Maps.- A.3.3 Manifolds.- References.
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paper_title: Winners don’t punish

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Many theories have been offered to explain the evolution of cooperation in humans. One proposal is that costly punishment can promote cooperation. Everyone benefits on average, the theory goes, despite the cost to those doing the punishing. But most of our interactions are repeated, and in such cases punishment can lead to retaliation. Using a variant of the 'Prisoner's Dilemma' game, Dreber et al. find that punishment increases the frequency of cooperation, but not the average payoff. Costly punishments confer no overall advantage to the group. And players who end up with the highest total payoff ('winners') tend not to use punishment, while those with the lowest payoff ('losers') punish most frequently. It seems that costly punishment may not have evolved to promote cooperation, but for some other purpose. An experimental economics approach finds that punishment increases the frequency of cooperation, but not the average payoff. Thus, the option of costly punishment does not confer an advantage to the group. Moreover, players who end up with the highest total payoff ('winners') do not use punishment, whereas players who end up with the lowest payoff ('losers') use punishment most frequently. A key aspect of human behaviour is cooperation1,2,3,4,5,6,7. We tend to help others even if costs are involved. We are more likely to help when the costs are small and the benefits for the other person significant. Cooperation leads to a tension between what is best for the individual and what is best for the group. A group does better if everyone cooperates, but each individual is tempted to defect. Recently there has been much interest in exploring the effect of costly punishment on human cooperation8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23. Costly punishment means paying a cost for another individual to incur a cost. It has been suggested that costly punishment promotes cooperation even in non-repeated games and without any possibility of reputation effects10. But most of our interactions are repeated and reputation is always at stake. Thus, if costly punishment is important in promoting cooperation, it must do so in a repeated setting. We have performed experiments in which, in each round of a repeated game, people choose between cooperation, defection and costly punishment. In control experiments, people could only cooperate or defect. Here we show that the option of costly punishment increases the amount of cooperation but not the average payoff of the group. Furthermore, there is a strong negative correlation between total payoff and use of costly punishment. Those people who gain the highest total payoff tend not to use costly punishment: winners don’t punish. This suggests that costly punishment behaviour is maladaptive in cooperation games and might have evolved for other reasons.
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paper_title: Reward and punishment

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Minigames capturing the essence of Public Goods experiments show that even in the absence of rationality assumptions, both punishment and reward will fail to bring about prosocial behavior. This result holds in particular for the well-known Ultimatum Game, which emerges as a special case. But reputation can induce fairness and cooperation in populations adapting through learning or imitation. Indeed, the inclusion of reputation effects in the corresponding dynamical models leads to the evolution of economically productive behavior, with agents contributing to the public good and either punishing those who do not or rewarding those who do. Reward and punishment correspond to two types of bifurcation with intriguing complementarity. The analysis suggests that reputation is essential for fostering social behavior among selfish agents, and that it is considerably more effective with punishment than with reward.
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paper_title: Territorial Developments Based on Graffiti: a Statistical Mechanics Approach

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We study the well-known sociological phenomenon of gang aggregation and territory formation through an interacting agent system defined on a lattice. We introduce a two-gang Hamiltonian model where agents have red or blue affiliation but are otherwise indistinguishable. In this model, all interactions are indirect and occur only via graffiti markings, on-site as well as on nearest neighbor locations. We also allow for gang proliferation and graffiti suppression. Within the context of this model, we show that gang clustering and territory formation may arise under specific parameter choices and that a phase transition may occur between well-mixed, possibly dilute configurations and well separated, clustered ones. Using methods from statistical mechanics, we study the phase transition between these two qualitatively different scenarios. In the mean-field rendition of this model, we identify parameter regimes where the transition is first or second order. In all cases, we have found that the transitions are a consequence solely of the gang to graffiti couplings, implying that direct gang to gang interactions are not strictly necessary for gang territory formation; in particular, graffiti may be the sole driving force behind gang clustering. We further discuss possible sociological -- as well as ecological -- ramifications of our results.
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paper_title: DOES CRIME JUST MOVE AROUND THE CORNER? A CONTROLLED STUDY OF SPATIAL DISPLACEMENT AND DIFFUSION OF CRIME CONTROL BENEFITS

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Recent studies point to the potential theoretical and practical benefits of focusing police resources on crime hot spots. However, many scholars have noted that such approaches risk displacing crime or disorder to other places where programs are not in place. Although much attention has been paid to the idea of displacement, methodological problems associated with measuring it have often been overlooked. We try to fill these gaps in measurement and understanding of displacement and the related phenomenon of diffusion of crime control benefits. Our main focus is on immediate spatial displacement or diffusion of crime to areas near the targeted sites of an intervention. Do focused crime prevention efforts at places simply result in a movement of offenders to areas nearby targeted sites —"do they simply move crime around the corner"? Or, conversely, will a crime prevention effort focusing on specific places lead to improvement in areas nearby — what has come to be termed a diffusion of crime control benefits? Our data are drawn from a controlled study of displacement and diffusion in Jersey City, New Jersey. Two sites with substantial street-level crime and disorder were targeted and carefully monitored during an experimental period. Two neighboring areas were selected as “catchment areas” from which to assess immediate spatial displacement or diffusion. Intensive police interventions were applied to each target site but not to the catchment areas. More than 6,000 20-minute social observations were conducted in the target and catchment areas. They were supplemented by interviews and ethnographic field observations. Our findings indicate that, at least for crime markets involving drugs and prostitution, crime does not simply move around the corner. Indeed, this study supports the position that the most likely outcome of such focused crime prevention efforts is a diffusion of crime control benefits to nearby areas.
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paper_title: Geographic Profiling from Kinetic Models of Criminal Behavior

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We consider the problem of estimating the probability density of the “anchor point” (residence, place of work, etc.) of a criminal offender given a set of observed spatial locations of crimes committed by the offender. Starting from kinetic models of criminal motion and target selection, we derive the probability density of anchor points using the Fokker–Planck equation and Bayes' theorem. Here, geographic inhomogeneities such as housing densities and geographic barriers (bodies of water, parks, etc.) are naturally incorporated into the probability density estimate, as well as directional bias and distance to crime preferences in offender target selection. The resulting equations are steady state advection-diffusion-reaction PDEs. We test our methodology against crime data provided by the Los Angeles Police Department, and our results highlight the benefits of incorporating these elements of criminal behavior and geographic inhomogeneities into profiling estimates.
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paper_title: Sentence Severity and Crime: Accepting the Null Hypothesis

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The literature on the effects of sentence severity on crime levels has been reviewed numerous times in the past twenty-five years. Most reviews conclude that there is little or no consistent evidence that harsher sanctions reduce crime rates in Western populations. Nevertheless, most reviewers have been reluctant to conclude that variation in the severity of sentence does not have differential deterrent impacts. A reasonable assessment of the research to date-with a particular focus on studies conducted in the past decade-is that sentence severity has no effect on the level of crime in society. It is time to accept the null hypothesis.
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paper_title: Hot spots policing and crime prevention: A systematic review of randomized controlled trials

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Crime scholars and practitioners have argued that police actions should be focused on high-risk crime places rather than spread thinly across the urban landscape. This review examines five randomized controlled trials of the effects of concentrating police enforcement efforts on crime hot spots. The findings of these evaluations suggest that focused police actions can prevent crime and disorder in crime hot spots. A meta-analysis of the effect sizes from the five experiments reveals a statistically significant mean effect size for hot spots policing interventions; this suggests overall reductions in citizen calls for service in the treatment hot spots relative to the control hot spots. These studies also suggest that focused police actions at specific locations do not necessarily result in crime displacement. Although these evaluations reveal that these programs work in preventing crime, additional research is needed to unravel other important policy-relevant issues such as community reaction to focused police enforcement efforts.
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paper_title: The evolution of antisocial punishment in optional public goods games

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Cooperation, where one individual incurs a cost to help another, is a fundamental building block of the natural world and human society. It has been suggested that costly punishment can promote the evolution of cooperation, with the threat of punishment deterring free-riders. Recent experiments, however, have revealed the existence of 'antisocial' punishment, where non-cooperators punish cooperators. While various theoretical models find that punishment can promote the evolution of cooperation, these models a priori exclude the possibility of antisocial punishment. Here we extend the standard theory of optional public goods games to include the full set of punishment strategies. We find that punishment no longer increases cooperation, and that selection favours substantial levels of antisocial punishment for a wide range of parameters. Furthermore, we conduct behavioural experiments, showing results consistent with our model predictions. As opposed to an altruistic act that promotes cooperation, punishment is mostly a self-interested tool for protecting oneself against potential competitors.
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paper_title: Universal bursty behaviour in human violent conflicts

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Understanding the mechanisms and processes underlying the dynamics of collective violence is of considerable current interest. Recent studies indicated the presence of robust patterns characterizing the size and timing of violent events in human conflicts. Since the size and timing of violent events arises as the result of a dynamical process, we explore the possibility of unifying these observations. By analyzing available catalogs on violent events in Iraq (2003–2005), Afghanistan (2008–2010) and Northern Ireland (1969–2001), we show that the inter-event time distributions (calculated for a range of minimum sizes) obeys approximately a simple scaling law which holds for more than three orders of magnitude. This robust pattern suggests a hierarchical organization in size and time providing a unified picture of the dynamics of violent conflicts.
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paper_title: Distance to the scaling law: a useful approach for unveiling relationships between crime and urban metrics

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We report on a quantitative analysis of relationships between the number of homicides, population size and other ten urban metrics. By using data from Brazilian cities, we show that well defined average scaling laws with the population size emerge when investigating the relations between population and number of homicides as well as population and urban metrics. We also show that the fluctuations around the scaling laws are log-normally distributed, which enabled us to model these scaling laws by a stochastic-like equation driven by a multiplicative and log-normally distributed noise. Because of the scaling laws, we argue that it is better to employ logarithms in order to describe the number of homicides in function of the urban metrics via regression analysis. In addition to the regression analysis, we propose an approach to correlate crime and urban metrics via the evaluation of the distance between the actual value of the number of homicides (as well as the value of the urban metrics) and the value that is expected by the scaling law with the population size. This approach have proved to be robust and useful for unveiling relationships/behaviors that were not properly carried out by the regression analysis, such as i) the non-explanatory potential of the elderly population when the number of homicides is much above or much below the scaling law, ii) the fact that unemployment has explanatory potential only when the number of homicides is considerably larger than the expected by the power law, and iii) a gender difference in number of homicides, where cities with female population below the scaling law are characterized by a number of homicides above the power law.
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paper_title: Where Size Matters: Agglomeration Economies of Illegal Drug Markets in Philadelphia

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There is a debate over whether police attention focused on an illegal drug market causes dealers to spatially displace their activities “around the corner” therefore having no positive impact on the aggregate level of illegal drug sales in the city. The alternative perspective is that focused police attention lowers the rate of illegal drug sales in the city. Recent research in Jersey City, New Jersey has demonstrated that focused police attention does not simply move illegal drug dealing around the corner. The present analysis explains why this finding is likely to be common in other cities using the economic theory of “agglomeration economies.” Agglomeration economies illustrate that taking the largest and most profitable site from illegal drug dealers will make dealing in the surrounding neighborhoods less rather than more profitable and lead to a smaller marketplace overall. The empirical analysis focuses on Philadelphia, Pennsylvania.
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paper_title: Repeat Burglary Victimisation: Spatial and Temporal Patterns

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To date there has been little Australian research on repeat victimisation. This is a study of repeat burglary in an area of Brisbane using police calls for service data. We demonstrate: (a) the prevalence of residential repeat victim addresses (‘hot dots’) is of a similar magnitude to that found in studies in the United Kingdom; (b) the time distributions of revictimisation are identical with those found in studies in the UK and elsewhere; (c) ‘hot spots’ (small areas with high crime density) can be identified by statistical analyses of spatial concentrations of incidents; (d) unstable hot spots tend to be temporary aggregations of hot dots, whereas stable hot spots seem to reflect more the social and physical characteristics of certain localities; and (e) the overall incidence of burglary could be reduced by at least 25 per cent if all repeat victimisation could be eliminated. There are a number of areas where concepts and techniques for repeat victim research could potentially be strengthened: (a) clarifying the connections between hot dots and hot spots, particularly through exploration of the concept of a ‘near repeat address’; (b) applying survival analysis to the data on the time periods between victimisations; and (c) using moving average techniques to examine changes in the spatial distributions of burglary over time.
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paper_title: External conversions of player strategy in an evolutionary game: A cost-benefit analysis through optimal control

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presence of criminal informants leads to diminishing crime, in this paper we investigate the active recruitment of informants from the general population via external intervention, albeit at a cost to society. While higher recruitment levels may be the most beneficial in abating crime, these are also more expensive. We thus formulate our optimal control problem to account for finite resources, incurred costs and expected benefits, and determine the most favourable recruitment strategy under given constraints. We consider the cases of targeted and untargeted recruitment, and allow recruitment costs to depend on past cumulative payoffs within a given memory time-frame so that conversion of more successful individuals may be more costly than that of less successful ones. Our optimal control problem is expressed via three control functions subject to a system of delay differential equations, and is numerically solved, analysed and discussed under different settings and in different parameter regimes. We find that the optimal strategy can change drastically and abruptly as parameters and resource constraints vary, and that increased information on individual player strategies leads to only slightly decreased minimal costs.
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paper_title: Scaling laws in the dynamics of crime growth rate

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The increasing number of crimes in areas with large concentrations of people have made cities one of the main sources of violence. Understanding characteristics of how crime rate expands and its relations with the cities size goes beyond an academic question, being a central issue for contemporary society. Here, we characterize and analyze quantitative aspects of murders in the period from 1980 to 2009 in Brazilian cities. We find that the distribution of the annual, biannual and triannual logarithmic homicide growth rates exhibit the same functional form for distinct scales, that is, a scale invariant behavior. We also identify asymptotic power-law decay relations between the standard deviations of these three growth rates and the initial size. Further, we discuss similarities with complex organizations.
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paper_title: Statistical physics of social dynamics

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Statistical physics has proven to be a fruitful framework to describe phenomena outside the realm of traditional physics. Recent years have witnessed an attempt by physicists to study collective phenomena emerging from the interactions of individuals as elementary units in social structures. A wide list of topics are reviewed ranging from opinion and cultural and language dynamics to crowd behavior, hierarchy formation, human dynamics, and social spreading. The connections between these problems and other, more traditional, topics of statistical physics are highlighted. Comparison of model results with empirical data from social systems are also emphasized.
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paper_title: Social Change and Crime Rate Trends: A Routine Activity Approach

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In this paper we present a "routine activity approach" for analyzing crime rate trends and cycles. Rather than emphasizing the characteristics of offenders, with this approach we concentrate upon the circumstances in which they carry out predatory criminal acts. Most criminal acts require convergence in space and time of likely offenders, suitable targets and the absence of capable guardians against crime. Human ecological theory facilitates an investigation into the way in which social structure produces this convergence, hence allowing illegal activities to feed upon the legal activities of everyday life. In particular, we hypothesize that the dispersion of activities away from households and families increases the opportunity for crime and thus generates higher crime rates. A variety of data is presented in support of the hypothesis, which helps explain crime rate trends in the United States 1947-1974 as a byproduct of changes in such variables as labor force participation and single-adult households.
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paper_title: Positive Interactions Promote Public Cooperation

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The public goods game is the classic laboratory paradigm for studying collective action problems. Each participant chooses how much to contribute to a common pool that returns benefits to all participants equally. The ideal outcome occurs if everybody contributes the maximum amount, but the self-interested strategy is not to contribute anything. Most previous studies have found punishment to be more effective than reward for maintaining cooperation in public goods games. The typical design of these studies, however, represses future consequences for today’s actions. In an experimental setting, we compare public goods games followed by punishment, reward, or both in the setting of truly repeated games, in which player identities persist from round to round. We show that reward is as effective as punishment for maintaining public cooperation and leads to higher total earnings. Moreover, when both options are available, reward leads to increased contributions and payoff, whereas punishment has no effect on contributions and leads to lower payoff. We conclude that reward outperforms punishment in repeated public goods games and that human cooperation in such repeated settings is best supported by positive interactions with others.
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paper_title: Criminal Defectors Lead to the Emergence of Cooperation in an Experimental, Adversarial Game

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While the evolution of cooperation has been widely studied, little attention has been devoted to adversarial settings wherein one actor can directly harm another. Recent theoretical work addresses this issue, introducing an adversarial game in which the emergence of cooperation is heavily reliant on the presence of ‘‘Informants,’’ actors who defect at first-order by harming others, but who cooperate at second-order by punishing other defectors. We experimentally study this adversarial environment in the laboratory with human subjects to test whether Informants are indeed critical for the emergence of cooperation. We find in these experiments that, even more so than predicted by theory, Informants are crucial for the emergence and sustenance of a high cooperation state. A key lesson is that successfully reaching and maintaining a low defection society may require the cultivation of criminals who will also aid in the punishment of others.
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paper_title: Dissipation and displacement of hotspots in reaction-diffusion models of crime

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The mechanisms driving the nucleation, spread, and dissipation of crime hotspots are poorly understood. As a consequence, the ability of law enforcement agencies to use mapped crime patterns to design crime prevention strategies is severely hampered. We also lack robust expectations about how different policing interventions should impact crime. Here we present a mathematical framework based on reaction-diffusion partial differential equations for studying the dynamics of crime hotspots. The system of equations is based on empirical evidence for how offenders move and mix with potential victims or targets. Analysis shows that crime hotspots form when the enhanced risk of repeat crimes diffuses locally, but not so far as to bind distant crime together. Crime hotspots may form as either supercritical or subcritical bifurcations, the latter the result of large spikes in crime that override linearly stable, uniform crime distributions. Our mathematical methods show that subcritical crime hotspots may be permanently eradicated with police suppression, whereas supercritical hotspots are displaced following a characteristic spatial pattern. Our results thus provide a mechanistic explanation for recent failures to observe crime displacement in experimental field tests of hotspot policing.
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paper_title: Recidivism and Rehabilitation of Criminal Offenders: A Carrot and Stick Evolutionary Game

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Motivated by recent efforts by the criminal justice system to treat and rehabilitate nonviolent offenders rather than focusing solely on their punishment, we introduce an evolutionary game theoretic model to study the effects of “carrot and stick” intervention programs on criminal recidivism. We use stochastic simulations to study the evolution of a population where individuals may commit crimes depending on their past history, surrounding environment and, in the case of recidivists, on any counseling, educational or training programs available to them after being punished for their previous crimes. These sociological factors are embodied by effective parameters that determine the decision making probabilities. Players may decide to permanently reform or continue engaging in criminal activity, eventually reaching a state where they are considered incorrigible. Depending on parameter choices, the outcome of the game is a society with a majority of virtuous, rehabilitated citizens or incorrigibles. Since total resources may be limited, we constrain the combined punishment and rehabilitation costs per crime to be fixed, so that increasing one effort will necessarily decrease the other. We find that the most successful strategy in reducing crime is to optimally allocate resources so that after being punished, criminals experience impactful intervention programs, especially during the first stages of their return to society. Excessively harsh or lenient punishments are less effective. We also develop a system of coupled ordinary differential equations with memory effects to give a qualitative description of our simulated societal dynamics. We discuss our findings and sociological implications.
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paper_title: Understanding recurrent crime as system-immanent collective behavior

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Containing the spreading of crime is a major challenge for society. Yet, since thousands of years, no effective strategy has been found to overcome crime. To the contrary, empirical evidence shows that crime is recurrent, a fact that is not captured well by rational choice theories of crime. According to these, strong enough punishment should prevent crime from happening. To gain a better understanding of the relationship between crime and punishment, we consider that the latter requires prior discovery of illicit behavior and study a spatial version of the inspection game. Simulations reveal the spontaneous emergence of cyclic dominance between “criminals”, “inspectors”, and “ordinary people” as a consequence of spatial interactions. Such cycles dominate the evolutionary process, in particular when the temptation to commit crime or the cost of inspection are low or moderate. Yet, there are also critical parameter values beyond which cycles cease to exist and the population is dominated either by a stable mixture of criminals and inspectors or one of these two strategies alone. Both continuous and discontinuous phase transitions to different final states are possible, indicating that successful strategies to contain crime can be very much counter-intuitive and complex. Our results demonstrate that spatial interactions are crucial for the evolutionary outcome of the inspection game, and they also reveal why criminal behavior is likely to be recurrent rather than evolving towards an equilibrium with monotonous parameter dependencies.
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paper_title: New insights into the spatial and temporal distribution of repeat victimization

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Research has demonstrated an elevated risk of burglary following an initial incident. The present study examines the time course of repeat victimization, and extends understanding by examining the relationships between repeat victimization and deprivation, and burglary 'hotspots'. Consistent with other studies, the rate of repeat victimization was higher than that expected on the basis of statistical likelihood. Interestingly, the time course of repeat victimization conformed to an exponential model. Two alternative hypotheses are presented to attempt to explain this relationship. One highlights the increased vulnerability of a household following an initial burglary; the other attempts to explain the variation in repeat victimization in terms of characteristics of the offender. Other findings indicate a clear relationship between repeat victimization and deprivation, and suggest that the geographical location of repeat victimizations may well contribute to the definition of burglary 'hotspots'. The results have clear implications for proactive policing and policy making.
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paper_title: The Stability of Space-Time Clusters of Burglary

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This research, inspired by the precepts of optimal foraging theory, suggests that areas where domestic burglaries cluster shift over time, such that the location of clusters is not predictable over periods of three or more months. However, although clusters do not remain in the same location over time (i.e. are not stable over prolonged periods) they do tend to move in a 'slippery' manner, moving to nearby areas at successive points in time. The implications of the findings for hot-spotting and crime prevention are discussed.
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paper_title: How Do Residential Burglars Select Target Areas?: A New Approach to the Analysis of Criminal Location Choice

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This paper introduces the discrete spatial choice approach to the study of criminal target choice. The approach is used to assess whether residential burglars are attracted to target areas that are affluent, accessible, and poorly guarded. In addition, the importance of these criteria is postulated to vary across burglars. The theory is tested using data on 548 residential burglaries, committed by 290 burglars from the city of The Hague, the Netherlands. The likelihood of a neighbourhood's being selected for burglary is heightened by its ethnic heterogeneity, its percentage of single-family dwellings, and its proximity to where the offender lives. The results and prospects of the discrete spatial choice approach for spatial target selection research are discussed.
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paper_title: Cooperation Prevails When Individuals Adjust Their Social Ties

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Conventional evolutionary game theory predicts that natural selection favours the selfish and strong even though cooperative interactions thrive at all levels of organization in living systems. Recent investigations demonstrated that a limiting factor for the evolution of cooperative interactions is the way in which they are organized, cooperators becoming evolutionarily competitive whenever individuals are constrained to interact with few others along the edges of networks with low average connectivity. Despite this insight, the conundrum of cooperation remains since recent empirical data shows that real networks exhibit typically high average connectivity and associated single-to-broad-scale heterogeneity. Here, a computational model is constructed in which individuals are able to self-organize both their strategy and their social ties throughout evolution, based exclusively on their self-interest. We show that the entangled evolution of individual strategy and network structure constitutes a key mechanism for the sustainability of cooperation in social networks. For a given average connectivity of the population, there is a critical value for the ratio W between the time scales associated with the evolution of strategy and of structure above which cooperators wipe out defectors. Moreover, the emerging social networks exhibit an overall heterogeneity that accounts very well for the diversity of patterns recently found in acquired data on social networks. Finally, heterogeneity is found to become maximal when W reaches its critical value. These results show that simple topological dynamics reflecting the individual capacity for self-organization of social ties can produce realistic networks of high average connectivity with associated single-to-broad-scale heterogeneity. On the other hand, they show that cooperation cannot evolve as a result of "social viscosity" alone in heterogeneous networks with high average connectivity, requiring the additional mechanism of topological co-evolution to ensure the survival of cooperative behaviour.
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paper_title: Evolution of collective action in adaptive social structures

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Many problems in nature can be conveniently framed as a problem of evolution of collective cooperative behaviour, often modelled resorting to the tools of evolutionary game theory in well-mixed populations, combined with an appropriate N-person dilemma. Yet, the well-mixed assumption fails to describe the population dynamics whenever individuals have a say in deciding which groups they will participate. Here we propose a simple model in which dynamical group formation is described as a result of a topological evolution of a social network of interactions. We show analytically how evolutionary dynamics under public goods games in finite adaptive networks can be effectively transformed into a N-Person dilemma involving both coordination and co-existence. Such dynamics would be impossible to foresee from more conventional 2-person interactions as well as from descriptions based on infinite, well-mixed populations. Finally, we show how stochastic effects help rendering cooperation viable, promoting polymorphic configurations in which cooperators prevail.
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paper_title: Reacting Differently to Adverse Ties Promotes Cooperation in Social Networks

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We investigate how diversity in individual responses to unwanted interactions affects the evolution of cooperation modeled as a 2-person prisoner's dilemma. We combine adaptive networks and evolutionary game theory, showing analytically how the coevolution of social dynamics, network dynamics, and behavioral differences benefit the entire community even though myopic individuals still act in their own interest. As defectors are wiped out, surviving cooperators maintain the full diversity of behavioral types, establishing cooperation as a robust evolutionary strategy. The present framework can be used in other problems where the feedback between topology and dynamics affects the overall behavior of the system.
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paper_title: Statistical mechanics of complex networks

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The emergence of order in natural systems is a constant source of inspiration for both physical and biological sciences. While the spatial order characterizing for example the crystals has been the basis of many advances in contemporary physics, most complex systems in nature do not offer such high degree of order. Many of these systems form complex networks whose nodes are the elements of the system and edges represent the interactions between them. ::: Traditionally complex networks have been described by the random graph theory founded in 1959 by Paul Erdohs and Alfred Renyi. One of the defining features of random graphs is that they are statistically homogeneous, and their degree distribution (characterizing the spread in the number of edges starting from a node) is a Poisson distribution. In contrast, recent empirical studies, including the work of our group, indicate that the topology of real networks is much richer than that of random graphs. In particular, the degree distribution of real networks is a power-law, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network. ::: The scale-free topology of real networks has very important consequences on their functioning. For example, we have discovered that scale-free networks are extremely resilient to the random disruption of their nodes. On the other hand, the selective removal of the nodes with highest degree induces a rapid breakdown of the network to isolated subparts that cannot communicate with each other. ::: The non-trivial scaling of the degree distribution of real networks is also an indication of their assembly and evolution. Indeed, our modeling studies have shown us that there are general principles governing the evolution of networks. Most networks start from a small seed and grow by the addition of new nodes which attach to the nodes already in the system. This process obeys preferential attachment: the new nodes are more likely to connect to nodes with already high degree. We have proposed a simple model based on these two principles wich was able to reproduce the power-law degree distribution of real networks. Perhaps even more importantly, this model paved the way to a new paradigm of network modeling, trying to capture the evolution of networks, not just their static topology.
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paper_title: Repeat Burglary Victimisation: Spatial and Temporal Patterns

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To date there has been little Australian research on repeat victimisation. This is a study of repeat burglary in an area of Brisbane using police calls for service data. We demonstrate: (a) the prevalence of residential repeat victim addresses (‘hot dots’) is of a similar magnitude to that found in studies in the United Kingdom; (b) the time distributions of revictimisation are identical with those found in studies in the UK and elsewhere; (c) ‘hot spots’ (small areas with high crime density) can be identified by statistical analyses of spatial concentrations of incidents; (d) unstable hot spots tend to be temporary aggregations of hot dots, whereas stable hot spots seem to reflect more the social and physical characteristics of certain localities; and (e) the overall incidence of burglary could be reduced by at least 25 per cent if all repeat victimisation could be eliminated. There are a number of areas where concepts and techniques for repeat victim research could potentially be strengthened: (a) clarifying the connections between hot dots and hot spots, particularly through exploration of the concept of a ‘near repeat address’; (b) applying survival analysis to the data on the time periods between victimisations; and (c) using moving average techniques to examine changes in the spatial distributions of burglary over time.
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paper_title: EFFECTS OF ATTRACTIVENESS, OPPORTUNITY AND ACCESSIBILITY TO BURGLARS ON RESIDENTIAL BURGLARY RATES OF URBAN NEIGHBORHOODS

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This study assesses the effects of attractiveness, opportunity and accessibility to burglars on the residential burglary rates of urban neighborhoods, combining two complementary lines of investigation that have been following separate tracks in the literature. As a complement to standard measures of attractiveness and opportunity, we introduce and specify a spatial measure of the accessibility of neighborhoods to burglars. Using data on about 25, 000 attempted and completed residential burglaries committed in the period 1996–2001 in the city of The Hague, the Netherlands, we study the variation in burglary rates across its 89 residential neighborhoods. Our results suggest that all three factors, attractiveness, opportunity and accessibility to burglars, pull burglars to their target neighborhoods.
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paper_title: Space–Time Patterns of Risk: A Cross National Assessment of Residential Burglary Victimization

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Using epidemiological techniques for testing disease contagion, it has recently been found that in the wake of a residential burglary, the risk to nearby homes is temporarily elevated. This paper demonstrates the ubiquity of this phenomenon by analyzing space–time patterns of burglary in 10 areas, located in five different countries. While the precise patterns vary, for all areas, houses within 200 m of a burgled home were at an elevated risk of burglary for a period of at least two weeks. For three of the five countries, differences in these patterns may partly be explained by simple differences in target density. The findings inform theories of crime concentration and offender targeting strategies, and have implications for crime forecasting and crime reduction more generally.
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paper_title: Coevolutionary games - a mini review

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Prevalence of cooperation within groups of selfish individuals is puzzling in that it contradicts with the basic premise of natural selection. Favoring players with higher fitness, the latter is key for understanding the challenges faced by cooperators when competing with defectors. Evolutionary game theory provides a competent theoretical framework for addressing the subtleties of cooperation in such situations, which are known as social dilemmas. Recent advances point towards the fact that the evolution of strategies alone may be insufficient to fully exploit the benefits offered by cooperative behavior. Indeed, while spatial structure and heterogeneity, for example, have been recognized as potent promoters of cooperation, coevolutionary rules can extend the potentials of such entities further, and even more importantly, lead to the understanding of their emergence. The introduction of coevolutionary rules to evolutionary games implies, that besides the evolution of strategies, another property may simultaneously be subject to evolution as well. Coevolutionary rules may affect the interaction network, the reproduction capability of players, their reputation, mobility or age. Here we review recent works on evolutionary games incorporating coevolutionary rules, as well as give a didactic description of potential pitfalls and misconceptions associated with the subject. In addition, we briefly outline directions for future research that we feel are promising, thereby particularly focusing on dynamical effects of coevolutionary rules on the evolution of cooperation, which are still widely open to research and thus hold promise of exciting new discoveries.
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paper_title: New insights into the spatial and temporal distribution of repeat victimization

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Research has demonstrated an elevated risk of burglary following an initial incident. The present study examines the time course of repeat victimization, and extends understanding by examining the relationships between repeat victimization and deprivation, and burglary 'hotspots'. Consistent with other studies, the rate of repeat victimization was higher than that expected on the basis of statistical likelihood. Interestingly, the time course of repeat victimization conformed to an exponential model. Two alternative hypotheses are presented to attempt to explain this relationship. One highlights the increased vulnerability of a household following an initial burglary; the other attempts to explain the variation in repeat victimization in terms of characteristics of the offender. Other findings indicate a clear relationship between repeat victimization and deprivation, and suggest that the geographical location of repeat victimizations may well contribute to the definition of burglary 'hotspots'. The results have clear implications for proactive policing and policy making.
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paper_title: Criminals Treated as Predators to Be Harvested: A Two Prey One Predator Model with Group Defense, Prey Migration and Switching

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A mathematical model is formulated and analysed to study the dynamics of a one predator - two prey eco-system using the logistic equation in which the predator switches between habitats and is being harvested. Constant effort and Constant yield harvesting functions are applied to the predators. The Constant effort strategy as opposed constant yield strategy may lead to an additional equilibrium in which the predators are extinct, whereas in the Constant yield stategy the only equilibrium is the coexistence one. In both cases, computer simulations are performed to study the effects of various parameters on the dynamics of the system. These studies show that depending on parameter values, a stable equilibrium or a limit cycle orbit is possible with both harvesing types.
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paper_title: Modeling the Underlying Dynamics of the Spread of Crime

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The spread of crime is a complex, dynamic process that calls for a systems level approach. Here, we build and analyze a series of dynamical systems models of the spread of crime, imprisonment and recidivism, using only abstract transition parameters. To find the general patterns among these parameters--patterns that are independent of the underlying particulars--we compute analytic expressions for the equilibria and for the tipping points between high-crime and low-crime equilibria in these models. We use these expressions to examine, in particular, the effects of longer prison terms and of increased incarceration rates on the prevalence of crime, with a follow-up analysis on the effects of a Three-Strike Policy.
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paper_title: A triangle model of criminality

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This paper is concerned with a quantitative model describing the interaction of three sociological species, termed as owners, criminals and security guards, and denoted by X, Y and Z respectively. In our model, Y is a predator of the species X, and so is Z with respect to Y. Moreover, Z can also be thought of as a predator of X, since this last population is required to bear the costs of maintaining Z.
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paper_title: Pattern formation outside of equilibrium

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A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.
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paper_title: Statistical Models of Criminal Behavior: The Effects of Law Enforcement Actions

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We extend an agent-based model of crime-pattern formation initiated in Short et al. by incorporating the effects of law enforcement agents. We investigate the effect that these agents have on the spatial distribution and overall level of criminal activity in a simulated urban setting. Our focus is on a two-dimensional lattice model of residential burglaries, where each site (target) is characterized by a dynamic attractiveness to burglary and where criminal and law enforcement agents are represented by random walkers. The dynamics of the criminal agents and the target-attractiveness field are, with certain modifications, as described in Short et al. Here the dynamics of enforcement agents are affected by the attractiveness field via a biasing of the walk, the detailed rules of which define a deployment strategy. We observe that law enforcement agents, if properly deployed, will in fact reduce the total amount of crime, but their relative effectiveness depends on the number of agents deployed, the deployme...
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paper_title: Global Bifurcation of Solutions for Crime Modeling Equations

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We study pattern formation in a quasi-linear system of two elliptic equations that was developed by Short et al. [Math. Models Methods Appl. Sci., 18 (2008), pp. 1249–1267] as a model for residential burglary. That model is based on the observation that the rate of burglaries of houses that have been burglarized recently and their close neighbors is typically higher than the average rate in the larger community, which creates hotspots for burglary. The patterns generated by the model describe the location of those hotspots. We prove that the system supports global bifurcation of spatially varying solutions from the spatially constant equilibrium, leading to the formation of spatial patterns. The analysis is based on recent results on global bifurcation in quasi-linear elliptic systems derived by Shi and Wang [J. Differential Equations, 7 (2009), pp. 2788–2812]. We show in some cases that near the bifurcation point the bifurcating spatial patterns are stable.
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paper_title: Dissipation and displacement of hotspots in reaction-diffusion models of crime

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The mechanisms driving the nucleation, spread, and dissipation of crime hotspots are poorly understood. As a consequence, the ability of law enforcement agencies to use mapped crime patterns to design crime prevention strategies is severely hampered. We also lack robust expectations about how different policing interventions should impact crime. Here we present a mathematical framework based on reaction-diffusion partial differential equations for studying the dynamics of crime hotspots. The system of equations is based on empirical evidence for how offenders move and mix with potential victims or targets. Analysis shows that crime hotspots form when the enhanced risk of repeat crimes diffuses locally, but not so far as to bind distant crime together. Crime hotspots may form as either supercritical or subcritical bifurcations, the latter the result of large spikes in crime that override linearly stable, uniform crime distributions. Our mathematical methods show that subcritical crime hotspots may be permanently eradicated with police suppression, whereas supercritical hotspots are displaced following a characteristic spatial pattern. Our results thus provide a mechanistic explanation for recent failures to observe crime displacement in experimental field tests of hotspot policing.
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paper_title: Self-Exciting Point Process Modeling of Crime

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Highly clustered event sequences are observed in certain types of crime data, such as burglary and gang violence, due to crime-specific patterns of criminal behavior. Similar clustering patterns are observed by seismologists, as earthquakes are well known to increase the risk of subsequent earthquakes, or aftershocks, near the location of an initial event. Space–time clustering is modeled in seismology by self-exciting point processes and the focus of this article is to show that these methods are well suited for criminological applications. We first review self-exciting point processes in the context of seismology. Next, using residential burglary data provided by the Los Angeles Police Department, we illustrate the implementation of self-exciting point process models in the context of urban crime. For this purpose we use a fully nonparametric estimation methodology to gain insight into the form of the space–time triggering function and temporal trends in the background rate of burglary.
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paper_title: Geographic Profiling from Kinetic Models of Criminal Behavior

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We consider the problem of estimating the probability density of the “anchor point” (residence, place of work, etc.) of a criminal offender given a set of observed spatial locations of crimes committed by the offender. Starting from kinetic models of criminal motion and target selection, we derive the probability density of anchor points using the Fokker–Planck equation and Bayes' theorem. Here, geographic inhomogeneities such as housing densities and geographic barriers (bodies of water, parks, etc.) are naturally incorporated into the probability density estimate, as well as directional bias and distance to crime preferences in offender target selection. The resulting equations are steady state advection-diffusion-reaction PDEs. We test our methodology against crime data provided by the Los Angeles Police Department, and our results highlight the benefits of incorporating these elements of criminal behavior and geographic inhomogeneities into profiling estimates.
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paper_title: Cooperation and punishment in an adversarial game: how defectors pave the way to a peaceful society.

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The evolution of human cooperation has been the subject of much research, especially within the framework of evolutionary public goods games, where several mechanisms have been proposed to account for persistent cooperation. Yet, in addressing this issue, little attention has been given to games of a more adversarial nature, in which defecting players, rather than simply free riding, actively seek to harm others. Here, we develop an adversarial evolutionary game using the specific example of criminal activity, recasting the familiar public goods strategies of punishers, cooperators, and defectors in this light. We then introduce a strategy-the informant-with no clear analog in public goods games and show that individuals employing this strategy are a key to the emergence of systems where cooperation dominates. We also find that a defection-dominated regime may be transitioned to one that is cooperation-dominated by converting an optimal number of players into informants. We discuss these findings, the role of informants, and possible intervention strategies in extreme adversarial societies, such as those marred by wars and insurgencies.
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paper_title: Topology independent impact of noise on cooperation in spatial public goods games

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We study the evolution of cooperation in public goods games on different regular graphs as a function of the noise level underlying strategy adoptions. We focus on the effects that are brought about by different group sizes of public goods games in which individuals participate, revealing that larger groups of players may induce qualitatively different behavior when approaching the deterministic limit of strategy adoption. While by pairwise interactions an intermediate uncertainty by strategy adoptions may ensure optimal conditions for the survival of cooperators at a specific graph topology, larger groups warrant this only in the vicinity of the deterministic limit independently from the underlying graph. These discrepancies are attributed to the indirect linkage of otherwise not directly connected players, which is brought about by joint memberships within the larger groups. Thus, we show that increasing the group size may introduce an effective transition of the interaction topology, and that the latter shapes the noise dependence of the evolution of cooperation in case of pairwise interactions only.
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paper_title: Social diversity promotes the emergence of cooperation in public goods games

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Although humans often cooperate with each other, the temptation to forego the public good mostly wins over collective cooperative action, leading to the so-called 'tragedy of the commons'. Many existing models treat individuals as equivalent, ignoring diversity and population structure. Santos et al. show theoretically that social diversity, introduced via heterogeneous graphs, promotes the emergence of cooperation in public goods games. Humans often cooperate with each other, but the temptation to forgo the public good mostly wins over collective cooperative action. Many existing models treat individuals as equivalent, ignoring diversity and population structure; however, here it's shown theoretically that social diversity, introduced via heterogeneous graphs, promotes the emergence of cooperation in public goods games. Humans often cooperate in public goods games1,2,3 and situations ranging from family issues to global warming4,5. However, evolutionary game theory predicts4,6 that the temptation to forgo the public good mostly wins over collective cooperative action, and this is often also seen in economic experiments7. Here we show how social diversity provides an escape from this apparent paradox. Up to now, individuals have been treated as equivalent in all respects4,8, in sharp contrast with real-life situations, where diversity is ubiquitous. We introduce social diversity by means of heterogeneous graphs and show that cooperation is promoted by the diversity associated with the number and size of the public goods game in which each individual participates and with the individual contribution to each such game. When social ties follow a scale-free distribution9, cooperation is enhanced whenever all individuals are expected to contribute a fixed amount irrespective of the plethora of public goods games in which they engage. Our results may help to explain the emergence of cooperation in the absence of mechanisms based on individual reputation and punishment10,11,12. Combining social diversity with reputation and punishment will provide instrumental clues on the self-organization of social communities and their economical implications.
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paper_title: Penalty has no Impact on Crime: A Game-Theoretic Analysis

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Existing approaches consider crime as either the consequence of antecedent social conditions or the outcome of a rational calculation by a predator who chooses crime as a utility-maximizing career. Consequently, these approaches propose either an improvement in social conditions or an increase in penalties as a means to reduce criminal activity. This article adopts a game-theoretic framework and examines crime as a game between criminals and the police. On realistic grounds, this approach represents an improvement on the conventional economic analysis of crime, concluding that under a wide variety of conditions (described by axioms 1 through 4), an increase in the severity of the penalty has no impact on criminal behavior at equilibrium. In fact, an increase in the penalty reduces the frequency of law enforcement at equilibrium. The major policy implication is that in order to reduce criminal activity at equilibrium, one has to modify the payoff structure of the police. Several variations of the model are...
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paper_title: What if criminals optimize their choice? Optimal strategies to defend public goods

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We investigate optimal strategies to defend valuable goods against the attacks of a thief. Given the value of the goods and the probability of success for the thief, we look for the strategy that assures the largest benefit to each player irrespective of the strategy of his opponent. Two complementary approaches are used: agent-based modeling and game theory. It is shown that the compromise between the value of the goods and the probability of success defines the mixed Nash equilibrium of the game, that is compared with the results of the agent-based simulations and discussed in terms of the system parameters.
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paper_title: Evolutionary games on graphs

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Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.
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paper_title: Evolution of in-group favoritism

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In-group favoritism is a central aspect of human behavior. People often help members of their own group more than members of other groups. Here we propose a mathematical framework for the evolution of in-group favoritism from a continuum of strategies. Unlike previous models, we do not pre-suppose that players never cooperate with out-group members. Instead, we determine the conditions under which preferential in-group cooperation emerges, and also explore situations where preferential out-group helping could evolve. Our approach is not based on explicit intergroup conflict, but instead uses evolutionary set theory. People can move between sets. Successful sets attract members, and successful strategies gain imitators. Individuals can employ different strategies when interacting with in-group versus out-group members. Our framework also allows us to implement different games for these two types of interactions. We prove general results and derive specific conditions for the evolution of cooperation based on in-group favoritism.
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paper_title: Risk of collective failure provides an escape from the tragedy of the commons

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From group hunting to global warming, how to deal with collective action may be formulated in terms of a public goods game of cooperation. In most cases, contributions depend on the risk of future losses. Here, we introduce an evolutionary dynamics approach to a broad class of cooperation problems in which attempting to minimize future losses turns the risk of failure into a central issue in individual decisions. We find that decisions within small groups under high risk and stringent requirements to success significantly raise the chances of coordinating actions and escaping the tragedy of the commons. We also offer insights on the scale at which public goods problems of cooperation are best solved. Instead of large-scale endeavors involving most of the population, which as we argue, may be counterproductive to achieve cooperation, the joint combination of local agreements within groups that are small compared with the population at risk is prone to significantly raise the probability of success. In addition, our model predicts that, if one takes into consideration that groups of different sizes are interwoven in complex networks of contacts, the chances for global coordination in an overall cooperating state are further enhanced.
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paper_title: External conversions of player strategy in an evolutionary game: A cost-benefit analysis through optimal control

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presence of criminal informants leads to diminishing crime, in this paper we investigate the active recruitment of informants from the general population via external intervention, albeit at a cost to society. While higher recruitment levels may be the most beneficial in abating crime, these are also more expensive. We thus formulate our optimal control problem to account for finite resources, incurred costs and expected benefits, and determine the most favourable recruitment strategy under given constraints. We consider the cases of targeted and untargeted recruitment, and allow recruitment costs to depend on past cumulative payoffs within a given memory time-frame so that conversion of more successful individuals may be more costly than that of less successful ones. Our optimal control problem is expressed via three control functions subject to a system of delay differential equations, and is numerically solved, analysed and discussed under different settings and in different parameter regimes. We find that the optimal strategy can change drastically and abruptly as parameters and resource constraints vary, and that increased information on individual player strategies leads to only slightly decreased minimal costs.
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paper_title: Evolution and the theory of games

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The modern theory of evolutionary dynamics is founded upon the remarkable insights of R. A. Fisher and Sewall Wright and set forth in the loci classici The Genetical Theory of Natural Selection (1930) and ‘Evolution in Mendelian Populations’ (1931). By the time of the publication of Wright’s paper in 1931 all of the theory of population genetics, as it is presently understood, was established. It is a sign of the extraordinary power of these early formulations, that nothing of equal significance has been added to the theory of population genetics in the thirty years that have passed since that time. Yet we cannot take this period to mean that we now have an adequate theory of evolutionary dynamics. On the contrary, the theory of population genetics, as complete as it may be in itself, fails to deal with many problems of primary importance for an understanding of evolution.
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paper_title: The Evolution of Homophily

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Biologists have devoted much attention to assortative mating or homogamy, the tendency for sexual species to mate with similar others. In contrast, there has been little theoretical work on the broader phenomenon of homophily, the tendency for individuals to interact with similar others. Yet this behaviour is also widely observed in nature. Here, we model how natural selection can give rise to homophily when individuals engage in social interaction in a population with multiple observable phenotypes. Payoffs to interactions depend on whether or not individuals have the same or different phenotypes, and each individual has a preference that determines how likely they are to interact with others of their own phenotype (homophily) or of opposite phenotypes (heterophily). The results show that homophily tends to evolve under a wide variety of conditions, helping to explain its ubiquity in nature.
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paper_title: Understanding Crime Statistics: Revisiting the Divergence of the NCVS and UCR

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Introduction: 1. Introduction James P. Lynch and Lynn A. Addington Part I. Overview of the Two National Measures of U.S. Crime: 2. Introduction to the National Crime Victimization Survey Michael Rand and Callie Rennison 3. Introduction to the Uniform Crime Reporting Program Cynthia Barnett-Ryan Part II. Defining Divergence and Convergence: 4. What is convergence, and what do we know about it? David McDowall and Colin Loftin Part III. Sources of Divergence in the NCVS: 5. Methodological change in the NCVS and the effect on convergence Shannan M. Catalano 6. Series victimizations and divergence Mike Planty 7. Exploring differences in estimates of visits to emergency rooms for injuries from assaults using the NCVS and NHAMCS Jacqueline Cohen and James P. Lynch Part IV. Sources of Divergence in the UCR: 8. Using NIBRS to study methodological sources of divergence between the UCR and NCVS Lynn A. Addington 9. Explaining the divergence between UCR and NCVS aggravated assault trends Richard Rosenfeld 10. Missing UCR data and divergence of the NCVS and UCR trends Michael D. Maltz Conclusion James P. Lynch and Lynn A. Addington.
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paper_title: Criminal Defectors Lead to the Emergence of Cooperation in an Experimental, Adversarial Game

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While the evolution of cooperation has been widely studied, little attention has been devoted to adversarial settings wherein one actor can directly harm another. Recent theoretical work addresses this issue, introducing an adversarial game in which the emergence of cooperation is heavily reliant on the presence of ‘‘Informants,’’ actors who defect at first-order by harming others, but who cooperate at second-order by punishing other defectors. We experimentally study this adversarial environment in the laboratory with human subjects to test whether Informants are indeed critical for the emergence of cooperation. We find in these experiments that, even more so than predicted by theory, Informants are crucial for the emergence and sustenance of a high cooperation state. A key lesson is that successfully reaching and maintaining a low defection society may require the cultivation of criminals who will also aid in the punishment of others.
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paper_title: Understanding recurrent crime as system-immanent collective behavior

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Containing the spreading of crime is a major challenge for society. Yet, since thousands of years, no effective strategy has been found to overcome crime. To the contrary, empirical evidence shows that crime is recurrent, a fact that is not captured well by rational choice theories of crime. According to these, strong enough punishment should prevent crime from happening. To gain a better understanding of the relationship between crime and punishment, we consider that the latter requires prior discovery of illicit behavior and study a spatial version of the inspection game. Simulations reveal the spontaneous emergence of cyclic dominance between “criminals”, “inspectors”, and “ordinary people” as a consequence of spatial interactions. Such cycles dominate the evolutionary process, in particular when the temptation to commit crime or the cost of inspection are low or moderate. Yet, there are also critical parameter values beyond which cycles cease to exist and the population is dominated either by a stable mixture of criminals and inspectors or one of these two strategies alone. Both continuous and discontinuous phase transitions to different final states are possible, indicating that successful strategies to contain crime can be very much counter-intuitive and complex. Our results demonstrate that spatial interactions are crucial for the evolutionary outcome of the inspection game, and they also reveal why criminal behavior is likely to be recurrent rather than evolving towards an equilibrium with monotonous parameter dependencies.
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paper_title: Evolutionary Games and Population Dynamics

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Every form of behavior is shaped by trial and error. Such stepwise adaptation can occur through individual learning or through natural selection, the basis of evolution. Since the work of Maynard Smith and others, it has been realized how game theory can model this process. Evolutionary game theory replaces the static solutions of classical game theory by a dynamical approach centered not on the concept of rational players but on the population dynamics of behavioral programs. In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behavior, and of the closely related interactions among species in ecological communities. Replicator equations describe how successful strategies spread and thereby create new conditions that can alter the basis of their success, i.e., to enable us to understand the strategic and genetic foundations of the endless chronicle of invasions and extinctions that punctuate evolution. In short, evolutionary game theory describes when to escalate a conflict, how to elicit cooperation, why to expect a balance of the sexes, and how to understand natural selection in mathematical terms. ::: ::: Comprehensive treatment of ecological and game theoretic dynamics ::: Invasion dynamics and permanence as key concepts ::: Explanation in terms of games of things like competition between species
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paper_title: Community detection using spectral clustering on sparse geosocial data

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In this article we identify social communities among gang members in the Hollenbeck policing district in Los Angeles, based on sparse observations of a combination of social interactions and geographic locations of the individuals. This information, coming from LAPD Field Interview cards, is used to construct a similarity graph for the individuals. We use spectral clustering to identify clusters in the graph, corresponding to communities in Hollenbeck, and compare these with the LAPD's knowledge of the individuals' gang membership. We discuss different ways of encoding the geosocial information using a graph structure and the influence on the resulting clusterings. Finally we analyze the robustness of this technique with respect to noisy and incomplete data, thereby providing suggestions about the relative importance of quantity versus quality of collected data.
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paper_title: The structure and dynamics of multilayer networks

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In the past years, network theory has successfully characterized the interaction among the constituents of a variety of complex systems, ranging from biological to technological, and social systems. However, up until recently, attention was almost exclusively given to networks in which all components were treated on equivalent footing, while neglecting all the extra information about the temporal- or context-related properties of the interactions under study. Only in the last years, taking advantage of the enhanced resolution in real data sets, network scientists have directed their interest to the multiplex character of real-world systems, and explicitly considered the time-varying and multilayer nature of networks. We offer here a comprehensive review on both structural and dynamical organization of graphs made of diverse relationships (layers) between its constituents, and cover several relevant issues, from a full redefinition of the basic structural measures, to understanding how the multilayer nature of the network affects processes and dynamics.
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paper_title: Interacting Particle Systems

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The Construction, and Other General Results.- Some Basic Tools.- Spin Systems.- Stochastic Ising Models.- The Voter Model.- The Contact Process.- Nearest-Particle Systems.- The Exclusion Process.- Linear Systems with Values in [0, ?)s.
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paper_title: Once Upon a Crime: Towards Crime Prediction from Demographics and Mobile Data

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In this paper, we present a novel approach to predict crime in a geographic space from multiple data sources, in particular mobile phone and demographic data. The main contribution of the proposed approach lies in using aggregated and anonymized human behavioral data derived from mobile network activity to tackle the crime prediction problem. While previous research efforts have used either background historical knowledge or offenders' profiling, our findings support the hypothesis that aggregated human behavioral data captured from the mobile network infrastructure, in combination with basic demographic information, can be used to predict crime. In our experimental results with real crime data from London we obtain an accuracy of almost 70% when predicting whether a specific area in the city will be a crime hotspot or not. Moreover, we provide a discussion of the implications of our findings for data-driven crime analysis.
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paper_title: Error and attack tolerance of complex networks

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Many complex systems display a surprising degree of tolerance against errors. For example, relatively simple organisms grow, persist and reproduce despite drastic pharmaceutical or environmental interventions, an error tolerance attributed to the robustness of the underlying metabolic network1. Complex communication networks2 display a surprising degree of robustness: although key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network. The stability of these and other complex systems is often attributed to the redundant wiring of the functional web defined by the systems' components. Here we demonstrate that error tolerance is not shared by all redundant systems: it is displayed only by a class of inhomogeneously wired networks, called scale-free networks, which include the World-Wide Web3,4,5, the Internet6, social networks7 and cells8. We find that such networks display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected even by unrealistically high failure rates. However, error tolerance comes at a high price in that these networks are extremely vulnerable to attacks (that is, to the selection and removal of a few nodes that play a vital role in maintaining the network's connectivity). Such error tolerance and attack vulnerability are generic properties of communication networks.
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paper_title: Evolutionary dynamics of group interactions on structured populations: A review

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Interactions among living organisms, from bacteria colonies to human societies, are inherently more complex than interactions among particles and non-living matter. Group interactions are a particularly important and widespread class, representative of which is the public goods game. In addition, methods of statistical physics have proved valuable for studying pattern formation, equilibrium selection and self-organization in evolutionary games. Here, we review recent advances in the study of evolutionary dynamics of group interactions on top of structured populations, including lattices, complex networks and coevolutionary models. We also compare these results with those obtained on well-mixed populations. The review particularly highlights that the study of the dynamics of group interactions, like several other important equilibrium and non-equilibrium dynamical processes in biological, economical and social sciences, benefits from the synergy between statistical physics, network science and evolutionary game theory.
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paper_title: Identifying The Effect Of Unemployment On Crime

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Previous estimates of the effect of unemployment on crime commonly omit determinants of criminal behavior that vary with the business cycle, creating correlation between unemployment rates and the residuals in aggregate crime regressions. In this paper, we employ several strategies that attempt to minimize or break this correlation and eliminate the accompanying omitted variables bias to estimates of the effect of unemployment on crime. Using a state-level panel for the period from 1970 to 1993, we explore the sensitivity of crime-unemployment elasticity estimates to explicit controls for per-capita alcohol consumption, a factor that has been shown in the past to be pro-cyclical and a partial determinant of criminal behavior. In addition, we use prime defense contracts per-capita at the state level as an instrument for state unemployment rates. Both controlling for alcohol consumption and using instrumental variables to correct for omitted variables bias yields large effects of unemployment on the seven felony offenses recorded by the Department of Justice. Moreover, in contrast to previous research, we find significant and sizable positive effects of unemployment on the rates of specific violent, as well as property crimes.
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paper_title: Modelling Social Segregation

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This paper proposes a multilevel modelling approach to the analysis of social segregation in schools. Using data on free school meal eligibility it shows that the underlying variation between schools for the period 1994-1999 has increased. It also shows that the change is greater for selective than non-selective local education authorities (LEAs). It is suggested that the approach of this paper can be applied generally to the modelling of social segregation at institution level.
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paper_title: Detecting criminal organizations in mobile phone networks

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Abstract The study of criminal networks using traces from heterogeneous communication media is acquiring increasing importance in nowadays society. The usage of communication media such as mobile phones and online social networks leaves digital traces in the form of metadata that can be used for this type of analysis. The goal of this work is twofold: first we provide a theoretical framework for the problem of detecting and characterizing criminal organizations in networks reconstructed from phone call records. Then, we introduce an expert system to support law enforcement agencies in the task of unveiling the underlying structure of criminal networks hidden in communication data. This platform allows for statistical network analysis, community detection and visual exploration of mobile phone network data. It enables forensic investigators to deeply understand hierarchies within criminal organizations, discovering members who play central role and provide connection among sub-groups. Our work concludes illustrating the adoption of our computational framework for a real-word criminal investigation.
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paper_title: Losing Legitimacy: Street Crime And The Decline Of Social Institutions In America

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* Understanding Postwar Crime Trends * Riding the Wave: Street Crime Trends in Postwar America * Offender Characteristics and Crime Trends in Postwar America * Evaluating Common Explanations of Crime * Crime and Social Institutions * Crime and American Political Institutions * Crime and American Economic Institutions * Crime and Changes in the American Family * Institutional Responses to the Legitimacy Crisis: Criminal Justice, Education, and Welfare * Crime and Institutional Legitimacy in Postwar America
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paper_title: Territorial Developments Based on Graffiti: a Statistical Mechanics Approach

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We study the well-known sociological phenomenon of gang aggregation and territory formation through an interacting agent system defined on a lattice. We introduce a two-gang Hamiltonian model where agents have red or blue affiliation but are otherwise indistinguishable. In this model, all interactions are indirect and occur only via graffiti markings, on-site as well as on nearest neighbor locations. We also allow for gang proliferation and graffiti suppression. Within the context of this model, we show that gang clustering and territory formation may arise under specific parameter choices and that a phase transition may occur between well-mixed, possibly dilute configurations and well separated, clustered ones. Using methods from statistical mechanics, we study the phase transition between these two qualitatively different scenarios. In the mean-field rendition of this model, we identify parameter regimes where the transition is first or second order. In all cases, we have found that the transitions are a consequence solely of the gang to graffiti couplings, implying that direct gang to gang interactions are not strictly necessary for gang territory formation; in particular, graffiti may be the sole driving force behind gang clustering. We further discuss possible sociological -- as well as ecological -- ramifications of our results.
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paper_title: The Great American Crime Decline

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PART I WHAT HAPPENED IN THE 1990S? 1. The Size and Character of the Crime Decline 2. The Environment for Optimism: Crime Trends and Attitudes about the Effectiveness of Crime Policies PART II THE SEARCH FOR CAUSES 3. The Usual Suspects: Imprisonment, Demography, and the Economy 4. Progeny of the 1990s: Three New Explanations of Decline PART III TWO NEW PERSPECTIVES 5. Which Twin Has the Toni? Some Statistical Lessons from Canada 6. New York City's Natural Experiment PART IV TWENTY-FIRST CENTURY LESSONS 7. What Happens Next? 8. Seven Lessons from the 1990s Appendix 1: Crime and Abortion Policy in Europe, Canada, and Australia Appendix 2: Supplementary Statistics on Crime Trends in Canada during the 1990s Appendix 3: Trends for the City of New York and the United States during the 1990s Appendix 4: Measuring the Extent of Decline in Selected High-Decline Cities References Index
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paper_title: Evolution of networks

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We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of such a kind came into existence recently. This opens a wide field for the study of their topology, evolution, and complex processes occurring in them. Such networks possess a rich set of scaling properties. A number of them are scale-free and show striking resilience against random breakdowns. In spite of large sizes of these networks, the distances between most their vertices are short -- a feature known as the ``small-world'' effect. We discuss how growing networks self-organize into scale-free structures and the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation in these networks. We present a number of models demonstrating the main features of evolving networks and discuss current approaches for their simulation and analytical study. Applications of the general results to particular networks in Nature are discussed. We demonstrate the generic connections of the network growth processes with the general problems of non-equilibrium physics, econophysics, evolutionary biology, etc.
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paper_title: Statistical mechanics of complex networks

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The emergence of order in natural systems is a constant source of inspiration for both physical and biological sciences. While the spatial order characterizing for example the crystals has been the basis of many advances in contemporary physics, most complex systems in nature do not offer such high degree of order. Many of these systems form complex networks whose nodes are the elements of the system and edges represent the interactions between them. ::: Traditionally complex networks have been described by the random graph theory founded in 1959 by Paul Erdohs and Alfred Renyi. One of the defining features of random graphs is that they are statistically homogeneous, and their degree distribution (characterizing the spread in the number of edges starting from a node) is a Poisson distribution. In contrast, recent empirical studies, including the work of our group, indicate that the topology of real networks is much richer than that of random graphs. In particular, the degree distribution of real networks is a power-law, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network. ::: The scale-free topology of real networks has very important consequences on their functioning. For example, we have discovered that scale-free networks are extremely resilient to the random disruption of their nodes. On the other hand, the selective removal of the nodes with highest degree induces a rapid breakdown of the network to isolated subparts that cannot communicate with each other. ::: The non-trivial scaling of the degree distribution of real networks is also an indication of their assembly and evolution. Indeed, our modeling studies have shown us that there are general principles governing the evolution of networks. Most networks start from a small seed and grow by the addition of new nodes which attach to the nodes already in the system. This process obeys preferential attachment: the new nodes are more likely to connect to nodes with already high degree. We have proposed a simple model based on these two principles wich was able to reproduce the power-law degree distribution of real networks. Perhaps even more importantly, this model paved the way to a new paradigm of network modeling, trying to capture the evolution of networks, not just their static topology.
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paper_title: DECLINING VIOLENT CRIME RATES IN THE 1990S: Predicting Crime Booms and Busts

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▪ Abstract The United States in the 1990s has experienced the greatest sustained decline in violent crime rates since World War II—even though rates thus far have not fallen as rapidly as they increased during the crime boom of the 1960s and early 1970s. I review a set of exogenous and policy-related explanations for the earlier crime boom and for the crime bust of the 1990s. I argue that our understanding of crime trends is hampered by a lack of longitudinal analysis and by ahistorical approaches. I identify a set of questions, concepts, and research opportunities raised by taking a more comprehensive look at crime waves.
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paper_title: Does Unemployment Increase Crime?: Evidence from U.S. Data 1974-2000

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OLS may understate the effect of unemployment on crime because of the endogeneity problem (Raphael and Winter-Ember 2001). In this paper, we use changes in the real exchange rate, state manufacturing sector percentages, and state union membership rates as novel instrumental variables to carry out 2SLS estimations. We find a one-percentage-point increase in unemployment would increase property crime by 1.8 percent under the OLS method, but that the elasticity goes up to 4 percent under 2SLS. The larger 2SLS effect has significant policy implications because it explains 30 percent of the property crime change during the 1990s.
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paper_title: Mexico's Drug-Related Violence

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This report examines the causes for the escalation of the violence in Mexico. It provides a brief overview of Mexico's counterdrug efforts, a description of the major drug trafficking organizations (DTOs), the causes and trends in the violence, the Calderon government's efforts to crackdown on the DTOs, and the objectives and implementation of the Merida Initiative and other measures the U.S. government has taken to support Mexico in its battle with the drug traffickers.
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paper_title: The Corner and the Crew: The Influence of Geography and Social Networks on Gang Violence

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Nearly a century of empirical research examines how neighborhood properties influence a host of phenomena such as crime, poverty, health, civic engagement, immigration, and economic inequality. Theoretically bundled within these neighborhood effects are institutions' and actors' social networks that are the foundation of other neighborhood-level processes such as social control, mobilization, and cultural assimilation. Yet, despite such long-standing theoretical links between neighborhoods and social networks, empirical research rarely considers or measures dimensions of geography and social network mechanisms simultaneously. The present study seeks to fill this gap by analyzing how both geography and social networks influence an important social problem in urban America: gang violence. Using detailed data on fatal and non-fatal shootings, we examine effects of geographic proximity, organizational memory, and additional group processes (e.g., reciprocity, transitivity, and status seeking) on gang violence in Chicago and Boston. Results show adjacency of gang turf and prior conflict between gangs are strong predictors of subsequent gang violence. Furthermore, important network processes, including reciprocity and status seeking, also contribute to observed patterns of gang violence. In fact, we find that these spatial and network processes mediate racial effects, suggesting the primacy of place and the group in generating gang violence. Language: en
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paper_title: Ethnic Preferences and Residential Segregation: Theoretical Explorations Beyond Detroit

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We are strongly supportive of Fossett's theoretical approach and modeling methodology, which uses computational methods to perform thought experiments that generate compelling insights into the enigma of persistent residential segregation in the U.S. We also agree with his theoretical results, which challenge the prevailing view among demographers that institutional discrimination is the essential cause. However, we think he did not go far enough. Fossett limited his analysis to a narrow region of the parameter space that corresponded to conditions observed in one city at one time. This precludes generalization to other times and places and exploration of theoretically motivated “what if” scenarios that trespass beyond the Detroit city limits. When we extended the parameter space, we noticed two interesting results. First, Fossett's “paradox of weak minority preferences” requires qualification. Disproportionate in-group preferences among minorities are indeed segregation-promoting, not integration-promoti...
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paper_title: Understanding Organized Crime

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Understanding Organized Crime provides a comprehensive introduction to the subject of organized crime as it relates to the criminal investigation. Topics covered include definition(s) of organized crime, why it exists, how it has evolved throughout history, different types of organized crime and specific organizations, and strategies for fighting organized crime.
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paper_title: Project Safe Neighborhoods and Violent Crime Trends in US Cities: Assessing Violent Crime Impact

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Since the mid-1990s, a number of initiatives intended to address gang, gun and drug-related violence have arisen and demonstrated promise in reducing levels of violent crime. These initiatives have employed some combination of focused deterrence and problem-solving processes. These strategies formed the basis for Project Safe Neighborhoods (PSN), a national program implemented by the Department of Justice and coordinated by US Attorneys’ Offices. This paper is an initial attempt to assess the potential impact of the nationally implemented PSN initiative through an analysis of violent crime trends in all US cities with a population of 100,000 or above. While a number of site specific studies exist examining the potential impact of locally implemented PSN programs, to date no national-level study has examined whether PSN may have had an impact on violent crime trends. Cities included in the current study are distinguished on the basis of whether they were considered a treatment city by the PSN task force and by the level of implementation dosage of the PSN program. This allowed a comparison of 82 treatment cities and 170 non-treatment cities as well as a variable of dosage level. Hierarchical Generalized Linear Models (HGLM) were developed that controlled for other factors that may have affected the level of violent crime across the sample of cities. The results suggested that PSN treatment cities in higher dosage contexts experienced statistically significant, though modest, declines in violent crime whereas non-target cities and low dosage contexts experienced no significant changes in violent crime during the same period. The limitations of this initial analysis are noted but the evidence seems to suggest that the multi-agency, focused deterrence, problem solving approach holds promise for reducing levels of violent crime. At a minimum, these findings call for continued programmatic experimentation with data-driven, highly focused, deterrence-based violence reduction strategies.
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paper_title: Ethnic Preferences, Social Distance Dynamics, and Residential Segregation: Theoretical Explorations Using Simulation Analysis∗

paper_content:

In this paper I consider theories of residential segregation that emphasize social distance and ethnic preference dynamics. I argue that these theories are more compelling than many critics have supposed, and I conclude that they deserve to be considered more carefully. I then use simulation methodology to assess the potential impact of social distance and ethnic preference dynamics on ethnic segregation under certain theoretically interesting conditions. Based on the results from the simulation analyses, I offer three conclusions: (1) status preferences and status dynamics have the capacity to produce high levels of status segregation but do not produce high levels of ethnic segregation under the specified simulation conditions; (2) ethnic preferences can, under certain theoretically interesting conditions specified in these simulations, produce high levels of ethnic segregation in the absence of housing discrimination; and (3) ethnic preferences and social distance dynamics can, when combined with statu...
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paper_title: Dynamic models of segregation†

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Some segregation results from the practices of organizations, some from specialized communication systems, some from correlation with a variable that is non‐random; and some results from the interplay of individual choices. This is an abstract study of the interactive dynamics of discriminatory individual choices. One model is a simulation in which individual members of two recognizable groups distribute themselves in neighborhoods defined by reference to their own locations. A second model is analytic and deals with compartmented space. A final section applies the analytics to ‘neighborhood tipping.’ The systemic effects are found to be overwhelming: there is no simple correspondence of individual incentive to collective results. Exaggerated separation and patterning result from the dynamics of movement. Inferences about individual motives can usually not be drawn from aggregate patterns. Some unexpected phenomena, like density and vacancy, are generated. A general theory of ‘tipping’ begins to emerge.
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paper_title: Complex networks: Structure and dynamics

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Coupled biological and chemical systems, neural networks, social interacting species, the Internet and the World Wide Web, are only a few examples of systems composed by a large number of highly interconnected dynamical units. The first approach to capture the global properties of such systems is to model them as graphs whose nodes represent the dynamical units, and whose links stand for the interactions between them. On the one hand, scientists have to cope with structural issues, such as characterizing the topology of a complex wiring architecture, revealing the unifying principles that are at the basis of real networks, and developing models to mimic the growth of a network and reproduce its structural properties. On the other hand, many relevant questions arise when studying complex networks’ dynamics, such as learning how a large ensemble of dynamical systems that interact through a complex wiring topology can behave collectively. We review the major concepts and results recently achieved in the study of the structure and dynamics of complex networks, and summarize the relevant applications of these ideas in many different disciplines, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering. © 2005 Elsevier B.V. All rights reserved.
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paper_title: Trust : making and breaking cooperative relations

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Part 1 Trust considered: formal structures and social reality, Bernard Williams the biological evolution of co-operation and trust, Patrick Bateson individuals, interpersonal relations and trust, David Good trust as a commodity, Partha Dasgupta trust and political agency, John Dunn familiarity, confidence, trust - problems and alternatives, Niklas Luhmann. Part 2 Trust observed: three ironies in trust, Geoffrey Hawthorn the distraction of trust and its economic consequences in the case of 18th-century Naples, Anthony Pagden trust, cohesion and the social order, Ernest Gellner mafia - the price of distrust, Diego Gambetta kinship, contract and trust - the economic organization of migrants in an African city slum, Keith Hart neither friends nor strangers - informal networks of subcontracting in French industry, Edward Lorenz.
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paper_title: Community detection in graphs

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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i.e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e.g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.
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paper_title: Social Networks and the Risk of Gunshot Injury

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Direct and indirect exposure to gun violence have considerable consequences on individual health and well-being. However, no study has considered the effects of one's social network on gunshot injury. This study investigates the relationship between an individual's position in a high-risk social network and the probability of being a victim of a fatal or non-fatal gunshot wound by combining observational data from the police with records of fatal and non-fatal gunshot injuries among 763 individuals in Boston's Cape Verdean community. A logistic regression approach is used to analyze the probability of being the victim of a fatal or non-fatal gunshot wound and whether such injury is related to age, gender, race, prior criminal activity, exposure to street gangs and other gunshot victims, density of one's peer network, and the social distance to other gunshot victims. The findings demonstrate that 85 % all of the gunshot injuries in the sample occur within a single social network. Probability of gunshot victimization is related to one's network distance to other gunshot victims: each network association removed from another gunshot victim reduces the odds of gunshot victimization by 25 % (odds ratio = 0.75; 95 % confidence interval, 0.65 to 0.87). This indirect exposure to gunshot victimization exerts an effect above and beyond the saturation of gunshot victimization in one's peer network, age, prior criminal activity, and other individual and network variables.
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paper_title: Testing a promising homicide reduction strategy: re-assessing the impact of the Indianapolis “pulling levers” intervention

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Since the publication of analyses suggesting the significant impact on youth homicide of the Boston “pulling levers” intervention, a series of studies of similar strategies have indicated promise in reducing homicide and gun assaults. One of these studies was an assessment of a pulling levers strategy in Indianapolis, where trend analyses indicated a significant reduction in homicide following the intervention, while six other similar Midwestern cities did not experience a significant decline in homicide. We re-assess the results of the Indianapolis study by disaggregating the offenses into gang- and non-gang homicides. Given that the pulling levers program focused on influencing gangs and networks of chronic offenders, the impact of the intervention should be more apparent for gang homicides than for non-gang homicides. Alternatively, should the impact be similar for non-gang homicides, then it is more likely that the downward trend would be caused by unmeasured external forces. Coefficient-difference tests relying on estimates obtained from autoregressive integrated moving average (ARIMA) time–series models indicate that gang homicides declined significantly more than did non-gang homicides following the Indianapolis intervention. These findings suggest ‘something happened’ to gang homicides that did not happen to non-gang homicides, which adds further support that the pulling levers initiative was the driving force behind the overall reduction in homicide in Indianapolis.
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paper_title: The Relative Ineffectiveness of Criminal Network Disruption

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Researchers, policymakers and law enforcement agencies across the globe struggle to find effective strategies to control criminal networks. The effectiveness of disruption strategies is known to depend on both network topology and network resilience. However, as these criminal networks operate in secrecy, data-driven knowledge concerning the effectiveness of different criminal network disruption strategies is very limited. By combining computational modeling and social network analysis with unique criminal network intelligence data from the Dutch Police, we discovered, in contrast to common belief, that criminal networks might even become ‘stronger’, after targeted attacks. On the other hand increased efficiency within criminal networks decreases its internal security, thus offering opportunities for law enforcement agencies to target these networks more deliberately. Our results emphasize the importance of criminal network interventions at an early stage, before the network gets a chance to (re-)organize to maximum resilience. In the end disruption strategies force criminal networks to become more exposed, which causes successful network disruption to become a long-term effort.
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paper_title: DECOMPOSING VIOLENCE: CRIME CYCLES IN THE TWENTIETH CENTURY IN THE UNITED STATES

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I apply the Beveridge-Nelson business cycle decomposition method to the time series of murder in the United States (1900-2004). Separating out “permanent” from “cyclical” murder, I hypothesize that the cyclical part coincides with documented waves of organized crime, internal tensions, breakdowns in social order, crime legislation, alternation in power, social, and political unrest overseas as wars, and recently with the periodic terrorist attacks in the country.
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paper_title: Geographical influences of an emerging network of gang rivalries

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We propose an agent-based model to simulate the creation of street gang rivalries. The movement dynamics of agents are coupled to an evolving network of gang rivalries, which is determined by previous interactions among agents in the system. Basic gang data, geographic information, and behavioral dynamics suggested by the criminology literature are integrated into the model. The major highways, rivers, and the locations of gangs’ centers of activity influence the agents’ motion. We use a policing division of the Los Angeles Police Department as a case study to test our model. We apply common metrics from graph theory to analyze our model, comparing networks produced by our simulations and an instance of a Geographical Threshold Graph to the existing network from the criminology literature.
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paper_title: Recidivism and Rehabilitation of Criminal Offenders: A Carrot and Stick Evolutionary Game

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Motivated by recent efforts by the criminal justice system to treat and rehabilitate nonviolent offenders rather than focusing solely on their punishment, we introduce an evolutionary game theoretic model to study the effects of “carrot and stick” intervention programs on criminal recidivism. We use stochastic simulations to study the evolution of a population where individuals may commit crimes depending on their past history, surrounding environment and, in the case of recidivists, on any counseling, educational or training programs available to them after being punished for their previous crimes. These sociological factors are embodied by effective parameters that determine the decision making probabilities. Players may decide to permanently reform or continue engaging in criminal activity, eventually reaching a state where they are considered incorrigible. Depending on parameter choices, the outcome of the game is a society with a majority of virtuous, rehabilitated citizens or incorrigibles. Since total resources may be limited, we constrain the combined punishment and rehabilitation costs per crime to be fixed, so that increasing one effort will necessarily decrease the other. We find that the most successful strategy in reducing crime is to optimally allocate resources so that after being punished, criminals experience impactful intervention programs, especially during the first stages of their return to society. Excessively harsh or lenient punishments are less effective. We also develop a system of coupled ordinary differential equations with memory effects to give a qualitative description of our simulated societal dynamics. We discuss our findings and sociological implications.
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paper_title: Understanding recurrent crime as system-immanent collective behavior

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Containing the spreading of crime is a major challenge for society. Yet, since thousands of years, no effective strategy has been found to overcome crime. To the contrary, empirical evidence shows that crime is recurrent, a fact that is not captured well by rational choice theories of crime. According to these, strong enough punishment should prevent crime from happening. To gain a better understanding of the relationship between crime and punishment, we consider that the latter requires prior discovery of illicit behavior and study a spatial version of the inspection game. Simulations reveal the spontaneous emergence of cyclic dominance between “criminals”, “inspectors”, and “ordinary people” as a consequence of spatial interactions. Such cycles dominate the evolutionary process, in particular when the temptation to commit crime or the cost of inspection are low or moderate. Yet, there are also critical parameter values beyond which cycles cease to exist and the population is dominated either by a stable mixture of criminals and inspectors or one of these two strategies alone. Both continuous and discontinuous phase transitions to different final states are possible, indicating that successful strategies to contain crime can be very much counter-intuitive and complex. Our results demonstrate that spatial interactions are crucial for the evolutionary outcome of the inspection game, and they also reveal why criminal behavior is likely to be recurrent rather than evolving towards an equilibrium with monotonous parameter dependencies.
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paper_title: The Improbable Transformation of Inner-City Neighborhoods: Crime, Violence, Drugs, and Youth in the 1990s

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In a multi-level digital transmission system, the transmitting station transmits two particular different-level code signals alternately in response to a particular one of N kinds of input information to be transmitted. Whenever the two particular code signals are received, the receiving station converts them into the one particular kind of input information. By determining whether the two particular code signals appear alternately at the receiving station, it is possible to monitor the presence of code errors introduced in a transmission channel.
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paper_title: Correlation of positive and negative reciprocity fails to confer an evolutionary advantage: Phase transitions to elementary strategies

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Economic experiments reveal that humans value cooperation and fairness. Punishing unfair behavior is therefore common, and according to the theory of strong reciprocity, it is also directly related to rewarding cooperative behavior. However, empirical data fail to confirm that positive and negative reciprocity are correlated. Inspired by this disagreement, we determine whether the combined application of reward and punishment is evolutionary advantageous. We study a spatial public goods game, where in addition to the three elementary strategies of defection, rewarding and punishment, a fourth strategy combining the later two competes for space. We find rich dynamical behavior that gives rise to intricate phase diagrams where continuous and discontinuous phase transitions occur in succession. Indirect territorial competition, spontaneous emergence of cyclic dominance, as well as divergent fluctuations of oscillations that terminate in an absorbing phase are observed. Yet despite the high complexity of solutions, the combined strategy can survive only in very narrow and unrealistic parameter regions. Elementary strategies, either in pure or mixed phases, are much more common and likely to prevail. Our results highlight the importance of patterns and structure in human cooperation, which should be considered in future experiments.
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paper_title: Optimal distribution of incentives for public cooperation in heterogeneous interaction environments

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In the framework of evolutionary games with institutional reciprocity, limited incentives are at disposal for rewarding cooperators and punishing defectors. In the simplest case, it can be assumed that, depending on their strategies, all players receive equal incentives from the common pool. The question arises, however, what is the optimal distribution of institutional incentives? How should we best reward and punish individuals for cooperation to thrive? We study this problem for the public goods game on a scale-free network. We show that if the synergetic effects of group interactions are weak, the level of cooperation in the population can be maximized simply by adopting the simplest ''equal distribution'' scheme. If synergetic effects are strong, however, it is best to reward high-degree nodes more than low-degree nodes. These distribution schemes for institutional rewards are independent of payoff normalization. For institutional punishment, however, the same optimization problem is more complex, and its solution depends on whether absolute or degree-normalized payoffs are used. We find that degree-normalized payoffs require high-degree nodes be punished more lenient than low-degree nodes. Conversely, if absolute payoffs count, then high-degree nodes should be punished stronger than low-degree nodes.
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paper_title: Self-organization of punishment in structured populations

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Cooperation is crucial for the remarkable evolutionary success of the human species. Not surprisingly, some individuals are willing to bear additional costs in order to punish defectors. Current models assume that, once set, the fine and cost of punishment do not change over time. Here we show that relaxing this assumption by allowing players to adapt their sanctioning efforts in dependence on the success of cooperation can explain both the spontaneous emergence of punishment and its ability to deter defectors and those unwilling to punish them with globally negligible investments. By means of phase diagrams and the analysis of emerging spatial patterns, we demonstrate that adaptive punishment promotes public cooperation through the invigoration of spatial reciprocity, the prevention of the emergence of cyclic dominance, or the provision of competitive advantages to those that sanction antisocial behavior. The results presented indicate that the process of self-organization significantly elevates the effectiveness of punishment, and they reveal new mechanisms by means of which this fascinating and widespread social behavior could have evolved.
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paper_title: Sustainable institutionalized punishment requires elimination of second-order free-riders

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Although empirical and theoretical studies affirm that punishment can elevate collaborative efforts, its emergence and stability remain elusive. By peer-punishment the sanctioning is something an individual elects to do depending on the strategies in its neighborhood. The consequences of unsustainable efforts are therefore local. By pool-punishment, on the other hand, where resources for sanctioning are committed in advance and at large, the notion of sustainability has greater significance. In a population with free-riders, punishers must be strong in numbers to keep the "punishment pool" from emptying. Failure to do so renders the concept of institutionalized sanctioning futile. We show that pool-punishment in structured populations is sustainable, but only if second-order free-riders are sanctioned as well, and to a such degree that they cannot prevail. A discontinuous phase transition leads to an outbreak of sustainability when punishers subvert second-order free-riders in the competition against defectors.
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paper_title: Incentives and opportunism: from the carrot to the stick

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Cooperation in public good games is greatly promoted by positive and negative incentives. In this paper, we use evolutionary game dynamics to study the evolution of opportunism (the readiness to be swayed by incentives) and the evolution of trust (the propensity to cooperate in the absence of information on the co-players). If both positive and negative incentives are available, evolution leads to a population where defectors are punished and players cooperate, except when they can get away with defection. Rewarding behaviour does not become fixed, but can play an essential role in catalysing the emergence of cooperation, especially if the information level is low.
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paper_title: Evolutionary advantages of adaptive rewarding

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Our well-being depends on both our personal success and the success of our society. The realization of this fact makes cooperation an essential trait. Experiments have shown that rewards can elevate our readiness to cooperate, but since giving a reward inevitably entails paying a cost for it, the emergence and stability of such behavior remains elusive. Here we show that allowing for the act of rewarding to self-organize in dependence on the success of cooperation creates several evolutionary advantages that instill new ways through which collaborative efforts are promoted. Ranging from indirect territorial battle to the spontaneous emergence and destruction of coexistence, phase diagrams and the underlying spatial patterns reveal fascinatingly rich social dynamics that explain why this costly behavior has evolved and persevered. Comparisons with adaptive punishment, however, uncover an Achilles heel of adaptive rewarding, coming from over-aggression, which in turn hinders optimal utilization of network reciprocity. This may explain why, despite its success, rewarding is not as firmly embedded into our societal organization as punishment.
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paper_title: Reward and cooperation in the spatial public goods game

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The promise of punishment and reward in promoting public cooperation is debatable. While punishment is traditionally considered more successful than reward, the fact that the cost of punishment frequently fails to offset gains from enhanced cooperation has lead some to reconsider reward as the main catalyst behind collaborative efforts. Here we elaborate on the"stick versus carrot"dilemma by studying the evolution of cooperation in the spatial public goods game, where besides the traditional cooperators and defectors, rewarding cooperators supplement the array of possible strategies. The latter are willing to reward cooperative actions at a personal cost, thus effectively downgrading pure cooperators to second-order free-riders due to their unwillingness to bear these additional costs. Consequently, we find that defection remains viable, especially if the rewarding is costly. Rewards, however, can promote cooperation, especially if the synergetic effects of cooperation are low. Surprisingly, moderate rewards may promote cooperation better than high rewards, which is due to the spontaneous emergence of cyclic dominance between the three strategies.
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paper_title: Indirect reciprocity can stabilize cooperation without the second-order free rider problem

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Models of large-scale human cooperation take two forms. ‘Indirect reciprocity’1 occurs when individuals help others in order to uphold a reputation and so be included in future cooperation. In ‘collective action’2, individuals engage in costly behaviour that benefits the group as a whole. Although the evolution of indirect reciprocity is theoretically plausible3,4,5,6, there is no consensus about how collective action evolves. Evidence suggests that punishing free riders can maintain cooperation7,8,9, but why individuals should engage in costly punishment is unclear. Solutions to this ‘second-order free rider problem’ include meta-punishment10, mutation11, conformism12, signalling13,14,15 and group-selection16,17,18. The threat of exclusion from indirect reciprocity can sustain collective action in the laboratory19. Here, we show that such exclusion is evolutionarily stable, providing an incentive to engage in costly cooperation, while avoiding the second-order free rider problem because punishers can withhold help from free riders without damaging their reputations. However, we also show that such a strategy cannot invade a population in which indirect reciprocity is not linked to collective action, thus leaving unexplained how collective action arises.
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paper_title: Winners don’t punish

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Many theories have been offered to explain the evolution of cooperation in humans. One proposal is that costly punishment can promote cooperation. Everyone benefits on average, the theory goes, despite the cost to those doing the punishing. But most of our interactions are repeated, and in such cases punishment can lead to retaliation. Using a variant of the 'Prisoner's Dilemma' game, Dreber et al. find that punishment increases the frequency of cooperation, but not the average payoff. Costly punishments confer no overall advantage to the group. And players who end up with the highest total payoff ('winners') tend not to use punishment, while those with the lowest payoff ('losers') punish most frequently. It seems that costly punishment may not have evolved to promote cooperation, but for some other purpose. An experimental economics approach finds that punishment increases the frequency of cooperation, but not the average payoff. Thus, the option of costly punishment does not confer an advantage to the group. Moreover, players who end up with the highest total payoff ('winners') do not use punishment, whereas players who end up with the lowest payoff ('losers') use punishment most frequently. A key aspect of human behaviour is cooperation1,2,3,4,5,6,7. We tend to help others even if costs are involved. We are more likely to help when the costs are small and the benefits for the other person significant. Cooperation leads to a tension between what is best for the individual and what is best for the group. A group does better if everyone cooperates, but each individual is tempted to defect. Recently there has been much interest in exploring the effect of costly punishment on human cooperation8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23. Costly punishment means paying a cost for another individual to incur a cost. It has been suggested that costly punishment promotes cooperation even in non-repeated games and without any possibility of reputation effects10. But most of our interactions are repeated and reputation is always at stake. Thus, if costly punishment is important in promoting cooperation, it must do so in a repeated setting. We have performed experiments in which, in each round of a repeated game, people choose between cooperation, defection and costly punishment. In control experiments, people could only cooperate or defect. Here we show that the option of costly punishment increases the amount of cooperation but not the average payoff of the group. Furthermore, there is a strong negative correlation between total payoff and use of costly punishment. Those people who gain the highest total payoff tend not to use costly punishment: winners don’t punish. This suggests that costly punishment behaviour is maladaptive in cooperation games and might have evolved for other reasons.
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paper_title: Reward and punishment

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Minigames capturing the essence of Public Goods experiments show that even in the absence of rationality assumptions, both punishment and reward will fail to bring about prosocial behavior. This result holds in particular for the well-known Ultimatum Game, which emerges as a special case. But reputation can induce fairness and cooperation in populations adapting through learning or imitation. Indeed, the inclusion of reputation effects in the corresponding dynamical models leads to the evolution of economically productive behavior, with agents contributing to the public good and either punishing those who do not or rewarding those who do. Reward and punishment correspond to two types of bifurcation with intriguing complementarity. The analysis suggests that reputation is essential for fostering social behavior among selfish agents, and that it is considerably more effective with punishment than with reward.
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paper_title: Phase diagrams for the spatial public goods game with pool-punishment

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The efficiency of institutionalized punishment is studied by evaluating the stationary states in the spatial public goods game comprising unconditional defectors, cooperators, and cooperating pool punishers as the three competing strategies. Fines and costs of pool punishment are considered as the two main parameters determining the stationary distributions of strategies on the square lattice. Each player collects a payoff from five five-person public goods games, and the evolution of strategies is subsequently governed by imitation based on pairwise comparisons at a low level of noise. The impact of pool punishment on the evolution of cooperation in structured populations is significantly different from that reported previously for peer punishment. Representative phase diagrams reveal remarkably rich behavior, depending also on the value of the synergy factor that characterizes the efficiency of investments payed into the common pool. Besides traditional single- and two-strategy stationary states, a rock-paper-scissors type of cyclic dominance can emerge in strikingly different ways.
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paper_title: Coordinated punishment of defectors sustains cooperation and can proliferate when rare

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Because mutually beneficial cooperation may unravel unless most members of a group contribute, people often gang up on free-riders, punishing them when this is cost-effective in sustaining cooperation. In contrast, current models of the evolution of cooperation assume that punishment is uncoordinated and unconditional. These models have difficulty explaining the evolutionary emergence of punishment because rare unconditional punishers bear substantial costs and hence are eliminated. Moreover, in human behavioral experiments in which punishment is uncoordinated, the sum of costs to punishers and their targets often exceeds the benefits of the increased cooperation that results from the punishment of free-riders. As a result, cooperation sustained by punishment may actually reduce the average payoffs of group members in comparison with groups in which punishment of free-riders is not an option. Here, we present a model of coordinated punishment that is calibrated for ancestral human conditions and captures a further aspect of reality missing from both models and experiments: The total cost of punishing a free-rider declines as the number of punishers increases. We show that punishment can proliferate when rare, and when it does, it enhances group-average payoffs.
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paper_title: The evolution of antisocial punishment in optional public goods games

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Cooperation, where one individual incurs a cost to help another, is a fundamental building block of the natural world and human society. It has been suggested that costly punishment can promote the evolution of cooperation, with the threat of punishment deterring free-riders. Recent experiments, however, have revealed the existence of 'antisocial' punishment, where non-cooperators punish cooperators. While various theoretical models find that punishment can promote the evolution of cooperation, these models a priori exclude the possibility of antisocial punishment. Here we extend the standard theory of optional public goods games to include the full set of punishment strategies. We find that punishment no longer increases cooperation, and that selection favours substantial levels of antisocial punishment for a wide range of parameters. Furthermore, we conduct behavioural experiments, showing results consistent with our model predictions. As opposed to an altruistic act that promotes cooperation, punishment is mostly a self-interested tool for protecting oneself against potential competitors.
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paper_title: Social learning promotes institutions for governing the commons

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Cooperation in evolutionary games can be stabilized through punishment of non-cooperators, at a cost to those who do the punishing. Punishment can take different forms, in particular peer-punishment, in which individuals punish free-riders after the event, and pool-punishment, in which a fund for sanctioning is set up beforehand. These authors show that pool-punishment is superior to peer-punishment in dealing with second-order free-riders, who cooperate in the main game but refuse to contribute to punishment.
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paper_title: Positive Interactions Promote Public Cooperation

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The public goods game is the classic laboratory paradigm for studying collective action problems. Each participant chooses how much to contribute to a common pool that returns benefits to all participants equally. The ideal outcome occurs if everybody contributes the maximum amount, but the self-interested strategy is not to contribute anything. Most previous studies have found punishment to be more effective than reward for maintaining cooperation in public goods games. The typical design of these studies, however, represses future consequences for today’s actions. In an experimental setting, we compare public goods games followed by punishment, reward, or both in the setting of truly repeated games, in which player identities persist from round to round. We show that reward is as effective as punishment for maintaining public cooperation and leads to higher total earnings. Moreover, when both options are available, reward leads to increased contributions and payoff, whereas punishment has no effect on contributions and leads to lower payoff. We conclude that reward outperforms punishment in repeated public goods games and that human cooperation in such repeated settings is best supported by positive interactions with others.
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paper_title: Recidivism and Rehabilitation of Criminal Offenders: A Carrot and Stick Evolutionary Game

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Motivated by recent efforts by the criminal justice system to treat and rehabilitate nonviolent offenders rather than focusing solely on their punishment, we introduce an evolutionary game theoretic model to study the effects of “carrot and stick” intervention programs on criminal recidivism. We use stochastic simulations to study the evolution of a population where individuals may commit crimes depending on their past history, surrounding environment and, in the case of recidivists, on any counseling, educational or training programs available to them after being punished for their previous crimes. These sociological factors are embodied by effective parameters that determine the decision making probabilities. Players may decide to permanently reform or continue engaging in criminal activity, eventually reaching a state where they are considered incorrigible. Depending on parameter choices, the outcome of the game is a society with a majority of virtuous, rehabilitated citizens or incorrigibles. Since total resources may be limited, we constrain the combined punishment and rehabilitation costs per crime to be fixed, so that increasing one effort will necessarily decrease the other. We find that the most successful strategy in reducing crime is to optimally allocate resources so that after being punished, criminals experience impactful intervention programs, especially during the first stages of their return to society. Excessively harsh or lenient punishments are less effective. We also develop a system of coupled ordinary differential equations with memory effects to give a qualitative description of our simulated societal dynamics. We discuss our findings and sociological implications.
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Title: Statistical physics of crime: A review

Section 1: INTRODUCTION
Description 1: Introduce the "broken windows theory," describe crime as a complex phenomenon, mention crime deterrence policies, and outline well-known theories of criminal behavior.

Section 2: CRIME HOTSPOTS
Description 2: Discuss crime hotspot observations, describe a statistical model of criminal behavior focusing on residential burglary, explain the model dynamics and feedback loops, and summarize results and implications for hotspot suppression and policing.

Section 3: SELF-EXCITING POINT PROCESS MODELING
Description 3: Introduce self-exciting point processes, compare them to seismology methods, and discuss their application to urban crime, geographic profiling, and intra-gang violence.

Section 4: CRIME AS A SOCIAL DILEMMA
Description 4: Describe crime through the lens of evolutionary game theory, detail the adversarial evolutionary game with four competing strategies, and review human experiments testing the role of informants in crime reduction.

Section 5: NETWORKS OF CRIME, GANGS AND GEOGRAPHY
Description 5: Examine criminal networks, gang formations, and the geographic distribution of crime, review efforts to disrupt criminal networks, and analyze gang rivalry using agent-based and network models.

Section 6: REHABILITATION AND RECIDIVISM
Description 6: Explore the balance between punishment and rehabilitation in reducing recidivism, describe an evolutionary game model related to the "stick versus carrot" dilemma, and summarize findings for optimal resource allocation.

Section 7: SUMMARY AND OUTLOOK
Description 7: Summarize key insights from the review, discuss the implications of statistical physics in understanding crime, and outline potential directions for future research in crime modeling.