Evolutionary game theory describes systems where individual success is based on

Evolutionary game theory describes systems where individual success is based on the interaction with others. scenarios. For small mutation rates, cooperation (and punishment) is possible only if interactions are voluntary, whereas moderate mutation rates can lead to high levels of cooperation even in compulsory public goods games. This phenomenon is investigated through numerical simulations and analytical approximations. players, cooperation sustains a public resource. Contributing cooperators pay a cost to invest in a common good (12, 13). All contributions are summed up, multiplied by a factor (1 < < < 1 of the focal individual's own investment is recovered by the investor, it is best to defect and not to contribute. This generates a 661-19-8 supplier social dilemma (14): Individuals that free ride on the contributions of others and do not invest perform best. Such behavior spreads, and no one invests anymore. Consequently, the entire group suffers, because everyone is left with zero payoff instead of ? 1) (15). This outcome changes if individuals can identify and punish defectors. Punishment is costly and means that one individual imposes a fine on a defecting coplayer (7, 16C21). The establishment of such costly behavior is not trivial (22, 23): A single punishing cooperator performs poorly in a population of defectors. Moreover, punishment is not stable unless there are sanctions Rabbit polyclonal to Kinesin1 also on those who cooperate but do not punish. Otherwise, such second-order free riders can undermine a population of punishers and pave the way for the return of defectors. Recently, Fowler (24) has proposed that punishment is easily established if the game is based on voluntary participation rather than compulsory interactions. However, for infinite populations and vanishing mutation rates, the dynamics of the resulting deterministic replicator equations are bistable as well as structurally unstable (25). Nevertheless, Fowler’s intuition is confirmed for finite populations and small mutation rates (22). In this case, the initial conditions determine the outcome of the process. Methods Here, we focus on the effect of random exploration and demonstrate that the mutation rate can trigger qualitative changes in the evolutionary dynamics (26C30). To illustrate how increasing mutation probabilities affect the evolutionary dynamics, we address the evolution of cooperation and punishment in individuals is chosen at random from a finite population of individuals. If interactions are not mandatory, individuals can choose whether they participate in the public goods game (as cooperators or defectors ( = 1), he acts as a loner. The introduction of loners generates a cyclic dominance of strategies: If cooperators abound, defection spreads. If defectors prevail it is better to abstain and the average decreases. For < investments in the public good yield a positive return, and hence, cooperators thrive again. However, the increase of cooperators also increases and thus reestablishes the social dilemma. This rockCpaperCscissors like dynamics has been confirmed in behavioral experiments (8). Here, we consider also a fourth strategic type, the punishers (< dominates dominates = (individual and transform it into type enters in the transition probabilities. Thus, the stationary distribution only depends on the population size (see and ... Fig. 2. Imitation dynamics for different mutation rates. Symbols indicate results from individual-based 661-19-8 supplier simulations (averages over 109 imitation steps), and solid lines show the numerical solution of the FokkerCPlanck-equation, corresponding to a vanishing ... In voluntary public goods games without punishment, there is cyclic dominance. In finite populations, it manifests itself as follows: When defectors dominate, taking part in the game does not pay, and the loners that do not participate have the highest payoff. When there are no participants, a single cooperator does not have an advantage (because there is no one to play with). However, as soon as the second cooperator arises by neutral drift (which happens with probability = 1). A second participant arises by neutral drift with probability 2 and ultimately take over. If cooperation without punishment is established, defectors are advantageous and can invade. However, if punishers take over, it may take a long time before nonpunishing cooperators take over via neutral drift, because, on average, invasion attempts are necessary before fixation occurs. A detailed analysis of the transition matrix of the system shows that the system is in state with probability = 2/(8 + = (2 + = 0, punishers prevail for large and 0, this approach essentially recovers the replicator equation 661-19-8 supplier again (34, 661-19-8 supplier 35). The continuous presence of all strategic types for large is reflected by 661-19-8 supplier a drift away from the.