So far, we have discussed various types of properties and various results involving those properties. So let us do a quick recap. We have discussed iterated elimination of dominated strategies in order to find some equilibrium of the game. Then we have talked about preservation of equilibrium when we do this kind of iterated elimination. We have defined the stability notion by pure strategy Nash equilibrium and security notion by min max, max min strategies. And we have shown that these two properties, these two notions coincide in the case of this special game called the matrix games. And then we have also looked at certain kind of games where pure strategies may not exist. Pure strategy Nash equilibrium may not exist. And one such game is given in this figure where we cannot find a pure strategy Nash equilibrium. So that is one reason of refining the equilibrium notion as we have done in the past. When we could not find dominant strategy equilibrium, we went for the pure strategy Nash equilibrium. Now it's time to weaken it even further and therefore we might get some other equilibrium strategy. And also from an application point of view, if you think about the first example that we have given for the neighboring kingdoms dilemma, we have seen that we just made an assumption that the kingdoms can either invest entirely on agriculture or on warfare. That was for simplicity. But in practice, there are cases where the whole resource of a specific kingdom can be divided maybe equally between these two actions, agriculture and warfare, or maybe one third and two third. How should we represent that in the form of a game? So to denote that, we now come to the world of mixed strategies. So as the name suggests informally, this is a probability distribution over the strategies. So instead of picking the strategies as pure, we are just mixing them and we are doing this mixing in a probabilistic way. So in the same example, we can say that the player one is mixing these two strategies L and R in this proportion two third and one third. So with probability two third, it will pick L and with probability one third, it will pick R. Similarly, the other player will pick these two strategies with probability four by five and one by five. Alright, so let us make our notation a little more clear to formally represent all these things. So suppose we have a finite set A, then we are going to define this delta of A as the probability distributions on this set A. So what does that mean? So we have a vector. So P is a vector. So suppose A has three elements, let's say A1, A2, A3. Therefore P will be nothing but a vector of length three each representing each of these elements in A and they should sum to one. So let's say 0.2, 0.3 and 0.5 and 0.3. So that is one valid entry in this set delta of A, which is the set of all probability distributions over A. Now what is a mixed strategy for player I? So sigma I with which we are going to denote the mixed strategy of player I is a member of delta of Si. So Si in this case is the finite set and what we are going to say is that the agent I is putting certain probabilities on all these strategies that is available to it. And we are doing it in such a way that the sum, this is always non-negative and it sums to one. Very simple definition and because we are discussing non-cooperative games that no player is actually talking to each other and sharing information before taking their decisions, they choose their strategies independently and therefore the mixed strategies are also chosen independently. So all these probability distributions are actually independent of each other. So when we are talking about the joint probability distribution of player I picking S1 and player II is picking S2, that is just given by the product of the individual marginals. Similarly, these are all analogous definitions. So when we are using the utility of a player I at a mixed strategy profile, sigma I and sigma minus I and sigma I is nothing but one element in that delta of capital Si. And similarly for all the other players, if you list out their strategies, their mixed strategies, that vector of mixed strategy profile except player I is denoted by sigma of minus I. So this is the same notation as before. So how do we define, how do we write the utility of player I when the players are picking their mixed strategies? So what it means is that we first look at the utility at a pure strategy profile S1 to Sn and multiply that with the corresponding probability of picking that strategy profile. So because these are all independent, this will just be products and then you are going to sum over all possible strategies of all these players. So therefore you are getting an expected utility for all the strategy profiles where the expectation is taken with respect to this probability distribution according to their mixed strategies. So in this case, we are just overloading this notation. So utility of I for the pure strategies is also denoted by UI and we are also denoting the same utility I to denote the mixed strategies. Ideally it should have been different. We should have used different notations but because these are two different contexts and from the context you will be able to figure that out. So there is no need and in literature it is not really distinguished. So in this case I have explicitly written the whole utility expression just to make sure that you understand the whole expression how the utility at a mixed strategy is computed. So said as we mentioned before utility at a mixed strategy is the expectation of the utilities at the pure strategies. And so all the rules of all the known laws of expectation holds for instance linearity holds. So we will make use of this fact sometime later but this is just for an information. So what is an example of a mixed strategy and let me illustrate with an example what is the utility at a specific mixed strategy profile. So let us look at the same example that we have shown before. So the game is the penalty shootout game but now the players are not picking pure strategies but they are picking mixed strategies. Player one is picking this two third and one third and player two is picking four fifth and one fifth. So if you are looking at the utility of player one so we are only concerned about the utilities of player one in different strategy profiles. We are first going to write down the utility so let us say the first utility here for player one is minus one and we are going to multiply that with the probability of occurrence of this strategy profile. So L comma L can now happen with probability two third times four fifth because that is the way player two and player one can pick this strategy. Similarly if you look at one then you are going to multiply two third and one fifth and similarly you finish up one third times four fifth and one third time one fifth and multiply them with the corresponding utilities. This is the expected utility when player one is playing this particular strategy so sigma one is given by two third and one third and sigma two is given by four fifth and one fifth. Similarly you can write down the utility for player two where this numbers will get replaced by the second entries here. You can also talk about mixtures of mixed strategies that two mixed strategies are being mixed but then that will also give rise to a new mixed strategy and this kind of a notion is rarely used in practice but it is good to know for your information.


Hi everyone, I'm Joe for Jaspy's casebreaks.com coming at you with a quick little cello pack break 2019 2020 panini mosaic basketball cello pack number three one and seven with four NBA mixer spots being given away So as always we're gonna do the quick little pack break first and then we'll Rerandomize James at the end see who wins those mixer spots, but break first. Let's roll it randomize it one and a five six times for each list one two three four five and Six after six times. We got Shawn down to Kevin and then six times for the teams one two three Oh hit parades gonna come out with a soccer product, huh? There's trailblazers down to Rockets. That would be pretty cool Give that a shot Here's the first half of the list right here Zoom in with the Grizzlies Kevin with the pelicans You never know in a quick little cello pack break. There's the other half of the list right there. Let's sort by team Let's box these up. Let's print these out Got a D way to USA silver. That's pretty cool Miami heat with that one a Nicola Melli mosaic rookie and scofield in the pink camo We got deer and Fox it's Grayson Allen and rookie Luca Samanich pink camo for the spurs That'll be for Andrew Webb There you go That's it Shawn with the Hawks and a Kevin in the Wizards top four This is the whole point of this pack break by the way Not the break itself, but those four mixer spots at a brand new basketball mixer on jazzy's case breaks calm Check it out. Let's roll it. Let's randomize it three and a one top four after four one two Three and four after four times. We've got five down to 30. Thank you. We'll get them next time There'll be a few more of these that we'll have to do anyway So if you want to try again feel free on jazzy's case breaks calm Congrats to zoom in Danny Danny and Kevin M. There you go You are in the basketball mixer jazzy's case breaks calm. I'm Joe. I'll see you next time for the next one. Bye. Bye


Northern Eye Center in Pikeville. Your local vision experts experience doctors using state-of-the-art technology. Choose from top designer frames from Oakley, Ray-Ban, Nike, and more. We accept Medicaid and Medicare, plus most insurances are accepted. Northern Eye Center in Pikeville. Next to track your supply. The City of Pikeville in partnership with the Kentucky Department of Fish and Wildlife will be holding the Pikeville River Run kayaking event on Saturday, June 17th. The Kentucky Department of Fish and Wildlife, a new local conservation officer who had graduated from the academy was looking to do some community engagement type work and he had reached out to the city tourism and the city of Pikeville and wanted to work with us to host some type of outdoor recreational event in conjunction with them so we collaborated and we decided on the Pikeville River Run. Kayaks were provided for the first 20 people to register. Anyone registering now must bring their own kayaks. The kayak ride will stretch from Jubilee Christian Church to Texas Roadhouse and a catered lunch will be provided during the ride. PFD, life jacket, you know will be required obviously. People want to fish they can have at it but if they do fish they kind of need to keep up with the crowd. If they if they want to eat lunch and get the shuttle services so you know you're going to be with conservation officer you better make sure you got your fishing license. Shuttles will be provided to take participants back to their vehicles. Registration is required for the event but there is no deadline to register. Participants are advised to register as soon as possible to get an accurate number for food accommodations. To register for the Pikeville River Run you can visit the Pikeville City Tourism Facebook page. For Mountain Top News, I'm Kelsey Dean.


In our culture, it is about giving back. It is about recognizing where you come from. It is recognizing the disadvantage that I and others have come from. There is still a road to go. There is still things we could be doing better. We just need to listen, learn and share. It's not about giving us anything except respect. You know, just listen and learn and let's grow together because we love this country as much as anybody. It's about time we work together, not separately. You know, we are all one and we can learn from each other.


So this is with a joint work with Jonathan Hall and Dan Knuffle, both at Uber Technologies. Okay, so there's been kind of an enormous increase in the number of kind of on-platform marketplaces that have emerged, and all of them have to make some decisions about price structure, and some even have to make decisions about price level, where they actually decide sort of what things cost in that marketplace. And so kind of a question, when you have these platforms that are ostensibly sort of setting prices, what does that actually mean in a marketplace where people have options and can kind of come and go as they please? So I want to kind of start with a motivating example that's pretty close to my empirical setup. So imagine that Uber cuts fares in a city by 20 percent. Presumably passengers demand more trips at this new lower price, but with the price structure that Uber has used least historically, where drivers kind of take a fraction of the receipts, presumably drivers want to supply fewer trips at this new lower price. And so how does this gap actually get closed? And so that's really what this paper is about, or this talk is about, is to explore how this gap gets closed, and then to discuss some of the implications of the market adjustment process that sort of gets revealed when you look at it. So it's important to kind of go through exactly kind of how Uber does things, or at least how Uber did things. There's actually been some changes in the interim, but this is just a screenshot of a driver payout for a particular week. And you can see here that they were online for a little bit more than 40 hours, and their gross earnings here were $455. So this works up to about 1130 per hour. Now, the important thing, though, is that this is 40 hours online, is actually only would only be about 16 hours of transportation with the passenger are going to pick up a passenger at the average utilization of drivers in the US. And so this is a really important point that in this market when drivers mark themselves available for dispatch and are saying, like, I want to carry passengers, they're not always with passengers. So I imagine this is just a calendar entry I made. Imagine I turn the Uber app on at 1030. I mark myself available for dispatch, and then I'm kind of cruising around waiting for that first passenger. I finally, I get one, I take a trip, and then when that trip is over, I go back to this unmatched state, I get another trip, and then at about 215 here, I actually shut the app off, I stop working, I'm not available for dispatch, then I can choose later to say to come on. And anyway, just the ratio here of blue to red, the time that I'm actually spent transporting passengers to time I'm actually available for dispatch ends up being very important for understanding what's going on here. So when drivers only made money or make money when they're actually on a trip carrying passengers, and how the pricing worked was pretty similar to taxi at least at first, where there was multipliers kind of how per minute you're driving per mile. So we can think of what drivers are making, their hourly rate, it's and this is just our whether or not they're with a passenger, they're the flow of money they make while they're on a trip times the fraction of hours work that are actually on a trip. So it's really that it's that both that the money you make when you're carrying passengers times the fraction of an hour that you're actually with passengers the rest of the time you're not you're not getting paid. The flow of money while you're on a trip, it's the it's that base fare flow that multiplier times time and distance. But famously, also times a surge multiplier that uber can impose that kind of multiplies that amount to deal with, you know, ostensibly like short run fluctuations in demand and supply. Okay, so, you know, kind of thinking about this in like a very simple way, but I think you can get pretty far with a simple way of thinking about it. Imagine drivers are collectively deciding in some given week how many hours to spend online and be available for dispatch, and that this is sloping up in the in the effective wage that you can earn for an hour of transportation. Now, if you want to translate that into, you know, the product market here. So this hours worked is actually getting trans translated into hours of transportation. It's scaled by that utilization that I was discussing earlier.  So, you know, you can imagine the extreme case if utilization was zero, this would just be vertical along the y axis and no hours of transportation. If it was one, you know, everyone would be sort of with a passenger all the time. Okay. So this key point is that utilization can essentially shift this product market supply curve. All right. So and then on the passenger side, you think when trips are cheaper, people want to demand more of them. So we just have this downward sloping demand curve. And so, you know, what equilibrium here, unfortunately, it's not where the two curves cross. It's actually backed off from that a little bit. But that's just because I'm trying to write both the driver and the product market and the labor market sort of at the same time. But there's basically an hour of a price for an hour of transportation, and then a driver hourly earnings rate, which is essentially that flow times utilization. So now once the prices are lowered, all right, so when Ubersake goes and decreases that price, you have that increase where drivers want to take and drive more. But this is essentially a pay cut for drivers and they want to supply fewer. And this is just visually that gap that I was talking about sort of how does the actual market clear once they've made this sort of change. So, you know, you probably are already thinking about paths to a new equilibrium, like what could give that would bring you to a new equilibrium? You know, so maybe there's something about how I've driven these drawn these curves that maybe people are completely inelastic. Maybe drivers actually have a downward sloping labor supply curve, say through target earning or something like that. Maybe changes in surge essentially undo a fair change. So, you know, Uber kind of in their back pocket has this other way of adjusting prices. You can imagine if they cut prices by 20%, but just surge was always 20% higher. Well, it wouldn't quite, you know, it would basically wash out. You know, another possibility is that service quality deteriorates. So, you know, the idea that the demand curve is fixed may not actually be true. You could also have an increase in driver technical productivity, i.e. that utilization ends up increasing. And so drivers an hour work, even if they're supplying fewer, you get more hours of transportation from the same number of hours. And that's how you deal with the increase in demand. And so, you know, to preview the results, basically the last three stories or explanations end up being important. So there is a change in surge. There is a deterioration in service quality at lower prices, and it manifests itself as increased wait time. But there's also a pretty large increase in driver technical productivity that essentially you have higher utilization at lower prices and vice versa. And that part actually has kind of the most implications for how we think about, you know, sort of who gains and who loses in this market. But I'll talk more about that later. So that's just a preview. Let me talk about the empirics, how we're kind of arriving at some of these conclusions or how I'm arriving at them. So what I have is a panel of US cities spanning from 2014 to 2017. And so I have 43 of them, and I have a number of weeks. And what I observe each week is at the market level, I observe prices in that city, which I turn into a price index for that city in that particular week. And then I have a number of outcomes. So I can look at, say, you know, what the trip price index, but I can look at, say, what was the driver's hourly earnings rate? Or what was the wait time on average? Or what was the average surge? Or, you know, how many hours drivers were working? So essentially everything you might imagine you could measure on Uber, you know, I have it in a week panel, a city week panel. So where's the variation in prices coming from here? That price index? What's moving it around? Well, Uber's moving it around. You can see what I've annotated here are changes in that price index for each city. It's mostly fares going down and you can find Uber kind of bragging about UberX prices getting lower. You don't see, you can't seem to find any screenshots of them talking about prices rising. But there are prices increasing. In every city, actually, you do observe at least some price increases. So here we can see New York City got a 13% decrease and a 6% decrease about two years later. You can also hear some changes are clearly coordinated across cities. And what this is primarily, in January of 2015 and 2016, there were kind of large across the board price cuts in a lot of cities. You can also see there's some small between city differences in the precise week of a change. So you can kind of see some variation in precisely when things hit. And then you can also see that even though, even when prices changes were coordinated, you often had pretty substantial between city variation. So here at Atlanta and Detroit, Atlanta had about half the size of the price cut that Detroit did. So this is just distribution of fair changes in percentage terms. As I said, it's more decreases than increases, but you get a bit of both. So let me just start and show you some city week grand means. So I'm going to take my panel and just average things every week. So this is that base trip price index. So it's just normalized to one at the start of my panel. You can see that the general trend over this period of time was for this price index to decrease. And you can also see there's pretty large, those January cuts kind of pop out pretty clearly where they cut fairs in a bunch of cities all at once. This is surge. A little sustained evidence of a higher. Well, I'm realizing that my head is kind of blocking some of my notes. I'm going to trick my slides a touch. That's probably good. You can see that there's a, the surge rises following these January increases. You can kind of eyeball it, but there's not much evidence of a sustained change. The big change that you see that's quite clear is this change in utilization. So utilization is considerably higher relative to the start of the panel in overall. And you can kind of see right around the time of those fair cuts utilization kind of pops up and never really goes down again. So it just kind of just rises and seems to be sticky at that or stays at that new level. This is driver hourly earnings rate. Again, it's about the same at the start of the panel as the end of the panel on average. But you can see that there's like a, it's a little hard to eyeball, but there's like, it looks like there's a dip at first. And then maybe it, maybe it rises following those January fair cuts. Okay. Well, I can do a lot better than, than just kind of showing you grand means. Okay. So Ubers, you know, these price changes, the first thing you're kind of wondering about is like, well, you know, presumably Uber was responding to something in these markets when it decided to, John, there's a quick question, a clarifying question. Oh, sure. Quite understood it. Yes. Is the percentage cut of Uber constant over time? Oh, the percentage that they're taking like their percentage take rate? I think that's probably what it means. Yeah. I think that their take rate is about constant, but there, there are some changes in like, I think new drivers versus old, old drivers. But I don't think that there were, you know, I think it's, it's a roughly constant over this period. Okay. The, so the leaks about Uber's decision making on pricing. So, you know, you might be worried that they're kind of like strongly reacting to things that were going on. You might be thinking that they're reacting to what competitors are doing. So that being said, at this point in the U.S., Lyft was pretty nascent. However, you know, we can also get, we can get, you know, data on Lyft penetration. It doesn't seem to have affected things. But the, the, the basic kind of story, at least I can garner internally is that they were just kind of experimenting and didn't really quite know, you know, they were kind of advising, talking to like local cities and so I'm saying what kind of a price cut or price change could, could this market kind of, you know, accept, you know, to the extent they had models, they were basically like accounting identities. Like if we did this many trips at this price, you know, this is what would happen, not kind of, kind of predictive sort of forecasting models. But, you know, in any event, there's, there's quite a bit we can kind of do to, to deal with worries that they were conditioning on something in the city, given that we have this kind of long, long panel. So, you know, so these city specific changes in the base bear, they're not, they're clearly weren't random, you know, Uber even then had, had teams working on, on pricing. But they do seem to have been selecting on observables and not much evidence of, of forecasting. And so let me just talk a little bit about, yeah, going a little bit slow. So I'm going to speed it up a bit. So what I can do, you know, the first thing is just the simplest thing you might imagine was just two-way fixed effects, where I'm going to regress outcome in some city on a city specific effect. I'm going to have the base price index at that, at week in time, and a, a week specific effect, and then a city specific time trend. And I can kind of try variations of this, but it doesn't, doesn't make a huge amount of difference. So what I'm going to look at is what does it do to the prices that drivers were paying, or getting paid rather. So my independent variable here is just this log base fare index. You can see when, and so just this is all framed as if everything were price increases. However, you know, as you know, it was mostly price decreases, but so the log base fare index, when it goes up by about 10%, you get surge goes up by about, about, down by about 2%. So, you know, that, that story that maybe surge was kind of undoing some of the fare changes does, does, does matter. You do see a change in surge just overall. When you look at utilization, this is where you see like pretty, pretty large effects. So you have this increase in, in the price, you get a large decline in, in utilization. And the, you know, kind of putting those two together or multiplying them together, the change in the allow, the hourly earnings rate for drivers, it's positive, but you know, fairly close to, to zero. Well, you know, we can do a lot better than just kind of this, you know, just one regression, we can actually kind of trace out the, the adjustment process.  And then I'm going to look and see what's the cumulative effect over time. And that'll let me look in the pre period to see if anything was going on and then look at the adjustment in the, in the post period. So if we start again with surge, nothing really seems to be going on in the pre period. And then you can see that this is all relative to when a fare change happened at zero here. You see that decline in surge that, you know, that happens by the end of the period. It's closer to 30%. My point estimate was about, about 20%. Okay. So for utilization, again, nothing really going on in the pre period. And then you look at what happens in the post period you see with higher prices utilization starts to decline and pretty quickly. And then finally, for the hourly earnings rate, what's interesting is you kind of have this initial evidence of pass through. So imagine, you know, you have higher fares. At first drivers are making more per hour with these higher fares, but it starts to decline. And then, you know, by the end of the number of post periods I include, you know, you're pretty close to zero, at least the confidence interval includes no change. So initial pass through and then the steady decline. It seems to be what happens for an adjustment. Now, there's other outcomes related to market clearing.  But if you look at just the quantities that transpired, so sort of how many like the quantity of trips, driver compensation, etc. You know, what you see is the number of trips and hours and hours of passengers declines with these higher prices. The driver compensation effects, they're actually pretty sensitive to definition about sort of what costs you include. You know, it's a little bit challenging to sort of say what exactly you should count as an hour work. And I kind of refer you to the paper for details in wrestling with this, but it looks like it's mostly positive with a fair increase. The driver technical productivity, this one is quite clear that you see this decline in utilization with higher prices. There's some things that I talked about like surge goes down. There's also one thing I didn't talk about was in some cities, Uber was paying kind of nonlinear, had nonlinear incentive schemes and bonuses of various kinds. And so I look at the fraction of earnings that come with promotions. And a lot of them were kind of said as like earnings floors. And so you do see a decline in the earnings that come from promotions, though it's not huge. And the number of cities where they're actually doing this wasn't as big as you might think. For other supply measures, you do see an increase in hours work, which I take as kind of some evidence that drivers experience this as a wage increase. So like I said, the driver compensation measures generally positive, but a little bit, not telling a totally consistent story. But if you look at hours worked by drivers, it suggests that this higher price equilibrium was one that they prefer. Now, one thing I did not talk about, and this is where it gets into the, did the demand curve shift. This is the wait times. So when you request an Uber, you have to wait for it to arrive. And there's pretty clear evidence, like those top two, that with higher prices, wait times go down. If you kind of think just intuitively what's happening, imagine a world in which utilization was 100%. At any moment in time, there's no available cars. And so your wait time is really, really long. If utilization is really low, but the number of drivers out on the road is the same, the nearest, closest available car, or sorry, the nearest available car is likely to be closer to you. And so there seems to be this utilization wait time trade off that kind of comes up pretty, pretty clearly. So let me go back to the simple model. So to kind of put these different effects graphically, again, here it's just framed as a price decrease. So partially what you get is a surge adjustment, like surge takes and offsets some of these prices. So the price faced by passengers is effectively a bit higher. And then that kind of has the translates into an effect on drivers. You do get this increase in wait times, which passengers don't like waiting. And so I think it makes sense to think of this as a shift in in the demand curve. And then finally, you have this utilization, which essentially it actually works sort of inside and outside in the sense that with a higher utilization, every hour is more productive. But it also means that a given hour of work for a driver, they make more, even if the on-trip payment is lower, there's sort of less downtime. So you get sort of two, essentially two ways of raising the output in the product market. Okay, so let me talk through some of the implications. So there's this clear question. So it's in the chat. And he says he's worried that consumers are experiencing all this variation and might be just kind of fearful of, I guess, changes in general. So he asked if the uniform price changes provide a more solid test of what you're looking for? Like do the estimates look the same when you look at the kind of uniform changes that you saw versus these, I guess, city by city changes? Oh, yeah. I mean, so I mean, one of the things we do in our very long appendix is do like event studies around these like single changes like, you know, where like they changed everything once in January. So I think that somewhat alleviates the concern that it's kind of like fluctuating kind of rapidly. I think a concern, I would have this more on the driver side that they feel like they're getting jerked around and you kind of have less trust in Uber. I think on the passenger side, I mean, my mental model at least is that people kind of whip open the app, get an estimate of the price and sort of respond to it, you know, as if it were a spot market. But, you know, I don't have I don't have sources of variation that are kind of like just, you know, a one time thing, you know, it's it's it's inherently, you know, different markets having different different changes over time. I don't I don't know if I address that question. But let me see the language of it. All right. So let me all right. So let me just get back. So there seems to be this price utilization trade off at the market level with with higher prices, meaning lower utilization. But there also seems to be this utilization wait time trade off at the market level, where, you know, you take a new as you have a higher utilization, people have to wait longer for the next available. Next, next available. Okay. You know, the welfare effects of fairies increases, you know, like I said, my measures are a bit ambiguous for drivers, but I think probably probably negative, at least that where where Uber was was cutting things in the sense that it seemed to lower hourly earnings, at least in some specifications, or it seems also seems to raise them. But the increase in hours worked suggests that drivers were probably better off overall with with the higher higher prices. But let me try to step back in one second. You know, let me just give you kind of a simple model that I found I find useful to kind of think about this where so we know now that we kind of know that there was this quality response, let's imagine writing a better demand curve where we have changes in utilization affect passenger wait time. And so, you know, passengers are responding not just to the price they pay, but also the the disutility they get have to get from waiting longer, which is going to be just a function of market level utilization. And then on the driver side, they're just responding to the wage. Now it's possible that they have preferences over the degree of utilization other than through the effect it has on their wage.   So a higher utilization does have a higher cost to you because you end up spending more on gas. But I'm just going to assume they're responding to this like it like it was a wage. And so let me just kind of draw, you know, be, you know, Uber was changing these prices and you kind of seem to put the market in what looks like a different equilibrium where you have different price utilization tradeoffs. I'm going to draw these in a diagram where on the X axis, I'm going to put the level of driver utilization in the market. And then on the Y axis, I'm going to put the price that that passengers face. And if you take that, you know, with this with this drawing, the drivers want to be at a high utilization, because they, you know, an hour worked is almost exactly an hour hour paid. And they'd like the price to be really high. So they have no downtime. And when they're on a trip, they make plenty of money. The passengers, they would like low prices, obviously, but they would also like a very low utilization because that translates into a better wait time for them, they're waiting less for the next the next for their rides. And so what you what you have, if you take that market clearing condition, I wrote, there's a downward sloping line that says these are the these are the points that are actually possible. So these are possible equilibria. So Uber gets to kind of pick P. But then that that determines a utilization on on the on the X axis here. And so what you can we can show is that if you take and draw a driver and passenger in different curves, this there's points that are tangent to that possible equilibria. And you get a driver preferred equilibrium and a passenger preferred equilibrium. So these these are the, you know, the ones that they're the equilibria where they're the best off that they can be subject to this market clearing condition. And then there's a there's a region where prices are so high, both sides would like fair cuts. So the price is so high that there's so few passengers out there actually demanding trips that even though a trip, you know, a passenger pays a lot if you can get one, they're so rare that the driver would actually prefer you to lower prices and so with the passenger. And similarly, there's a point where prices are too low, and lower than what passengers would prefer. And the both sides are sort of sort of agree. It's not it's they the wait time is so bad that that passengers would actually prefer to pay a higher price to get it to get a lower to get a lower wait time. And, you know, depending on where you are here, the comparative static so if you have a price change in these different regions, it has different different effects. So, you know, if you're if you're in a in a region here where both sides would like a fair increase, a fair increase, you know, P going up is going to actually increase the quantity of trips. If you were back here, a price decrease is going to increase the quantity of trips and the hours hours work. The trade off zone is here, which is just between these two between these two kind of ideal preferred equilibria. And this is the place where drivers would like fair increases and passengers want want fair cuts. And if you take, you know, my results, this is this is the region that Uber seemed to be living in when it was cutting fair changes, cutting prices or change changing prices where when you cut prices, you you get an hours work increase. Sorry, hours were decreased from drivers and vice versa when you when you lower prices. So I think that, you know, essentially they were not and probably not in the region where you could unambiguously make both sides better off. Okay, so I actually I sped up, but I actually finished earlier than I thought. So my timing was a bit off, but that gives us more time for questions, which is, which is fine with me too. All right, thank you. Thank you, John. Yeah, super interesting. I am Camillo, one of you. Right, great. So first of all, thanks so much for the invitation to this that discuss this paper to the organizers. Thanks, John for the presentation. I think this is a very interesting paper with many good things. I'll discuss in the next few seconds, next few minutes. Then we start by saying one thing that I think in general is good about this paper relative to the papers. And if we think about empirical work on digital platforms, one thing is that the data that these platforms have is just amazing in many dimensions. And in particular, it is great to measure what goes on in the short run. So we see clickstream data or we see, I don't know, at least when I when I've used Uber data, I see what individual passengers and drivers do. And I see how they react to the prices they see in the app and stuff like that. And that's great. If you want to see what happens in the very short run, but it isn't that good when you want to measure what happens in the long run. And what many of us end up doing, and I am actually subject to this critique is we kind of end up searching under the lamppost. So we just end up focusing on what happens in the short run. And this paper is very interesting because it actually looks also at what happens in the long run. So I think that's one. And of course, there are many interesting questions. It's also very important for policy or if one understands what goes on in these markets. And this paper actually takes a look at that and tries to see what can we possibly uncover using this data. So kind of one other thing I wanted to say is there are a few things I'm going to mention that actually think that the presentation did better than the paper. So I'll kind of try to emphasize that. And one of the things, and let me just kind of say what is it I found most interesting about the paper as a whole. And it's the fact that we can see the adjustment from the short run to the long run, basically to put it into what John presented to us. Those event studies were we see how people react or how the market reacts initially to these price cuts and then little by little it adjusts all the way to the end. This transition from the short run to the long run is what I think is most interesting about this paper and how it shows how the whole market equilibrates. Now one thing is the short run is probably very well identified because of the exact timing of the shocks. The long run is maybe not that well identified because there are reasons when we might be worried about what's going on in the long run. But I just, given what I was saying before, identifying long run effects is just intrinsically way more complicated. So I don't think this is a weakness of the paper. I just think it's just the nature of identifying long run effects. But just I don't have any doubt that this transition from the short run to the long run is something that this paper actually identifies pretty well. Maybe the challenge is that the final level is not exactly well identified, but at least we get a really good sense of what's the initial response and in what direction does the transition from the short run to the long run goes. So I think that was great. Okay, moving on to other things I would have liked to see from the paper. So one thing I thought was that those event studies, which I thought were the best part, focused probably too much on the supply side. I also would have liked to see some of these events that is about the demand response. So potentially what could happen is that initially as there's a price cut, there's an initial shock in which demand reacts by increasing the number of trips demanded and then in the long run maybe as wait time start going up or I don't know how the whole market reaction is going to be. But I would also like to see how this short run to long run transition goes on the demand side to fully understand whether this is kind of how the whole market equipment looks like. And I think the other main thing I would have liked to see is so we saw this figure about where we have this xp axis so the utilization and prices. As I build up to that figure I would have liked to see how does an equilibrium look like kind of to some extent I think of this market a bit differently from what John does because how I think of this is price is a choice variable of the platform and then there's a market equilibrium that is a function of the choice variable. What happens is that the market clears through I don't know how you want to call it waiting times for utilization rates. So I probably would have liked to see a marketing which receives supply and demand as a function of this utilization rate see how that equilibrium looks like see how the market adjusts in response to a price decrease so maybe like there's a short run a shift both in supply and demand and then in the long run as these people as more drivers are allowed to buy a car and become real drivers as passengers know that these prices went down and therefore maybe decide to sell their car kind of see a short run shift and then a long run shift and see in this in this little figure in the simplified figure how this transition from the short run to the long run adjustments look like and I think that would have helped me understand really well how I said that this whole market dynamics look like and kind of rationalize in a way similar to what the last couple of like showed about about the short and long run discussions something like that looking at this access at this two axis between so a utilization rate in the vertical axis and number of trips in the horizontal axis so those are kind of the main things I would have liked to see but in general I mean I think these have very interesting paper I think there are many interesting things that we could we could see in this paper and as I said this whole transition to the to the long run equilibrium I think something super interesting and I don't think I had ever seen anything similar to this thanks so much Jen oh thank you very much


This week, we celebrate entrepreneurs across our country. Canadians who've built businesses, created good middle-class jobs, and shaped our communities. But this year has been a difficult year for many of them. COVID-19 has changed the way they run their business. Some have had to temporarily close their doors or change their operations entirely. And through it, Canadian entrepreneurs have risen to the challenge of the moment. With creativity, innovation, and resilience, they've shown what it means to be Canadian. And as a government, we will always be there to help them. We will continue to offer supports that will help keep their doors open and grow their businesses during this difficult time and beyond. Because we can only build back better if we lean on one another. So thank you to all of our entrepreneurs across the country for everything you do for our communities. And to all Canadians, let's do our part to show support and appreciation for their businesses. Let's buy local, order takeout if we can, and lend a helping hand. And together, let's continue the hard work to move Canada forward.