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# ECON 159: Game Theory

## Lecture 5

## - Nash Equilibrium: Bad Fashion and Bank Runs

### Overview

We first define formally the new concept from last time: Nash equilibrium. Then we discuss why we might be interested in Nash equilibrium and how we might find Nash equilibrium in various games. As an example, we play a class investment game to illustrate that there can be many equilibria in social settings, and that societies can fail to coordinate at all or may coordinate on a bad equilibrium. We argue that coordination problems are common in the real world. Finally, we discuss why in such coordination problems–unlike in prisoners’ dilemmas–simply communicating may be a remedy.

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html## Game Theory## ECON 159 - Lecture 5 - Nash Equilibrium: Bad Fashion and Bank Runs## Chapter 1. Nash Equilibrium: Definition [00:00:00]
What I want to do today is discuss Nash Equilibrium, see how we find that equilibrium into rather simple examples. And then in the second half of the day I want to look at an application where we actually have some fun and play a game. At least I hope it’s fun. But let’s start by putting down a formal definition. We only used a rather informal one last week, so here’s a formal one. A strategy profile–remember a profile is one strategy for each player, so it’s going to be S Now, this is by far the most commonly used solution concept in Game Theory. So those of you who are interviewing for McKenzie or something, you’re going to find that they’re going to expect you to know what this is. So one reason for knowing what it is, is because it’s in the textbooks, it’s going to be used in lots of applications, it’s going to be used in your McKenzie interview. That’s not a very good reason and I certainly don’t want you to jump to the conclusion that now we’ve got to Nash Equilibrium everything we’ve done up to know is in some sense irrelevant. That’s not the case. It’s not always going to be the case that people always play a Nash Equilibrium. For example, when we played the numbers game, the game when you chose a number, we’ve already discussed last week or last time, that the equilibrium in that game is for everyone to choose one, but when we actually played the game, the average was much higher than that: the average was about 13. It is true that when we played it repeatedly, it seemed to converge towards 1, but the play of the game when we played it just one shot first time, wasn’t a Nash Equilibrium. So we shouldn’t form the mistake of thinking people always play Nash Equilibrium or people, “if they’re rational,” play Nash Equilibrium. Neither of those statements are true. Nevertheless, there are some good reasons for thinking about Nash Equilibrium other than the fact it’s used by other people, and let’s talk about those a bit. So I want to put down some motivations here–the first motivation we already discussed last time. In fact, somebody in the audience mentioned it, and it’s the idea of “no regrets.” So what is this idea? It says, suppose we’re looking at a Nash Equilibrium. If we hold the strategies of everyone else fixed, no individual i has an incentive to deviate, to move away. Alright, I’ll say it again. Holding everyone else’s actions fixed, no individual has any incentive to move away. Let me be a little more careful here; no individual has any So why I call that “no regret”? It means, having played the game, suppose you did in fact play a Nash Equilibrium and then you looked back at what you had done, and now you know what everyone else has done and you say, “Do I regret my actions?” And the answer is, “No, I don’t regret my actions because I did the best I could given what they did.” So that seems like a fairly important sort of central idea for why we should care about Nash Equilibrium. Here’s a second idea, and we’ll see others arise in the course of today. A second idea is that a Nash Equilibrium can be thought of as self-fulfilling beliefs. So, in the last week or so we’ve talked a fair amount about beliefs. If I believe the goal keeper’s going to dive this way I should shoot that way and so on. But of course we didn’t talk about any beliefs in particular. These beliefs, if I believe that–if everyone in the game believes that everyone else is going to play their part of a particular Nash Equilibrium then everyone, will in fact, play their part of that Nash Equilibrium. Now, why? Why is it the case if everyone believes that everyone else is playing their part of this particular Nash Equilibrium that that’s so fulfilling and people actually will play that way? Why is that the case? Anybody? Can we get this guy in red?
So, we had this picture last time in the partnership game in which people were choosing effort levels. And this line was the best response for Player 1 as a function of Player 2’s choice. And this line was the best response of Player 2 as a function of Player 1’s choice. This is the picture we saw last time. And let’s just look at how those–it’s no secret here what the Nash Equilibrium is: the Nash Equilibrium is where the lines cross–but let’s just see how it maps out to those two motivations we just said. So, how about self-fulfilling beliefs? Well, if Player–sorry, I put 1, that should be 2–if Player 1 believes that Player 2 is going to choose this strategy, then Player 1 should choose this strategy. If Player 1 thinks Player 2 should take this strategy, then Player 1 should choose this strategy. If Player 1 thinks Player 2 is choosing this strategy, then Player I should choose this strategy and so on; that’s what it means to be best response. But if Player 1 thinks that Player 2 is playing exactly her Nash strategy then Player 1’s best response is to respond by playing his Nash strategy. And conversely, if Player 2 thinks Player 1 is playing his Nash strategy, then Player 2’s best response indeed is to play her Nash strategy. So, you can that’s a self-fulfilling belief. If both people think that’s what’s going to happen, that is indeed what’s going to happen. How about the idea of no regrets? So here’s Player 1; she wakes up the next morning–oh I’m sorry it was a he wasn’t it? He wakes up the next morning and he says, “I chose S So, I want to spend quite a lot of time today just getting used to the idea of Nash Equilibrium and trying to find Nash Equilibrium. (I got to turn off that projector that’s in the way there. Is that going to upset the lights a lot?) So okay, so what I want to do is I want to look at some very simple games with a small number of players to start with, and a small number of strategies, and I want us to get used to how we would find the Nash Equilibria in those simple games. We’ll start slowly and then we’ll get a little faster. ## Chapter 2. Nash Equilibrium: Examples [00:09:31]So, let’s start with this game, very simple game with two players. Each player has three strategies and I’m not going to motivate this game. It’s just some random game. Player 1 can choose up, middle, or down, and Player 2 can choose left, center, and right and the payoffs are as follows: (0,4) (4,0) (5,3) (4,0) (0,4) (5,3) again (3,5) (3,5) and (6,6). So, we could discuss–if we had more time, we could actually play this game–but isn’t a very exciting game, so let’s leave our playing for later, and instead, let’s try and figure out what are the Nash Equilibria in this game and how we’re going to go about finding it. The way we’re going to go about finding them is going to mimic what we did last time. Last time, we had a more complicated game which was two players with a continuum of strategies, and what we did was we figured out Player 1’s best responses and Player 2’s best responses: Player 1’s best response to what Player 2’s doing and Player 2’s best response to what Player 1 is doing; and then we looked where they coincided and that was the Nash Equilibrium. We’re going to do exactly the same in this simple game here, so we’re going to start off by figuring out what Player 1’s best response looks like. So, in particular, what would be Player 1’s best response if Player 2 chooses left? Let’s get the mikes up so I can sort of challenge people. Anybody? Not such a hard question. Do you want to try the woman in the middle? Who’s closest to the woman in the middle? Yeah.
Now, I want to try and convince you, particularly those of you who are worried by the homework assignments, that that was not rocket science. It’s not hard to find Nash Equilibria in games. It didn’t take us very long, and we went pretty slow actually. So let’s look at another example. Oh, before I do, notice this–before I leave this game I’m just going to make one other remark. Notice that in this game that each strategy of Player 1 is a best response to something, and each strategy of Player 2 is a best response to something. So, had we used the methods of earlier on in the class, that’s to say, deleting dominated strategies or deleting strategies that are never a best response, we’d have gotten nowhere in this game. So, Nash Equilibrium goes a little further in narrowing down our predictions. But we also learned something from that. We argued last time, in the last few weeks, that rationality, or even mutual knowledge of rationality or even common knowledge of rationality couldn’t really get us much further than deleting dominated strategies, or if you like, deleting strategies that are never best responses. So, here we’ve concluded that the Nash Equilibrium of this game is down right, a very particular prediction, but notice a perfectly rational player could here, could choose middle. The reason they could choose middle, Player 1 could choose middle is–could be that– they say (rationally) they should choose middle because they think Player 2 is choosing left. Then you say, “well, why would you think Player 2 is going to choose left?” Player 1 could say, “I think Player 2 is going to choose left because Player 2 thinks I’m going to play up.” And then you say, “but how could Player 2 possibly think that you’re going to play up?” And then Player 1 would say, “I think Player 2 thinks I’m going to play up because Player 2 thinks that I think that he’s going to play center.” And then you could say, “how could Player 2 play …” etc., etc., etc. And you could see you could work around a little cycle there. Nobody would be irrational about anything: Everything would be perfectly well justified in terms of beliefs. It’s just we wouldn’t have a nice fixed point. We wouldn’t have a nice point where it’s a simple argument. In the case of down right, Player 1 thinks it’s okay to play down because he thinks 2 is going to play right, and Player 2 thinks they’re going to play right because he thinks Player 1’s going to play down. So, just to underline what I’m saying rather messily there, rationality, and those kinds of arguments should not lead us to the conclusion that people necessarily play Nash Equilibrium. We need a little bit more; we need a little bit more than that. Nevertheless, we are going to focus on Nash Equilibrium in the course. Let’s have a look at another example. Again, we’ll keep it simple for now and we’ll keep to a two-player, three-strategy game; up, middle, down, left, center, right and this time the payoffs are as follows: (0,2) (2,3) (4,3) (11,1) (3,2) (0,0) (0,3) (1,0) and (8,0). So, this is a slightly messier game. The numbers are really just whatever came into my head when I was writing it down. Once again, we want to find out what the Nash Equilibrium is in this game and our method is exactly the same. We’re going to, for each player, figure out their best responses for each possible choice of the other player. So, rather than write it out on the–let me just go to my green circles and red squares and let me get my mikes up again, so we can cold call people a bit. Can we get the–where’s the mike? Thank you. So, Ale do you want to just grab somebody and ask them what’s the best response against left? Grab anybody. What’s the best one against left?
## Chapter 3. Nash Equilibrium: Relation to Dominance [00:23:13]So, what have we seen? We’ve seen how to find Nash Equilibrium. And clearly it’s very closely related to the idea of best response, which is an idea we’ve been developing over the last week or so. But let’s go back earlier in the course, and ask how does it relate to the idea of dominance? This will be our third concept in this course. We had a concept about dominance, we had a concept about best response, and now we’re at Nash Equilibrium. It’s, I think, obvious how it relates to best response: it’s when best responses coincide. How about how it relates to dominance? Well, to do that let’s go back. What we’re going to do is we’re going to relate the Nash Equilibrium to our idea of dominance, or of domination, and to do that an obvious place to start is to go back to a game that we’ve seen before. So here’s a game where Player 1 and Player 2 are choosing ά and β and the payoffs are (0,0) (3,-1) (-1,3) and (1,1). So, this is the game we saw the first time. This is the Prisoner’s Dilemma. We know in this game–I’m not going to bother to cold call people for it–we know in this game that β is dominated –is strictly dominated by ά. It’s something that we learned the very first time. Just to check: so against ά, choosing ά gets you 0, β gets you -1. Against β choosing ά gets you 3, β gets you 1, and in either case ά is strictly better, so ά strictly dominates β, and of course it’s the same for the column player since the game’s completely symmetric. So now, let’s find the Nash Equilibrium in this game. I think we know what it’s going to be, but let’s just do it in this sort of slow way. So, the best response to ά must be ά. The best response to β must be ά, and for the column player the best response to ά must be ά, and the best response to β must be ά. Everyone okay with that? I’m just kind of–I’m rushing it a bit because it’s kind of obvious, is that right? So, the Nash Equilibrium in this game is (ά, ά). In other words, it’s what we would have arrived at had we just deleted strictly dominated strategies. So, here’s a case where ά strictly dominates β, and sure enough Nash Equilibrium coincides, it gives us the same answer, both people choose ά in this game. So, there’s nothing–there’s no news here, I’m just checking that we’re not getting anything weird going on. So, let’s just be a bit more careful. How do we know it’s the case–I’m going to claim it’s the case, that no strictly dominated strategy–in this case β–no strictly dominated strategy could ever be played in a Nash Equilibrium. I claim–and that’s a good thing because we want these ideas to coincide–I claim that no strictly dominated strategy could ever be played in the Nash Equilibrium. Why is that the case? There’s a guy up here, yeah.
And again, so here’s the trivial example, not an interesting example, but it just makes the point. So here’s a 2 x 2 game. Player 1 can choose up or down and Player 2 can choose left or right, and the payoffs are really trivial: (1,1) (0,0) (0,0) (0,0). So, let’s figure out what the Nash Equilibrium is in this game and I’m not going to bother cold calling because it’s too easy. So the best response for Player 1, if Player 2 plays left is clear to choose up. And the best response of Player 1 if Player 2 chooses right is–well, either up or down will do, because either way he gets 0. So these are both best responses. Is that correct? They’re both best responses; they both did equally well. Conversely, Player 2’s best response if Player 1 chooses up is, sure enough, to choose left, and that’s kind of the answer we’d like to have, but unfortunately, when Player 1 plays down, Player 2’s best response is either left or right. It makes no difference. They get 0 either way. So, what are the Nash Equilibria in this game? So, notice the first observation is that there’s more than one Nash Equilibrium in this game. We haven’t seen that before. There’s a Nash Equilibrium with everybody in the room I think, I hope, thinks it’s kind of the sensible prediction in this game. In this game, I think all of you, I hope, all of you if you’re Player 1 would choose up and all of you for Player 2 would choose left. Is that right? Is that correct? It’s hard to imagine coming up with an argument that wouldn’t lead you to choose up and left in this game. However, unfortunately, that is–this isn’t unfortunate, up left is a Nash Equilibrium but so is down right. If Player 2 is choosing right, your best response weakly is to choose down. If Player 1 is choosing down, Player 2’s best response weakly is to choose right. Here, this is arriving because of the definition of Nash; it’s a very definite definition. I deleted it now. When we looked at the definition we said, something is a Nash Equilibrium was each person is playing a best response to each other; another way of saying that is no player has a strict incentive to deviate. No player can do strictly better by moving away. So here at down right Player 1 doesn’t do strictly better; it’s just a tie if she moves away. And Player 2 doesn’t do strictly better if he moves away. It’s a tie. He gets 0 either way. So, here we have something which is going to worry us going on in the course. Sometimes we’re getting–not only are we getting many Nash Equilibria, that’s something which–that shouldn’t worry us, it’s a fact of life. But in this case one of the Nash Equilibria seems silly. If you went and tried to explain to your roommates and said, “I predict both of these outcomes in this game,” they’d laugh at you. It’s obvious in some sense that this has to be the sensible prediction. So, just a sort of worrying note before we move on. So, this was pretty formal and kind of not very exciting so far, so let’s try and move on to something a little bit more fun. ## Chapter 4. Pareto Efficient Equilibria in Coordination Games: The Investment Game [00:31:53]So, what I want to do now is I want to look at a different game. Again, we’re going to try and find Nash Equilibrium in this game but we’re going to do more than that, we’re going to talk about the game a bit, and a feature of this game which is–to distinguish it from what we’ve done so far–is the game we’re about to look at involves many players, although each player only has a few strategies. So, what I want to do is I want to convince you how to find–to discuss how to find Nash Equilibria in the game which, unlike these games, doesn’t just have two players–it has many players–but fortunately, not many strategies per player. So let me use this board. So this is going to be called The Investment Game and we’re going to play this game, although not for real. So, the players in this game, as I’ve just suggested, the players are going to be you. So, everyone who is getting sleepy just looking at this kind of analysis should wake up now, you have to play. The strategies in this game are very simple, the strategy sets, or the strategy alternatives. Each of you can choose between investing nothing in a class project, $0, or invest $10. So, I’m sometimes going to refer to investing nothing as not investing, is that okay? That seems like a natural to do. You’re either going to invest $10 or nothing, you’re not going to invest. So that’s the players and those are the strategies, so as usual we’re missing something. What we’re missing are the payoffs. So here are the payoffs; so the payoffs are as follows: if you don’t invest, if you do not invest, you invest nothing, then your payoff is $0. So nothing ventured nothing gained: natural thing. But if you do invest $10, remember each of you is going to invest $10 then your individual payoffs are as follows. Here’s the good news. You’re going to get a profit of $5. The way this is going to work is you’re going to invest $10 so you’ll make a gross profit of $15 minus the $10 you originally invested for a net of $5. So a net profit–so $5 net profit, that’s the good news. But that requires more than 90% of the class to invest, greater than or equal to 90% of the class to invest. If more than 90% of the class invests, you’re going to make essentially 50% profit. Unfortunately, the bad news is you’re going to lose your $10, get nothing back so this is a net loss, if fewer than 90% of the class invest. I mean a key rule here; you’re not allowed to talk to each other: no communication in the class. No hand signals, no secret winks, nothing else. So, everyone understand the game? Including up in the balcony, everyone understand the game? So, what I want you to do–I should say first of all, we can’t play this game for real because there’s something like 250 of you and I don’t have that kind of cash lying around. So we’re not–pretend we’re playing this for real. So, without communicating I want each of you to write on the corner of your notepad whether you’re going to invest or not. You can write Y if you’re going to and N if you’re not going to invest. Don’t discuss it with each other; just write down on the corner of your notepad Y if you’re going to invest and N if you’re not going to invest. Don’t discuss it guys. Now, show your neighbor what you did, just so you can–your neighbor can make you honest. Now, let’s have a show of hands, so what I want to do is I want to have a show of hands, everybody who invested. Don’t look around; just raise your hands, everyone who invested? Everyone who didn’t invest! Oh that’s more than 10%. Let’s do that again. So everyone who invested raised their hands … and everyone who didn’t invest raise their hands. So I don’t know what that is, maybe that’s about half. So now I’m thinking we should have played this game for real. I want to get some discussion going about this. I’m going to discuss this for a while; there’s a lot to be said about this game. Let me borrow that, can I borrow this? So this guy; so what did you do?
Okay, now we’ve got this game up on the board, I want to spend a while discussing it because it’s kind of important. So, what I want to do now is I want to remind us what happened just now. So, what happened just now? Can we raise the yeses again, the invest again. Raise the not invested, not invest. And I want to remind you guys you all owe me $10. What I want to do is I want to play it again. No communication, write it down again on the corner of your notepad what you’re going to do. Don’t communicate you guys; show your neighbor. And now we’re going to poll again, so ready. Without cheating, without looking around you, if you invested–let Jude get a good view of you–if you invested raise your hand now. If you didn’t invest–okay. All right, can I look at the investors again? Raise your hands honestly; we’ve got a few investors still, so these guys really owe me money now, that’s good. Let’s do it again, third time, hang on a second. So third time, write it down, and pretend this is real cash. Now, if you invested the third time raise your hand. There’s a few suckers born everyday but basically. So, where are we heading here? Where are we heading pretty rapidly? We’re heading towards an equilibrium; let’s just make sure we confirm that. So everyone who didn’t invest that third time raise your hands. That’s pretty close; that show of hands is pretty close to a Nash Equilibrium strategy, is that right? So, here’s an example of a third reason from what we already mentioned last time, but a third reason why we might be interested in Nash Equilibria. There are certain circumstances in which play converges in the natural sense–not in a formal sense but in a natural sense–to an equilibrium. With the exception of a few dogged people who want to pay for my lunch, almost everyone else was converging to an equilibrium. So play converged fairly rapidly to the Nash Equilibrium. But we discussed there were two Nash Equilibria in this game.; Is one of these Nash Equilibria, ignoring me for a second, is one of these Nash Equilibria better than the other? Yeah, clearly the “everyone investing” Nash Equilibrium is the better one, is that right? Everyone agree? Everyone investing is a better Nash Equilibrium for everyone in the class, than everyone not investing, is that correct? Nevertheless, where we were converging in this case was what? Where we’re converging was the bad equilibrium. We were converging rapidly to a very bad equilibrium, an equilibrium which no one gets anything, which all that money is left on the table. So how can that be? How did we converge to this bad equilibrium? To be a bit more formal, the bad equilibrium and no invest equilibrium here, is
Notice that what happened here, the way we spiraled down coincides with something we’ve talked about Nash Equilibrium already, it coincides with this idea of a self-fulfilling prediction. Provided you think other people are not going to invest, you’re not going to invest. So, it’s a self-fulfilling prediction to take you down to not investing. Conversely, provided everyone thinks everyone else is going to invest, then you’re going to go up to the good equilibrium. I think that corresponds to what the gentleman said in the middle about a bare market versus a bull market. If it was a bare market, it looked like everyone else didn’t have confidence in everyone else investing, and then that was a self-fulfilling prophesy and we ended up with no investment. Now, we’ve seen bad outcomes in the class before. For example, the very first day we saw a Prisoner’s Dilemma. But I claim that though we’re getting a bad outcome here in the class, this is not a Prisoner’s Dilemma. Why is this not a Prisoner’s Dilemma? What’s different between–I mean both games have an equilibrium which is bad. Prisoner’s Dilemma has the bad equilibrium when nobody tidies their room or both guys go to jail, but I claim this is not a Prisoner’s Dilemma. Get the guy behind you.
## Chapter 5. Pareto Efficient Equilibria in Coordination Games: Other Examples [00:53:11]So, I claim that actually this is not a rare thing in society at all. There are lots of coordination problems in society. There are lots of things that look like coordination games. And often, in coordination games bad outcomes result and I want to spend most of the rest of today talking about that, because I think it’s important, whether you’re an economist or whatever, so let’s talk about it a bit. What else has the structure of a coordination game, and therefore can have the outcome that people can be uncoordinated or can coordinate in the wrong place, and you end up with a bad equilibrium? What else looks like that? Let’s collect some ideas. I got a hand way at the back. Can you get the guy who is just way, way, way at the back, right up against the–yes, there you go, great thank you. Wait until the mike gets to you and then yell.
So it used to the case in New Haven that there were different–actually there aren’t many anymore–but there used to be different bars around campus (none of which you were allowed to go to, so you don’t know about) but anyway, lots of different bars around campus. And there’s a coordination game where people coordinate on Friday night–or to be more honest, the graduate students typically Thursday night. So it used to be the case that one of those bars downtown was where the drama school people coordinated, and another one was where the economists coordinated, and it was really good equilibrium that they didn’t coordinate at the same place. So one of the things you have to learn when you go to a new town is where is the meeting point for the kind of party I want to go to. Again, you’re going to have a failure of coordination, everyone’s wandering around the town getting mugged. What other things look like coordination problems like that? Again, way back in the corner there, right behind you, there you go.
There are other technological network goods like this. These are called network externalities. An example here would be high definition television. You want to have one technological standard that everyone agrees on for things like high definition televisions because then everyone can produce TVs to that standard and goods that go along with that standard, and of course it–each company who’s producing a TV and has a standard line would like theirs to be chosen as the standard. Again, you could end up at the wrong place. You could end up with a bad equilibrium. How about political bandwagons? In politics, particularly in primaries, there may be advantage on the Democratic side or on the Republican side, in having you all vote for the same candidate in the primary, so they get this big boost and it doesn’t seem like your party’s split and so on. And that could end up–and again, I’m going to remain neutral on this–it just could end up with the wrong candidate winning. There’s a political bandwagon effect, the person who wins New Hampshire and Iowa tends then to win everything, so that’s another example. Any other economic examples? Can we get this guy in here?
However, if people lose confidence in the bank and start drawing their deposits out then the bank hasn’t got enough cash in its vaults to cover those deposits and the bank goes under. Now, I used to say at this point in the class, none of you will have ever seen a bank run because they stopped happening in America more or less in the mid 30s. There were lots and lots of bank runs in America before the 1930s, but since federal deposit insurance came in, there’s far fewer. However, I really can’t say that today because there’s a bank run going on right now. There’s as bank run going on actually in England with a company called Northern Security–no, Northern Rock–it’s called Northern Rock, as we speak, and it really is a bank run. I mean, if you looked at the newspaper yesterday on
So, what I want to do is, I want to pick on somebody in the class now–everyone understands this game, everyone understands there’s two equilibria, everyone understands that one equilibrium is better. Let’s play the game again. Let’s choose the game again, but before I do I’m going to give the mike to Patrick here and Patrick is going to have exactly five seconds to persuade you. Stand up. Patrick’s going to have five seconds to persuade you to tell you whatever he likes starting now.
Now, remember the Prisoner’s Dilemma, in the Prisoner’s Dilemma, if Patrick–Patrick could have got up in the Prisoner’s Dilemma and given the same speech and said look guys, we’re all better off if we choose β in the Prisoner’s Dilemma than if we choose ά; roughly the same speech. What will you have done in the Prisoner’s Dilemma? You would have all chosen ά anyway. So Patrick tried to persuade you, or Patrick communicating to you that you do better by choosing β in the Prisoner’s Dilemma doesn’t work but here–don’t go yet. Here it does work. Why does Patrick–why is Patrick persuasive in this game but he isn’t persuasive in the Prisoner’s Dilemma? Can we get the mike on Katie again? Why is Patrick persuasive in this game and not before?
But a Nash Equilibrium can be a self-enforcing agreement. We can agree that we’re going to play invest in this game, and indeed we will play invest without any side payments, without anybody threatening to break your leg, without any contracts, without any regulation or the law. I’m assuming Patrick isn’t that violent. We’re going to end up doing the right thing here because it’s in our own interest to do so. So coordination problems which we’ve agreed are all over society, whether it comes to bank runs or bubbles in the market, or fashion in the Midwest, they’re all over society. Communication can make a difference and we’ll pick that theme up on Monday. [end of transcript] Back to Top |
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