06 nash equilibrium dating and cournot mov
In that game, if you remember what the best responses looked like, they looked like this where this was the effort of Player 1; this was the effort of Player 2. Professor Ben Polak: All right, so unlike the other game, the two examples of coordination games we saw so far were really pure coordination problems. But here, there's a potential source of conflict here. So this game's called The Battle of the Sexes and we'll see it in various forms over the course of the semester. Games like it, they are coordination games but different people disagree about where you'd like to coordinate. So those of you who have, don't worry, I mean this will be a bit review, but we'll see it more through the eyes of Game Theory this time, and for those of you who haven't, don't worry we're going to go through it.This was the best response of Player 1 and this was the best response of Player 2. Student: Both players doing Bourne Ultimatum and both players doing Good Shepherd. Both people would rather be at an equilibrium than to be mal-coordinated or uncoordinated, but Player 1 wants to go to Bourne Ultimatum and Player 2 wants to go to Good Shepherd, and actually I thought Nina's strategy there was pretty good. So much for talking about coordination games and helping you with your dating strategy. So this is a classic game, perhaps it's one of the most famous games, and therefore worth studying in the class.You don't want to end up uncoordinated on down left or up right. So in this game if you just played it, it's quite likely you're going to end up uncoordinated, but if you have a little bit of leadership can say okay let's make sure this is where we coordinate, or let's make sure this is where we coordinate. And I don't want to overplay the social importance of this, but go back a couple of years to what was happening in the aftermath of Katrina and realize how important--how bad things get when things fail to be coordinated.One other remark before we leave this, in the game we played last time, in the investment game, one feature of that game was that the more you thought other people were going to invest, the more you wanted to invest.And let's have a look at the movies concerned here and we'll draw--there's three possible movies. Why is this a more difficult game to attain coordination in? One extreme case is perfect competition and the other extreme case is monopoly.The movies we're going to look at are The Bourne Ultimatum, and the movie called Good Shepherd, and a movie called Snow White and I'll explain the game in more detail in a second. So Nina, shout out to the crowd what it is you've--where it is you've chosen to go. Professor Ben Polak: Bourne Ultimatum; and David where do you choose to go? Professor Ben Polak: They're going to coordinate; that's very good. Professor Ben Polak: So they're still managing to coordinate but you--okay, so thank you for this couple, let's give them a round of applause. Student: Can I say the best response is the Nash Equilibrium? So this is really the first attempt, way back in the nineteenth century to study a market that's somewhere in the middle, where it happens most markets are--there are two firms. We're interested in what's going to happen in these markets. So the players in this game are two firms and the strategies in this game for the firms--and this is going to turn out to be important--the strategies are the quantities that they produce of an identical product.In the coordination game, where the idea is to try and get people to coordinate on a particular equilibria rather than on another equilibria, or worse still, to be uncoordinated entirely.In those kind of games, leadership can help tremendously. So these games, these coordination games, are games where there is a "scope for leadership." Just to see that in a very simple example, again, we don't use such a complicated example as the one we looked at last time, you could imagine a game, a really trivial coordination game, which looked like this (1,1) (0,0) (0,0) (1,1).
But one thing we can do is tell you where leadership may help.
And they've decided to go to the Criterion [New Haven movie theatre], or the local movie house, and there were these three movies showing, and they're all excited about going to this movie except being Economics majors and not very good at dating, they have forgotten to tell each other which movie they're actually going to go to. So basically the idea is that the more these firms produce, so the more the total quantity produced q, the lower is the price in the marketplace for this product.
They're going to meet in there on the--in the back row probably and--but they're not telling us which movie. So here are the preferences for these movies of Player 1 and Player 2, and you can see from these preferences, from these payoffs, that the best thing for Player 1 is for both players, both people to meet and go to the Bourne Ultimatum; this is the action movie. Let's just draw a picture of that; we'll come back to this in a minute. Actually, let's save myself some time and bring this down. It tells me--the other way around--to look at how prices correspond to quantities, it tells me the quantity demanded at any given price. Meanwhile, let's just finish up what we're doing here and put in payoffs.
Now, it used to be in the old days before I had kids, I could list off 15 current movies and help you a bit more with your dating strategy by giving you instant movie reviews, but now I have kids, I get to see precisely two movies a year, and the two movies I got to see this year were The Bourne Ultimatum and the Good Shepherd. Professor Ben Polak: David so--do you know each other? Professor Ben Polak: No you're--so you're about to go on a date. I don't know what this tells us about David and Nina, but don't let them off the hook quite yet. I think we can all see that we might not have done. We said that coordination games are helped by communication. We may come back and pick on you later on in the course, but we'll leave it for now. And then from a welfare point of view, from a policy point of view, we're interested about whether this is good for consumers or good for producers or what. So they are the quantities they produce, each of them produces, of an identical product.
And now I think about it, both of those have Matt Damon in it. So Nina's preferences are Player 1's preferences here. So let's imagine we're playing the game again, once again, you're going to the movies, once again the first one didn't happen so you didn't--for some reason it was cancelled that night because someone had a bad cold or something. So in this case, the communication worked but am I right in thinking that the communication isn't such an instant solution as it was in the game we saw last time? So as far as the consumers are concerned, these two products are perfect substitutes.
Quite a lot of you; this is a movie, it has pretty good action, virtually no plot. The basic lesson of this movie is--and you probably knew this already--everyone at Yale is a spy … The third movie is Snow White, which I haven't gone out to see but my four-year old daughter has seen on 24 of the last 27 nights on video. Student: Looks like you want to go to Bourne Ultimatum. And the cost of production in this game is simply going to be cq.