耶鲁大学博弈论公开课 - 第21集 纳什均衡之坏风气与银行挤兑

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

由 Groq Whisper 转录 → M2.7 B 方案整文标点 + 分段 → M2.7 段号保留翻译 → 逐段对照。

[段 1]

Okay, so last time we came across a new idea, although it wasn’t really new for a lot of you, and that was the idea of Nash equilibrium. and what I want to do today is discuss Nash equilibrium see how we find Nash equilibrium in some rather simple examples and then in the second half of today I want to look at an application where we actually have some fun and play a game which I hope it’s fun alright 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, profile is one strategy for each player, so it’s going to be S1 star, S2 star, all the way up to SN star, if there are N players playing the game. So this profile is a Nash equilibrium and I just going to write NE in this class for Nash equilibrium from now on if for each i so for each player i her choice, so her choice here is si star, that’s i is part of that profile, is a best response, is the best response to the other player’s choices. The other player’s choices. Of course the other player’s choices here are S minus I star. So everyone is playing a best response to everyone else. Alright. Now this is by far the most commonly used solution concepts in game theory.

[译文 1]

好的，上一次我们遇到了一个新概念，虽然对你们很多人来说这并不是什么新东西，那就是纳什均衡。今天我想做的是讨论纳什均衡，看看如何在一些相当简单的例子中找到纳什均衡，然后在下半场我想看一个应用，在那里我们实际上可以找点乐子，玩一个游戏，我希望那会很有趣，好吧。但让我们从给出一个正式定义开始。上周我们用的只是一个相当不正式的版本，所以这里是一个正式的定义：一个策略组合。记住，组合是每个玩家的一种策略，所以如果有N个玩家在玩游戏，它将是S1*、S2*，一直到SN*。所以这个组合是一个纳什均衡，在这个课堂上我就用NE来表示纳什均衡。如果对于每个i（即对于每个玩家i），她的选择，也就是这里的选择si*，是i在该组合中的部分，是一个最佳反应，是对其他玩家选择的最佳反应。其他玩家的选择。当然，其他玩家的选择这里是S-i*。所以每个人都在对其他每个人执行最佳反应。好的。现在这是博弈论中最常用的解概念。

[段 2]

So those of you who are interviewing for McKinsey or something, you’re going to find that they’re going to expect you to know what this is. Alright? 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 McKinsey interview. That’s not a very good reason, right? And I certainly don’t want you to jump to the conclusion that now we got to Nash equilibrium everything we done up to now is somehow in some sense irrelevant That not the case It 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 one, but the play of the game when we played it just one shot first time wasn’t a Nash equilibrium. So we shouldn’t fall into the mistake of thinking people always play Nash equilibrium or people, if they’re rational, play Nash equilibrium. Neither of those statements are true.

[译文 2]

所以你们当中那些正在面试麦肯锡或什么的，你们会发现他们会期望你们知道这是什么。好吧？那么知道这个的一个原因是它在教科书里，它将在很多应用中被使用，它将在你的麦肯锡面试中被使用。这不是一个很好的理由，对吧？我当然不希望你们匆忙得出结论说现在我们有了纳什均衡，我们之前做的一切在某种意义上有种不相关了。事实并非如此。人们并不总是会玩纳什均衡。例如，当我们玩数字游戏时，当我们选择数字的游戏，我们在上周或上次已经讨论过，那个游戏中的均衡是每个人选择1，但当我们实际玩这个游戏时，平均值比那高得多，大约是13。确实，当我们反复玩的时候，它似乎收敛到1，但当我们只玩一次第一次时，游戏的玩法并不是纳什均衡。所以我们不应该犯这样的错误，认为人们总是玩纳什均衡，或者如果人们是理性的，就玩纳什均衡。这两种说法都不是真的。

[段 3]

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 I said again holding everyone else actions fixed no individual has any incentive to move away And let me be a little bit more careful here. No individual has any strict incentive to move away. We’ll see that that actually matters. So no individual can do strictly better by moving away. All right? no individual can do strictly strictly better by deviating comma, holding everyone else fixed. Alright? So what I call that no regret, it means having played the game. Suppose you did in fact play a Nash equilibrium, and then you look back at what you’ve 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.

[译文 3]

然而，除了它被其他人使用这个事实之外，有一些很好的理由来思考纳什均衡。让我们谈谈这些。所以我想在这里提出一些动机。第一个动机我们上次已经讨论过了；实际上，观众中有人提到了它，那就是无悔的概念。那么这个想法是什么？它说，假设我们看一个纳什均衡，如果我们固定其他人的策略，没有个体会愿意偏离、移动离开。我再说一遍，固定其他人的行为，没有个体会愿意离开。让我在这里更谨慎一点。没有个体会严格地有动机离开。我们会看到这实际上很重要。所以没有个人能够通过离开做得严格更好。好吗？没有个人能够通过偏离，严格地严格地做得更好，逗号，固定其他人不动。好吧？我所说的“无悔”是什么意思，它意味着已经玩了这个游戏。假设你确实玩了一个纳什均衡，然后你回顾你所做的，现在你知道其他人做了什么，然后你说，我后悔我的行为吗？答案是，不，我不后悔我的行为，因为给定他们所做的，我做了我能做的最好的。

[段 4]

So that seems like a fairly important central idea for why we should care about Nash equilibrium. Here’s a second idea, and we’ll see others arrive. given what they did. So that seems like a fairly important 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. The 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 goalkeeper is 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, 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? Why is it the case that if everyone believes that everyone else is playing their part of this particular Nash equilibrium, that that’s self-fulfilling, and people actually will play that way. Why is that the case? Anybody? Yeah, can we get this guy in red? Yeah Because your own Nash equilibrium strategy is the best response against those Exactly exactly So it really it almost a repeat of the first thing If I think everyone else is going to play their particular if I think players 2 through n are going to play S2 star through SN star, then by definition, my best response is to play S1 star, so I will in fact play my part of the Nash Equilibrium.

[译文 4]

所以这似乎是一个相当重要的核心思想，为什么我们应该关心纳什均衡。这里有第二个想法，我们会在今天的课程中看到其他想法出现。第二个想法是纳什均衡可以被认为是一种自我实现的信念。所以在过去一周左右，我们已经相当多的谈论了信念。如果我相信守门员会往这边扑，我应该往那边射。等等。但当然我们没有讨论任何特定的信念。这些信念，如果我相信，如果游戏中的每个人都相信其他人会玩一个特定纳什均衡的各自部分，那么每个人实际上都会玩那个纳什均衡的各自部分。现在为什么？为什么？如果每个人都相信其他人在玩这个特定纳什均衡的各自部分，那是自我实现的，而人们实际上会那样玩，这是为什么呢？有人吗？是的，我们能叫一下穿红衣服的那位吗？是的。因为你自己的纳什均衡策略是对那些的最佳反应。没错没错。所以这真的，几乎是第一个东西的重复。如果我认为其他每个人都会玩他们的特定部分…如果我认为玩家2到n会玩S2到SN，那么根据定义，我的最佳反应是玩S1*，所以我实际上会玩我的纳什均衡部分。

[段 5]

Alright, good, good. So as part of the definition, we can see these are self-fulfilling beliefs. Let’s just remind ourselves how that arose in the example we looked at at the end last time. I’m not going to go back and reanalyze it, but I just want to sort of make sure that we followed it. 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 natural equilibrium is. The natural equilibrium is where the lines cross. But let’s just see how it maps up to those two motivations we just said. So how about self-fulfilling beliefs? Well if player Sorry I put a 1 and a 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 is choosing this strategy, then player 1 should choose this strategy. If player 1 thinks player 2 is choosing this strategy, then player 1 should choose this strategy, and so on. That’s what it means to be a best response.

[译文 5]

好吧，好的，好的。作为定义的一部分，我们可以看到这些是自我实现的信念。让我们提醒自己这在上次结束时我们看的例子中是如何出现的。我不打算回去重新分析，但我只是想确保我们跟上了。所以上次在这个图中，在合作游戏中，人们正在选择努力水平。这条线是玩家1作为玩家2选择的函数的最佳反应。这条线是玩家2作为玩家1选择的函数的最佳反应。这是我们上次看到的图。让我们看看这些…这里的自然均衡是什么，这不是什么秘密。自然均衡是线条交叉的地方。但让我们看看它如何对应到我们刚才说的那两个动机。那么自我实现的信念呢？好吧，如果玩家…抱歉，我标了1和2。如果玩家1相信玩家2会选择这个策略，那么玩家1应该选择这个策略。如果玩家1认为玩家2选择这个策略，那么玩家1应该选择这个策略。如果玩家1认为玩家2选择这个策略，那么玩家1应该选择这个策略，以此类推。这就是成为最佳反应的含义。

[段 6]

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 see 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 I have no regrets. So here’s player one, she wakes up the next morning, it was he wasn’t it, he wakes up the next morning and he says, I chose S1 star, do I regret this? Well now he knows what player two chose, player two chose S2 star, and he says, no, that’s the best I could have done. Given that player two did in fact choose S2 star, I have no regrets about choosing S1 star that in fact was my best response And notice that wouldn be true at some other outcome So for example if player 1 had chosen S1 star but player 2 had chosen some other strategy, let’s say S2 prime, then player 1 would have regrets. Player 1 would wake up the next morning and say, oh, I thought player 1 was going to play S2 star. In fact, she chose S2 prime.

[译文 6]

但如果玩家1认为玩家2正在玩她的确切纳什策略，那么玩家1的最佳反应是通过玩他的纳什策略来回应。反过来，如果玩家2认为玩家1在玩他的纳什策略，那么玩家2的最佳反应确实是玩她的纳什策略。所以你可以看到这是一个自我实现的信念。如果两个人都认为那将会发生，那确实就是将要发生的。无悔的想法怎么样？这里是玩家一，她第二天早上醒来…是他，不是吗？他第二天早上醒来，他说：“我选择了S1*，我后悔吗？”好吧，现在他知道玩家二选择了什么，玩家二选择了S2*，他说：“不，那是我能做的最好的。”鉴于玩家二确实选择了S2*，我对我选择S1没有后悔，那实际上是我的最佳反应。注意，在其他结果下那不会是真的。例如，如果玩家1选择了S1但玩家2选择了其他策略，比方说S2’，那么玩家1就会后悔。玩家1第二天早上醒来会说：“哦，我以为玩家2会玩S2*。实际上，她选择了S2’。”

[段 7]

I regret having chosen S1 star. I would have rather chosen S1 prime. So only at the Nash equilibrium are there no regrets. Everyone okay with that? This is just revisiting really what we did last time and underlining these points. All right. 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’m going to turn off that projector that’s in the way there. If I can. Is that going to upset the lights a lot? All right. 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. Okay? We’ll start slowly, and then we’ll get a little faster. Okay, so let’s start with this game. Very simple game with two players… Each player has three strategies. I’m not going to motivate this game, it’s just some random game. Player one can choose up, middle or down. And player two can choose left, centre 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 it isn’t a particularly exciting game, so let’s leave our playing for later.

[译文 7]

我后悔选择了S1星，我本应该选择S1素。所以只有在纳什均衡中才没有遗憾。大家对此有问题吗？这只是重温我们上次做的事情并强调这些要点。好吧。所以我今天想花很多时间来习惯纳什均衡的概念，并尝试找到纳什均衡。我要把那个挡路的投影仪关掉。如果可以的话。这会不会让灯光很不稳定？好吧。我想做的是，我想先看一些玩家数量很少、策略数量很少的简单游戏。我想让我们习惯如何在这些简单游戏中找到纳什均衡。好吗？我们会慢慢开始，然后会快一点。好吧，让我们从这个游戏开始。一个非常简单的双人游戏……每个玩家有三种策略。我不会为这个游戏做铺垫，这只是一个随机的游戏。玩家一可以选择上、中或下。玩家二可以选择左、中和右。收益如下。0、4、4、0、5、3、4、0、0、4、5、3，再次是3、5、3、5，以及6、6。如果我们有时间的话，我们可以讨论，甚至可以实际玩这个游戏，但这不是一个特别令人兴奋的游戏，所以让我们把玩的部分留到以后。

[段 8]

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 them. And 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 in which there was two players with a continuum of strategies and what we did was we figured out player 1 best responses and player 2 best responses player 1 best response to what player 2 doing and player 2 best response to what player 1 doing and then we looked where they coincided, and that was the Nash equilibrium. And 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. Alright? So in particular, what would be player one’s best response if player two chooses left? What would be player one’s best response if player two chooses left? Let’s get the mics 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 closer to the woman in the middle middle, M ok so player 1’s best response in this case is middle alright because 4 is bigger than 0 and is bigger than 3 alright so to mark that fact what we can do is let’s put a circle like in green let put a circle round that 4 Okay Not hard right So let do it again What is player one best response if player two chooses centre?

[译文 8]

相反，让我们尝试找出这个游戏中的纳什均衡以及我们如何去找到它们。我们找到它们的方法将模仿我们上次做的事情。上次我们有一个更复杂的游戏，其中有连续统策略的两个玩家，我们做的是我们找出玩家1的最佳反应和玩家2的最佳反应，玩家1对玩家2所做的最佳反应，玩家2对玩家1所做的最佳反应，然后我们看它们在哪里重合，那就是纳什均衡。在这个简单的游戏中我们要做完全相同的事情。所以我们要先开始弄清楚玩家1的最佳反应是什么样的。好吧？特别是，如果玩家二选择左，玩家一的最佳反应是什么？如果玩家二选择左，玩家一的最佳反应是什么？让我们把麦克风调高，这样我可以挑战大家。有人吗？这不是一个很难的问题。你想试试坐在中间的那位女士吗？坐在中间的那位女士更近，M好的，所以玩家一在这个情况下的最佳反应是中间，因为4大于0，大于3，好吧所以为了标记这个事实，我们可以做的是让我们用绿色画一个圆圈，把那个4圈起来。好吧，不难吧。让我们再来一次。如果玩家二选择中心，玩家一的最佳反应是什么？

[段 9]

What is player one’s best response if player two chooses centre? Let’s get somebody on the other side. You should feel free to cold call somebody here. How about cold calling the guy with the Yale football shirt on? Here we go. Up. All right. So up is the correct answer. All right. That’s it. One triumph for Yale football. Okay. So four is bigger than three, bigger than zero. All right. So good. Thank you. All right. And, Ali, why don’t you do the same? Why don’t you cold call somebody who’s going to tell me what’s the best response for player one to right? Down. Down. How about that? Down. Down. Okay. Okay. Okay, so best response is down because six is bigger than five, which is bigger than five. I mean, six is bigger than five. Okay. All right. All right. So what we’ve done here is we’ve found player one’s best response to left, best response to center and best response to right And in passing notice that each of player one strategies is a best response to something so nothing would be knocked out by our domination arguments here and nothing would be knocked out by our never a best response arguments here for player one Okay? Okay? Let’s do the same for player two. So why don’t I keep the mics doing some cold calling.

[译文 9]

如果玩家二选择中心，玩家一的最佳反应是什么？让我们找另一边的人。你可以随意冷不丁叫一个人。这边穿耶鲁足球队服的家伙怎么样？开始吧。向上。好吧。所以向上是正确的答案。好吧。就这样。耶鲁足球队的一次胜利。好吧。谢谢你。好的，阿里，你来做同样的事情吧。你为什么不冷不丁叫一个人来告诉我当玩家二选择右时，玩家一的最佳反应是什么？向下。向下。就这样。好吧，好吧，好吧，所以最佳反应是向下，因为6大于5，5大于5。我是说，6大于5。好吧。好吧。所以我们在这里做的是找到了玩家一对左的最佳反应，对中心的最佳反应和对右的最佳反应。顺便注意到，玩家一的每种策略都是对某些东西的最佳反应，所以在这里，我们的支配论证不会淘汰任何东西，我们的永远不会成为最佳反应的论证也不会淘汰玩家一的任何东西。好吧？好吧。让我们为玩家二做同样的事情。所以我不妨继续冷不丁叫一些人。

[段 10]

So do you want to cold call somebody at the back to tell me what is player two’s best response against up? What’s player two’s best response against up? Who’s struggling on that? Yeah, left. All right, so the gentleman in blue says left because four is bigger than three is bigger than zero. Let’s switch colors and switch polygons and put squares around these, okay? All right, I don’t insist on the circles and the squares. If you have a thing for hexagons, you can do that too. Whatever you want. All right, what’s player two’s, let’s write it in here, the answer. The answer was that the best response was left. All right, and player two’s best response to middle. So, Merti, do you want to grab somebody over there? Center. Shout it out. Center. All right, because four is bigger than three. Somebody over there? Center. Shout it out. Center. All right, because 4 is bigger than 3 to bigger than 0, so that’s center. And in my color coding, that gives me a square here. And finally, player 2’s best response to down. And your turn, Ollie. Let’s grab somebody. is less. I’m sorry, right. Okay, right. Okay, good, good, because 6 is bigger than 5 again. So here we go. Alright, so what we’ve done now is found player 1’s best response function. That was just the analog of finding the best response line we did here.

[译文 10]

你想冷不丁叫后面的人来告诉我当玩家一选择上时，玩家二的最佳反应是什么？当玩家一选择上时，玩家二的最佳反应是什么？谁对这个感到困难？是的，左边。好吧，穿蓝色衣服的那位先生说左边，因为4大于3大于0。让我们换颜色和换多边形，用正方形把这些圈起来，好吧？我不坚持用圆圈和正方形。如果你喜欢六边形，你也可以那样做。随你喜欢。好吧，玩家二的，让我们写在这里，答案。答案是最佳反应是左边。好吧，以及玩家二对中间的最佳反应。Merti，你想找那边的人吗？中心。喊出来。中心。好吧，因为4大于3。那边的人？中心。喊出来。中心。好吧，因为4大于3大于0，所以那是中心。在我颜色编码中，这给了我一个正方形在这里。最后，玩家二对下的最佳反应。轮到你了，Ollie。让我们找个人。更少。对不起，右边。好的，右边。好的，好的，因为6再次大于5。所以我们开始了。好吧，所以我们现在做的是找到了玩家1的最佳反应函数。那只是找到我们在这里做的最佳反应线的类比。

[段 11]

Here we drew it as a straight line in white, but we could have drawn it as a sequence of little circles in green. It would have looked like this, right? Same idea. We’re not going to do the whole thing, right? It’ll be a whole bunch of circles looking like this. And then we found player 2’s best response for each choice of player 1, and we used pink rectangles, and that’s the same idea as we did over here Here we did it in a continuous strategy using cult curves but it the same idea So imagine I drawing lots of pink rectangles and again I not going to do it but you can do it in your notes All right same basic idea And just as the Nash equilibrium must be where these best response lines coincided here, because that’s the point at which each player is playing a best response to each other, so the Nash equilibrium over here is, drumroll, do you want to cult call somebody? Do you want to cult just grab somebody in the row behind you or something, whatever? Yeah? Anybody? Anybody? Alright. Yeah, I think you were in an Italia soccer shirt. You’re going to get picked on. Okay, so what’s the Nash equilibrium here? The bottom right square. Alright, so the down right square. So the Nash equilibrium here is no prizes, no World Cup for that one, is down right.

[译文 11]

这里我们把它画成一条白色的直线，但我们也可以把它画成一系列绿色的小圆圈。它看起来会像这样，对吧？同样的想法。我们不打算做完整的事情，对吧？这将是一堆看起来像这样的圆圈。然后我们找到了玩家2对玩家1每个选择的最佳反应，我们用了粉红色的矩形，同样的想法就像我们在这里做的。这里我们在连续策略中用曲线做的，但这是同样的想法。想象我在画很多粉红色的矩形，我也不会做，但你们可以在笔记中做。同样的基本想法，正如纳什均衡必须是在这些最佳反应线重合的地方，因为那正是每个玩家都在对彼此做出最佳反应的点，所以这里的纳什均衡是，鼓声，你想叫一个人吗？你想叫坐在你后面那一排的某个人，或者别的什么，随便谁？好吗？有人吗？好吧。是的，我想你穿着一件意大利足球队服。你要被点名了。好吧，所以这里的纳什均衡是什么？右下角那个格子。好吧，所以右下角那个格子。所以这里的纳什均衡是没有奖品的世界杯，是右下角。

[段 12]

Alright? Alright. So why is that the Nash equilibrium? Because at that point, player 1 is playing a best response to player 2, and player 2 is playing a best response to player 1. Now I want to try and convince you, particularly those of you who are worried by the homework assignment, that that was not rocket science. Right? It’s not hard to find that equilibrium in games. All right well it didn take us very long and we went pretty slow actually All right so let look at another example Oh before I do notice that before I leave this game let make one other remark Notice in this game that each strategy of player one is a best response to something, and each strategy of player two is a best response to something. So had we used the methods of earlier on in the class, that’s to say, deleting dominating strategies, or deleting strategies that are never a best response, we’d have got nowhere in this game. All right? so Nash equilibrium has got us 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 as 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 downright a very particular prediction but notice a perfectly rational player could here, could choose middle.

[译文 12]

好吗？好吧。为什么那是纳什均衡？因为在那个点上，玩家1正在对玩家2做出最佳反应，而玩家2正在对玩家1做出最佳反应。现在我想说服你们，特别是那些对作业感到担忧的人，那不是什么高科技。对吧？在游戏中找到那个均衡并不难。好吧，我们没有花很长时间，而且我们实际上走得很慢。好吧，让我们看另一个例子，哦，在我做之前，注意，在我离开这个游戏之前，让我做一个其他的评论。注意在这个游戏中，玩家一的每种策略都是对某些东西的最佳反应，玩家二的每种策略也是对某些东西的最佳反应。所以如果使用课早些时候的方法，也就是说，删除占优策略，或者删除永远不会成为最佳反应的策略，我们在这个游戏中不会有任何进展。好吧？所以纳什均衡让我们在缩小预测范围方面更进一步，但我们也从中学到了一些东西，我们上次在最后几周争论过，理性，甚至相互知道的理性，甚至共同知道的理性，实际上不能比删除被占优策略，或者如果你愿意，删除永远不会成为最佳反应的策略走得更远，所以在这里我们得出结论，这个游戏的纳什均衡是非常特定的预测，右下角，但注意一个完全理性的玩家在这里可以选择中间。

[段 13]

The reason they could choose middle, player one could choose middle, could be that if they say rationally they should choose middle because they think player two is choosing left. And you say, well why would you think player two is going to choose left? And player one could say I think player two is going to choose left because player two thinks I going to play up And then you say but how could player two possibly think that you going to play up And then player one would say I think player two thinks I going to play up because player two thinks that I think that he’s going to play center. And then you could say, how could player two, et cetera, et cetera, et cetera. And you could see, you could work yourself 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 have a nice point where it’s a simple argument in the case of down right player one thinks it’s okay to play down because he thinks two is going to play right and player two thinks it’s okay to play right because he thinks player one is going to play down so just to underline what I’m saying rather messily there rationality and those kind of arguments should not lead us to the conclusion that people necessarily play Nash equilibrium we need to look at more we need to look at more than that nevertheless we are going to focus on Nash equilibrium in the course.

[译文 13]

他们选择中间的原因可能是，如果他们理性地说，他们应该选择中间，因为他们认为player two会选left。然后你说，那你为什么会认为player two会选left呢？player one可能会说，我认为player two会选left，因为player two认为我会play up。然后你说，但player two怎么可能认为我会play up呢？然后player one会说，我认为player two认为我会play up，因为player two认为我认为他会play center。然后你可能会说，player two怎么可能……等等，等等，等等。你可以看到，你可以在这里绕出一个小循环。没有人会做任何非理性的事情。从信念的角度来看，一切都完全合理。只是我们没有一个很好的固定点。在down right的情况下，我们有一个很好的点，在那里有一个简单的论点——player one认为play down是可以的，因为他认为player two会play right，而player two认为play right是可以的，因为他认为player one会play down。所以只是想强调我说的那些相当混乱的内容——理性和这类论点不应该引导我们得出人们必然玩Nash equilibrium的结论。我们需要看得更远，我们需要看得比这更多。尽管如此，我们将在课程中关注Nash equilibrium。

[段 14]

All right. Let’s have a look at another example. And again, we’ll keep it simple for now and we’ll keep to a two-player, three-strategy game. Our and again we’ll keep it simple for now we’ll keep to a two player three strategy game up, middle, down left, centre, 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 were really just whatever came into my head when I was writing it down. And 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 in a four, let me just go straight to my green circles and red squares, and let me get my mics up again, so we can cold call people a bit. All right, can we get the… Where my Where the mic Oh thank you thank you All right so Ali do you want to just grab somebody and ask them what the best response against left Grab anybody. What’s the best response against left? Middle. Middle, okay, good, good. So middle is the best response against left because 11 is bigger than 0.

[译文 14]

好的，让我们看另一个例子。再一次，我们暂时保持简单，我们将坚持一个两人、三策略的游戏：上、中、下、左、中、右，而这次收益如下：0-2、2-3、4-3、11-1、3-2、0-0、0、3、1、0和8、0。所以这是一个稍微复杂的游戏。这些数字真的只是我在写下来时脑子里想到的。再一次，我们想找出这个游戏中的纳什均衡是什么。我们的方法完全一样。我们将，对于每个玩家，找出他们对其他玩家每个可能选择的最佳反应。所以与其写出来，让我直接用我的绿色圆圈和红色方块，让我再次准备好麦克风，这样我们可以点名提问一些人。好的，我们能…麦克风在哪？哦谢谢你谢谢你。好的，Ali，你想找个人问问当对手选择左侧时什么是最佳反应吗？随便找一个人问。当对手选择左侧时什么是最佳反应？中部。中部，好的，好的。所以中部是当对手选择左侧时的最佳反应，因为11大于0。

[段 15]

Alright, Merton, do you want to grab somebody, what’s the best response against centre? Middle. Middle again because 3 is bigger than 2 is bigger than 1. and grab somebody at the back and tell them what the best response is against right. Anybody? Anybody? Just dive in. Yep. Down. Okay, down. Good. All right, and let’s do the same for the column player. So watch the column player’s alley. Find somebody. Take the guy who’s two rows behind you who’s about to fall asleep and ask him, what’s the best response to up? The best response would be shh. For which player? For player two. What’s player two’s best response for up? Sorry, I had to jump in. Pick on someone else. That’s all right. Pick on the guy right behind you. What the best response for up C and R are tied So C or R All right so this is a slightly more tricky one right The best response to up is either C or R This is why we got you to sign those legal forms, right? Best response to up is either C or R. The best response to middle… Yeah, madam? Center. It’s center, thank you. And the best response to down… left. All right, so the best ones to down is left. And here again, it didn’t take us very long, we’re getting quicker at this, the Nash equilibrium in this case is…

[译文 15]

好的，Merton，你想找个人吗，对付centre的最佳应对是什么？

Middle（中）。

又是Middle，因为3大于2大于1。

然后找后排的一个人，告诉他们对付right的最佳应对是什么。

有人吗？有人吗？直接说吧。

是的。Down（下）。

好的，Down。好。

好的，我们对column玩家也做同样的事。

看column玩家的alley。找个人。

找坐在你后面两排的那个快要睡着的人问他，对付up的最佳应对是什么？

最佳应对是shh（嘘）。

对付哪个玩家？对付player two。

Player two对付up的最佳应对是什么？

抱歉，我插一句。换个人问吧。

没关系。换你后面那个人问。

对付up的最佳应对是什么？

C和R并列。

所以C或R。

好的，这是一个稍微难一点的题目，对付up的最佳应对是C或R。

这就是为什么我们让你们签那些法律表格，对吧？

对付up的最佳应对是C或R。

对付middle的最佳应对…

是的，女士？Center。

是center，谢谢。

对付down的最佳应对…

left（左）。

好的，对付down的最佳应对是left。

这里同样，我们没有花很长时间，我们越来越快了，这个案例中的Nash equilibrium是…

[段 16]

Let’s go back to the guy who is asleep and give him an easier question this time. So the Nash equilibrium in this case is? Nash equilibrium would be the 3, 2 combination. Exactly, okay, so the middle center. All right, and And notice this is a Nash equilibrium. Why is it a Nash equilibrium? Because each player is playing a best response to each other. Right? If I’m player one, and I think that player two is playing center, I should play middle. If I’m player two and I think player one is playing middle, I should play center. If, in fact, we play this way, neither person has any regrets. Notice they didn do particularly well in this game In particular player one would have liked to get this 11 and this 8 Right But they don regret their action because given that player two played center the best they could have got was 3 which they got by playing middle right Notice in passing in this game, notice in passing, that best responses needn’t be unique, right? Sometimes there can be a tie in your best response, okay? That can happen. All right, 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.

[译文 16]

让我们回到那个睡着的人那里，这次给他一个更简单的问题。那么这种情况下Nash均衡是什么？Nash均衡是3, 2的组合。完全正确，好，就是中间中间。好的，注意这是一个Nash均衡。为什么它是Nash均衡？因为每个参与者都在对彼此做出最佳反应。对吧？如果我是player one，我认为player two在选择center，我应该选择middle。如果我是player two，我认为player one在选择middle，我应该选择center。事实上，如果我们这样玩，没有人会后悔。注意他们在这场博弈中并没有做得特别好，特别是player one本希望能得到这个11和这个8。但他们并不后悔自己的行动，因为考虑到player two选择了center，他们最多能得到的就是3，而他们确实通过选择middle得到了3，对吧？顺便提一下，注意在这场博弈中，最佳反应不一定是唯一的，对吧？有时候你的最佳反应可能会有并列的情况，好吧？这是可能发生的。好的，我们看到了什么？我们看到了如何找到Nash均衡，显然它与最佳反应的概念密切相关，而这正是我们过去一周左右一直在发展的思想。

[段 17]

But let’s go back earlier in the course and ask, how does it relate to the idea of dominance? This is really 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. So what we’re going to do is we’re going to relate 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 error code: 502 is, well, either up or down will do, right? Because either way he gets, or she gets zero. So these are both best responses. Is that correct? They’re both best responses, they both do equally well. All right? And conversely, player two, player two’s best response, if player one chooses up, is sure enough to choose left, and that’s kind of the answer we’d like to have. But unfortunately, when player one plays down, player 2’s best response is either left or right it makes no difference, they get 0 either way alright ok, so what are the Nash equilibria in this game what are the Nash equilibria in this game so notice the first observation is, 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 a sensible prediction in this game.

[译文 17]

但是让我们回到课程前面，问问它与支配的概念有什么关系？这确实是本课程的第三个概念。我们有关于支配的概念，我们有关于最佳反应的概念，现在我们到了纳什均衡。我认为，它与最佳反应的关系是显而易见的，就是当最佳反应一致的时候。那么它与支配的关系如何呢？嗯，为了做到这一点，让我们回顾一下。所以我们要做的就是将纳什均衡与我们关于支配的概念联系起来。为了做到这一点，一个明显的起点是回到一个游戏：error code: 502，嗯，上或下都可以，对吧？因为无论哪种方式，他或她都得到0。所以这两个都是最佳反应。对吧？它们都是最佳反应，它们都表现同样好。对吧？反过来，玩家二，玩家二的最佳反应，如果玩家一选择上，确实应该选择左，这正是我们想要的答案。但不幸的是，当玩家一下下时，玩家二的最佳反应是左或右都可以，没有区别，无论哪种方式他们都得到0。好吧，那么这个游戏中的纳什均衡是什么？这个游戏中的纳什均衡是什么？所以注意第一个观察是，这个游戏中不止一个纳什均衡，我们之前没见过这个情况，有一个纳什均衡，房间里的每个人，我想，我希望，都认为这是这个游戏中一个相当合理的预测。

[段 18]

In this game, I think all of you, I hope, all of you if you’re player one would choose up and all of you if you’re player two would choose left. Is that right? Is that correct? It hard to imagine coming up with an argument that wouldn lead you to choose up and left in this game However unfortunately unfortunately this isn unfortunate up left is a Nash equilibrium, but so is down right. If player two is choosing right, your best response, weakly, is to choose down. if player one is choosing down player two’s best response weekly is to choose right and here this is arriving because of the definition of Nash it’s a very definite definition when we looked at the when we looked at the definition we said something is a Nash equilibrium as each person is playing a best response to each other and the 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 one doesn’t do strictly better, it’s just a tie if she moves away. And player two doesn’t do strictly better if he moves away, it’s a tie, he gets zero either way. So here we have something which is going to worry us going on in the course Sometimes we getting not only are we getting many Nash equilibria that something which shouldn worry us it a fact of life but in this case one of the Nash equilibria seems silly I mean, 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.

[译文 18]

在这一游戏中，我希望，如果你们是玩家一，你们会选择上；如果你们是玩家二，你们会选择左。对吗？正确吗？很难想象能提出一个论点，使得你不会在这一游戏中选择上和左。然而不幸的是，不幸的是，上左是一个纳什均衡，但下右也是一个纳什均衡。如果玩家二选择右，你的最佳反应（弱意义上的）是选择下。如果玩家一选择下，玩家二的最佳反应（弱意义上）是选择右。这里之所以出现这种情况，是因为纳什均衡的定义。这是一个非常明确的定义，当我们审视这个定义时，我们说，当每个人都在对彼此做出最佳反应时，这就是纳什均衡。换句话说就是，没有玩家有严格动机偏离，没有玩家能通过偏离严格地做得更好。所以在的下右这个位置，玩家一如果偏离，并不会严格地做得更好，只是平局。玩家二如果偏离，也不会严格地做得更好，只是平局，无论怎样他都得到零。所以这里有些事情会在整个课程中困扰我们。有时候我们得到的不仅是许多纳什均衡，这种事情不应该困扰我们，这是生活中的事实，但在这个案例中，其中一个纳什均衡似乎很愚蠢。我的意思是，如果你去试着向室友解释，说我预测这一游戏会出现这两个结果，他们会嘲笑你。

[段 19]

It’s obvious, in some sense, that this has to be the sensible prediction. Alright, so just a sort of worrying note before we move on. Okay, 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. Okay, 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 Equilibria 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, I want to discuss how to find Nash Equilibria in a game which, unlike these games, doesn’t just have two players, it has many players but fortunately not many strategies per player Alright So let me use this board alright so this is going to be called the investment game and we’re going to play this game although not for real alright so the players in this game as I just suggested the players are going to be you. Alright, so everyone who was getting sleepy just looking at this kind of analysis should wake up now, you have to play.

[译文 19]

在某种意义上，这显然是一个合理的预测。好的，在我们继续之前，先说一个令人担忧的问题。好了，到目前为止这些内容都相当正式，不太有趣，所以让我们试着继续讲一些更有趣的东西。好，我现在想做的是看一个不同的游戏。我们仍然要在这种游戏中找出纳什均衡，但我们要做更多的事情。我们要来讨论一下这个游戏。这个游戏有一个特点，可以将它与我们之前所做的区分开来，即我们接下来要看的这个游戏涉及许多玩家，尽管每个玩家只有很少的策略。所以我想做的是，我想说服你们如何找到，我想讨论如何在一种不像这些游戏那样只有两个玩家的游戏中找到纳什均衡，它有许多玩家，但幸好每个玩家的策略不多。好，让我用这块白板，这个游戏将被称为投资游戏，我们要玩这个游戏，虽然不是真实的。好，在这个游戏中，正如我刚才暗示的，玩家就是你们。好，每一个刚才看这种分析看到昏昏欲睡的人都应该现在醒来了，你们要参与进来。

[段 20]

Alright, and 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, zero, or invest $10. Alright? So I’m sometimes going to refer to investing nothing as not investing. Is that okay? Right? It seems like a natural thing. You’re either going to invest $10 or nothing, i.e. you’re not going to invest. Alright? So that’s the players and those are the strategies. So as usual, we’ll see you next time. an natural thing, so you’re either going to invest $10 or nothing a, you’re not going to invest. All right, so that’s the players, and those are the strategies, so as usual we’re missing something, what we’re missing are the payoffs. All right, so here are the payoffs. So the payoff as follows. If you don’t invest, if you do not invest, I, you invest nothing, then your payoff is zero. Right? So nothing ventured, nothing gained. Right, natural thing. Right? But if you do invest, so if you invest $10, remember each of you is going to be investing $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 in $10, so you’ll make a gross profit of $15 minus the 10 you originally invested for a net of five.

[译文 20]

好的，这个游戏中的策略非常简单，策略集合，或者说策略选择。你们每个人可以在一个课题项目中不投资，也就是零，或者投资$10之间做出选择。好吗？所以我有时候会把不投资称为不投入。可以吗？对？这看起来是很自然的事情。你要么投资$10，要么什么都不投，也就是你不打算投资。对吧？所以这就是玩家，这就是策略。和往常一样，我们还缺少一些东西，我们缺少的是收益。好，以下是收益。收益是这样的。如果你不投资，如果你不投资，你投资零，那么你的收益是零。对吧？俗话说，不入虎穴，焉得虎子。对吧，很自然的事情。对吧？但如果你投资了，那么如果你投资$10，记住你们每个人都要投资$10，那么你的个人收益如下。好消息来了。你将获得$5的利润。这个运作方式是你们将投资$10，所以你们将获得$15的毛利润减去最初投资的$10，净得5元。

[段 21]

Have I understand, right? So a net profit to $5, net profit. That’s the good news. But that requires more than 90% of the class to invest. Greater than equal to 90% of the class to invest. more than 90% of the class invest you’re going to make essentially 50% profit. And unfortunately, the bad news is you’re going to lose your $10, get nothing back. Right? So this is a net loss. If fewer than 90% of the class invest. All right, and we need a key rule here, you’re not allowed to talk to each other. Right? No communication in the class. No hand signals, no secret winks. Right, nothing else. All right. Okay. So everyone understand the game. Including up on the balcony. Everyone understand the game. All right. 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 in you and I don’t have that kind of cash line around. All right. So pretend we’re playing this for real, okay? 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. So you can write Y if you’re going to invest and N if you’re not going to invest. Don’t discuss it with each other.

[译文 21]

我理解对了吗？净赚$5，净利润。好消息。但那需要班上超过90%的人投资。需要班上大于或等于90%的人投资。超过90%的班人投资，你将获得大约50%的利润。不幸的是，坏消息是你将失去你的$10，什么都拿不回来。对吧？这是一笔净亏损。如果班上少于90%的人投资。好，这里需要一条关键规则，你们不允许互相交谈。对吧？课堂上不能交流。没有手势，没有秘密眼色。对，什么都不行。好。每个人理解这个游戏了吧。包括阳台上的人。每个人都理解这个游戏。好，所以我想让你们做的，我应该说，首先我们不能真的玩这个游戏，因为你们大约有250人，我没有那么多现金。对吧。所以假装我们在真的玩这个，好吗？假装我们在真的玩这个。所以不要交流，我要你们每个人在笔记本角上写下你是否要投资。所以如果你要投资就写Y，不投资就写N。不要互相讨论。

[段 22]

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. Don’t discuss it, guys. Don’t discuss it. And now show your neighbor what you did, just so you can your neighbor can make you make you honest. All right. Now, okay, let’s have a show of hands. All right. So what I want to do is I want to have a show of hands everybody who invested. Everyone invested. Don’t look around, just raise your hands. Everyone who invested. Everyone who invested. And everyone who didn’t invest. Oh, that’s more than 10%. All right. Let’s have. Let’s do it again. So everyone who invested, raise their hands, raise their hands. And everyone who didn’t invest, raise their hands. So I don’t know what that is. Maybe it’s about half. About half. So now I’m thinking we should have played this game for real. I wanted to just 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? All right. So this guy. Okay, so what did you do? I invest it. Why did you invest? Because I think I can lose $10. All right, all right. All right. So he’s rich. That’s okay. You can pay for lunch.

[译文 22]

就在笔记本角上写下，Y表示你要投资，N表示你不投资。不要。不要讨论，伙计们。不要讨论。现在让你旁边的人看看你写的是什么，这样让你旁边的人可以让你诚实。好，现在，好，让我们举手表决。好，我想做的是让所有投资了的人举手。每个人都投资了。不要四处看，举手。所有投资了的人。所有投资了的人。所有没投资的人。哦，那超过了10%。好。让我们再来一次。所有投资了的人，举手，举手。所有没投资的人，举手。我不知道那是多少。也许大约一半。大约一半。所以现在我想我们应该真的玩这个游戏。我只是想让大家讨论一下。我要讨论一会儿。这个游戏有很多值得讨论的地方。让我借用一下。我能借用一下吗？好，这个人。好，你做了什么？我投资了。你为什么投资？因为我觉得我可以损失$10。好，好，好。所以他有钱。没关系。你可以请午餐。

[段 23]

That’s all right. All right. Who didn’t invest? If there’s non-invested. Yeah. Here’s one. Okay. So why didn’t you invest? Shout it out, so everyone can hear. I didn’t invest because to make a profit, there needs to be at least a two-to-one chance that everyone else That 90% invests. All right. You mean you make an expected profit? Yeah, you only get half back, but you’d lose the whole thing. I see. Okay, okay, so you’re doing some kind of expected calculation. Other reasons, other reasons out there? What did you do? I invested. You invested. I’m finding the suckers on the room. Okay, so you invested. And why? Be easier stand to gain something. I don’t see why anybody would just not invest because they don’t, they would never gain anything. All right, so your name is… Clayton. So Clayton’s saying, only by investing, can I gain something here? Not investing seems… would just not invest because they would never gain anything. All right, so your name is Clayton. So Clayton’s saying, only by investing, can I gain something here? Not investing seems kind of, you know, doesn’t seem brave in some sense. Anyone else? Yeah. It’s basically the same game as the 1-1-0 game in terms. They’re both Nassi equilibrium. But the payoffs aren’t like the same scale. And yeah, you’d have to really risk averse not to invest.

[译文 23]

没关系。好，谁没投资？如果有没投资的人。是的。这里有一个。好，你为什么不投资？大声说出来，让每个人都能听到。我没投资是因为要获利，需要至少有两比一的机会让其他所有人都投资，让90%的人投资。好，你是说你要计算预期利润？是的，你只能拿回一半，但你将失去全部。我明白了。好，好，所以你在做某种预期计算。其他原因，其他原因呢？你做了什么？我投资了。你投资了。我在找房间里的冤大头。好，所以你投资了。为什么？因为投资才更容易有所收获。我不明白为什么有人会不投资，因为他们不投资就永远不会得到任何东西。好，你的名字是……Clayton。所以Clayton说的是，只有通过投资，我才能在这里获得一些东西？不投资看起来……他们永远不会得到任何东西。好，你的名字是Clayton。所以Clayton说的是，只有通过投资，我才能在这里获得一些东西？不投资看起来有点……在某种意义上看起来不够勇敢。还有别人吗？是的。这基本上和1-1-0游戏是同一个游戏。就纳什均衡而言，两者都是纳什均衡。但收益规模不一样。而且，如果你真的厌恶风险，你才不会不投资。

[段 24]

So I thought people would be… So you invested? I invested, yeah. All right, so let me give this to… All right, for I struck the sound system here. Okay, so we’ve got different answers out. Do people, could people hear each other’s answers a bit? Yeah? Yeah? Yeah? So we have lots of different views out here. We have half the people investing and half the people not investing, roughly, and I think you can make arguments either way, all right? So we’ll come back to whether it’s exactly the same as the game we just saw. So the argument that, I’m sorry, your name, that Patrick made is, it looks a lot like the game we saw before. before, we’ll see it is related. Clearly, it’s related in one sense, which we’ll discuss now. So, maybe I need this thing again. Sorry. So what are the Nash equilibrium in this game? What are the Nash equilibrium in this game? All right, we can call someone’s phone message, but in the meantime, what are the Nash equilibrium in this game? Yeah, let me get the woman up here. No one invests and everyone’s happy that they didn’t lose anything, or everyone’s everyone invests and everyone’s happy. Good, good, so I’ve forgotten your name. So Kate’s saying that there are two Nash Equilibria, and I was apologies to Jude, I’m going to put this on the board, all right, there are two Nash Equilibria here, all right?

[译文 24]

所以我以为人们会……所以你投资了？我投资了，是的。好，让我把这个给……好，我搞定了音响系统。好，我们得到了不同的答案。人们能听到彼此的答案吗？能听到吗？能听到吗？所以我们这里有各种不同的观点。我们大约一半的人在投资，一半的人没投资，我认为你们可以两边都找到论点，对吧？所以我们回过头来看它是否和我们刚才看到的游戏完全一样。所以你的名字是……Patrick提出的论点是，它看起来很像我们之前看到的游戏。之前的游戏，我们会看到它们是相关的。显然，在某种意义上它是相关的，我们现在就来讨论。好，也许我需要这个东西再说一遍。抱歉。这个游戏中的纳什均衡是什么？这个游戏中的纳什均衡是什么？好，我们可以叫一个人的电话留言，但与此同时，这个游戏中的纳什均衡是什么？好，让我把那位女士叫到这里来。没有人投资，每个人都很高兴他们没有损失任何东西，或者每个人都投资了，每个人都很高兴。好，好，我忘了你的名字。所以Kate说的是有两个纳什均衡，我对Jude道歉，我要把这个写在白板上，好，这里有两个纳什均衡，好吧？

[段 25]

One is all invest, and another one is one is no one invest. These are both national equilibria in this game. Let’s just check that they are, exactly the argument that Kate said, that if everyone invests, then no one would have any regrets, everyone’s best response would be to invest. And if nobody invests, then everyone would be happy not to have invested, that would be a best response. It’s just in terms of what Patrick said, it is a game with two equilibria like the previous game, and that there are other side. similarities to the previous game, but it’s a little bit of… The equilibrium in this case are not quite the same as the other game, and the other game, that other equilibrium, the 0-0 equilibrium, seemed like a silly equilibrium. It isn’t like we’d ever predict it happening. Whereas here, the equilibrium with nobody investing, actually is quite a plausible equilibrium. If I think no one else is investing, then I strictly prefer not to invest. Is that right? Is that right? Okay. So two remarks about this. I want to do more before I do a few remarks. Yeah, well, let’s have one remark at least. How did we find those Nash equilibrium? What was our sophisticated mathematical technique for finding the Nash equilibrium in this game? So we should… Can you get the mic on…

[译文 25]

一种是全部投资，另一种是没有人投资。这两种都是这个博弈中的国家均衡。让我们验证一下它们确实如此，凯特刚才说的论证完全正确：如果每个人都投资，那么没有人会有任何遗憾，每个人的最佳反应都是投资。而如果没有人投资，那么每个人都会乐于不投资，那也是一种最佳反应。用帕特里克的话说，这是一款像之前那款游戏一样有两个均衡的游戏，但两者之间有相似之处，不过……这款游戏中的均衡与那款游戏的均衡并不完全相同，而那款游戏中的另一个均衡，即0-0均衡，看起来像个愚蠢的均衡。我们不会预测它会发生。然而在这里，没有人投资的均衡实际上是一个相当合理的均衡。如果我认为没有其他人投资，那么我严格偏好不投资。对吗？是这样吗？好的。关于这一点我有两点要说。在我多说几点之前，我想先做更多内容。好吧，至少让我们先说一点。我们是怎么找到那些纳什均衡的？在这个游戏中寻找纳什均衡，我们用了什么复杂的数学技术？我们应该……能把麦克风递过来吗……

[段 26]

Is it Kate? Is that right? Yeah. So how do you find the Nash equilibrium? I looked for the only two places where there’s no regrets. All right. So in principle, you could have something, I mean, that works, but in principle you could have looked at every possible combination. And there’s lots of possible combinations. It could have been a combination where, you know, 1% invested and 99% didn’t, and 2% invested in 98 didn’t, and so on and so forth. We could have checked rigorously what everyone’s best response was in each case. But what do we actually end up doing in this game? What’s the method? Yeah, let me get the guy in… Yeah? You only consider situations where your action can have a different outcome, and those only occur when everyone’s investing or no one’s investing? That’s true, so that certainly makes it easier. I claim, however, I mean, you’re both of you being more rigorous and more mathematical than I’m tempted to be here. I think the easy method here, the easiest sophisticated math here, is to guess. All right? My guess is the easy thing to do is to guess what flight is to be in equilibrium here, and then what? And then check. All right? So a good method here in these games is to guess and check. And guess and check is really not a bad way to try and find national equilibrium.

[译文 26]

是凯特吗？是这样吗？好的。那么如何找到纳什均衡呢？我找了仅有的两个没有遗憾的地方。好吧。原则上，你可以考虑各种可能的结果组合，虽然有很多可能的组合，比如1%的人投资而99%的人不投资，2%的人投资而98%的人不投资等等。我们本可以严格验证每个人在每种情况下的最佳反应。但实际上我们在这个游戏中是怎么做的？方法是什么？是的，让我叫那个人……对吧？你只考虑那些你的行动能改变结果的情况，而这些情况只发生在所有人都投资或没有人投资的时候？确实如此，这确实让问题变得更简单了。然而，我声称，你们两个都比我在这里更严谨、更数学化。我认为这里最简单的方法，最容易的复杂数学，就是猜测。好的？我的猜测是，猜测什么是这里的均衡状态，然后呢？然后验证。所以在这些游戏中，一个好的方法就是猜测和验证。猜测和验证确实是寻找国家均衡的不错方法。

[段 27]

The reason it’s not a bad way is because checking is fairly easy. Right? guessing is hard. You might miss something. There might be enough equilibrium. stone somewhere. Oh, no, it’s not a stone. In America, it’s a rock. It’s not on a rock somewhere. All right. But checking that something to, some punitive equilibrium, some candidate equilibrium, checking whether it is stone somewhere. In America it’s a rock. It’s not a stone. In America it’s a rock somewhere. All right. But checking that something to, some pustive equilibrium, some candid equilibrium, checking whether it is an equilibrium is easy, because all you have to do is check that nobody wants to move away, and they want to delete. So I think in practice that’s what you’re going to end up doing in this game. And it turns out to be very easy to guess and check, which is why you’re able to find it. So guess and check is a very useful method in these games where there are lots and lots of players, but not many strategies per player. It works pretty well. All right. 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 ourselves what happened just now. So what happened just now?

[译文 27]

这个方法不错的原因在于验证相当容易。猜测很难，你可能会遗漏某些东西，可能存在足够多的均衡。石头在某个地方。哦，不，不是石头。在美国，那叫rock。不是在石头上的某个地方。好吧，但检查某个东西，某个惩罚性均衡，某个候选均衡，检查它是否是一个均衡很容易，因为你只需要检查没有人想要离开，他们想要删除。所以我认为在实践中你最终会在这个游戏中做这些。而且结果表明猜测和验证非常容易，这就是为什么你能够找到它。所以猜测和验证在玩家很多但每个玩家的策略不多的这些游戏中是非常有用的方法。它相当有效。好吧。好的。现在，我们把这款游戏写在黑板上了。我想花点时间来讨论它，因为它有点重要。所以我现在想做的是提醒我们自己刚才发生了什么。那么刚才发生了什么？

[段 28]

Can we raise the yeses again, that they invest again? And raise the non-investors, non-invest? And I want to remind you guys, you all owe me ten bucks. All right? All right. And what I want to do is I want to play it again. No communication. Write down again on the corner of your notepad what you’re going to do. Don’t communicate. Don’t communicate, you guys. All right, show your neighbor. All right, and now we’re going to poll again. So, ready, without cheating, without looking around you. If you invested, let you get a good view of you. If you invested, raise your hand now. And if you didn’t. You didn’t invest? Okay, okay. All right. Can I look at the investors again? Let’s raise your hands, honestly. All right, we’ve got a few investors still. So these guys really owe me money now. That’s good. All right, let’s do it again. All right. Third time. Hang on a second. Hang on second. So third time, write down. Pretend this is for real cash. All right. Now, if you invested the third time, raise your hand. All right. We got, all right? There’s a few suckers born every day, but basically, all right? So where are we heading here? Where are we heading pretty rapidly? Right? We’re heading towards an equilibrium, right? Just let’s make sure we, let’s confirm that.

[译文 28]

我们能再举起那些“是”的人吗，那些再次投资的人？然后举起那些非投资者，非投资？我想提醒你们，你们都欠我十美元。好吧？好的。我现在想做的是我想再玩一次。不许交流。在你的笔记本角落里写下你打算做什么。不要交流。不要交流，你们这些人。好吧，向你的邻居展示。现在我们要再次投票。准备好了，不要作弊，不要环顾四周。如果你投资了，让你看到自己的好视野。如果你投资了，现在举起你的手。如果你没有投资，你没有投资？好的，好的。好的。我能再看看那些投资者吗？诚实地举起你们的手。好的，我们有一些投资者了。所以这些人现在真的欠我钱了。很好。好的，让我们再来一次。第三次了。等一下，等一下。第三次，写下来。假装这是真实的现金。现在，如果你第三次投资了，举起你的手。好的，我们有，够了吧？有几个冤大头每天都在出生，但基本上，好的？我们要去哪里？我们要快速去哪里？我们在走向一个均衡，对吧？让我们确认一下。

[段 29]

So everyone who didn’t invest that third time, raise your hands. Right? 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, something 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 not the formal sense, with a natural sense, to an equilibrium. Right? And with the exception of a few dogged people who want to pay for my lunch, almost everyone else was converging to an equilibrium there. All right? So play converged fairly rapidly to the Nash equilibrium. the Nash equilibrium. All right? Well, we discussed there were two Nash equilibrium in this game. Is one of these Nash equilibrium, ignoring me for a second, is one of these Nash equilibrium 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? 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, which no one gets in the thing, which all that money is left on the table.

[译文 29]

所以每个第三次没有投资的人，举起你们的手。对吧？那一举手表决，相当接近一个纳什均衡策略。对吗？这里有一个第三个原因的例子，我们上次已经提到过，但第三个原因，为什么我们可能对纳什均衡感兴趣。在某些情况下，博弈会以自然的方式（不是正式的方式，而是自然的方式）收敛到一个均衡。对吧？除了少数固执的人想为我付午餐钱，几乎所有其他人都在向一个均衡收敛。好吧？所以博弈相当快速地收敛到纳什均衡。好吧？嗯，我们讨论过这个游戏中有两个纳什均衡。忽略我一会儿，这两个纳什均衡中有一个比另一个更好吗？是的，显然所有人投资的纳什均衡是更好的那个，对吧？每个人都同意，对于班上的每个人来说，所有人投资是一个比所有人都不投资更好的纳什均衡。对吗？是这样吗？然而，我们当时在收敛到哪里呢？在这个案例中，我们收敛到的是哪个？我们收敛到的是一个糟糕的均衡。我们正在快速地收敛到一个非常糟糕的均衡，在这种情况下没有人得到任何东西，所有那些钱都被留在了桌上。

[段 30]

So how can that be? How do we converge to this bad equilibrium? To be a bit more formal, the bad equilibrium, the no invest equilibrium here, is Pareto-dominated by the good equilibrium. Everybody is strictly better off at the good equilibrium than at the bad equilibrium. Pareto-dominates, right, to use an expression that you probably learned to 150 or 115. Nevertheless, we’re going to the bad one, we’re heading to the bad equilibrium. Why did we end up going to the bad equilibrium rather than the good equilibrium? Yeah, can we get the guy in the gray? Yeah. Well, it was a bit of a bare market for investors, wasn’t it? Just now, you mean it? All right, it’s okay. Say what you mean a bit more, so yeah, that’s good, say a bit more. So it seemed like people didn’t have a lot of confidence that other people were going to invest, and so it became a successively less desirable option to invest. All right, so what way of saying that was when we started out, we were roughly even, roughly half half, but that was already bad for the people who invested, all right, and then, so we started out at half half, which was below that critical threshold of 90%, is that right? And from then on in, we just tied. humble down. All right? So one way to say this, and one way to think about that, below that critical threshold of 90%, is that right?

[译文 30]

那么这是怎么回事？我们怎么会收敛到这个糟糕的均衡？更正式地说，这里的糟糕均衡，这个不投资均衡，被好的均衡帕累托支配了。在好的均衡处，每个人都比在坏的均衡处严格更好。帕累托支配，对吧，用你们可能在150或115课上学过的表达。尽管如此，我们正在走向糟糕的那个，我们正在走向糟糕的均衡。为什么我们最终走向了糟糕的均衡而不是好的均衡？是的，我们能叫那个穿灰色衣服的人吗？是的。嗯，对于投资者来说，这当时是一个相当空头的市场，不是吗？就在刚才，你的意思是？好吧，没关系。说得更清楚一点，所以是的，那很好，多说一点。所以看起来人们不太相信其他人会投资，所以投资变成了一个越来越不理想的选择。好吧。我们开始的时候，大约是五五开，但那时对于那些投资者来说已经不好了，对吧，然后，所以我们从五五开开始，那已经在90%的临界点以下了，对吗？从此之后，我们就只是……谦虚下来了。

[段 31]

And from then on in, we just tumble down. All right? So one way to say this, and one way to think about that, is it may matter, in this case, where we started. Right? Suppose the first time we played the game in this class this morning, suppose that 93% of the class had invested, in which case those 93% would all have made money. Right? Now, my guess is, I can’t prove this, my guess is we might have converged the other way and converged up to the good equilibrium. Does that make sense? So people figured out that people who didn’t invest the first time, actually they paid the best response to the class, so they stayed put, and those of you did invest, a lot of you started not investing, as you got caught up in this spiral downward, and we end up not investing. But had we started off above the critical threshold, the threshold here is 90%, and had you made money the first time around, then it would have been the non-investors that would have regretted their choice, and they might have switched into investing. And we might, I’m not saying we necessarily, but we might have gone the other way. Yeah. Let me get a mic on. What if it is in like a 30-70 thing where 70% invested in? Yeah, that’s a good question.

[译文 31]

从那之后，我们就一路下跌。好的？这么说吧，想一想这个问题，这可能取决于我们从哪里开始。对吧？假设今天早上我们第一次玩这个游戏时，假设有93%的人进行了投资，在这种情况下，那93%的人都会赚钱。对吧？我的猜测是，我无法证明这一点，但我的猜测是，我们可能会以另一种方式收敛，向上收敛到好的均衡点。能理解吗？所以人们发现，那些第一次没有投资的人，实际上他们对整个班级来说是最佳反应，所以他们保持不动，而那些投资了的人，你们中很多人在卷入这个螺旋式下降的过程中，开始不再投资，最终我们没有投资。但如果我们在临界阈值之上开始，这里的阈值是90%，如果你们第一次就赚了钱，那么那些不投资者就会后悔他们的选择，他们可能会转向投资。我们可能——我不是说我们一定会——但我们可能会走向另一个方向。好的，让我把麦克风打开。如果是一个30-70的情况，70%投资了怎么办？是的，这是个好问题。

[段 32]

Suppose we’ve been close to the threshold but below. So I don’t know is the answer, obviously, because we didn’t do the experiment, but it seems likely that the higher, the closer we got to the threshold, the better chance there would have been going up. My guess is, is this is a guess. My guess is if we started below the threshold, we’d probably have come down, and if we started to be, above the threshold, we’d probably have gone up, but that’s not a theorem. I’m just speculating on what might have happened. Speculating on your speculations. All right. So here we have a game with two equilibria, one is good, one is bad. One is really quite bad. It’s Pareto-dominated. All right. And notice that what happened here, the way we spiral down, coincides with something we’ve talked about nationally equilibrium already. It coincides with this idea of a self-fulfilling prediction, 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. And that I think corresponds to what the gentleman said in the middle about a bare market versus a bull market. 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 prophecy, and we ended up with no investment.

[译文 32]

假设我们已经接近阈值但低于它。所以我不知道答案，显然，因为我们没有做这个实验，但看起来可能的是，我们越接近阈值，向上的机会就越大。我的猜测是，这只是猜测。我的猜测是，如果我们从阈值以下开始，我们可能会下跌，如果我们从阈值以上开始，我们可能会上涨，但这不是定理。我只是在推测可能发生的情况。在你的推测上做推测。好的。这里有一个有两个均衡点的游戏，一个是好的，一个是坏的。其中一个真的相当糟糕。它被帕累托支配了。好的。注意这里发生的事情，我们螺旋式下降的方式，与我们之前讨论过的国家均衡相符。它与自我实现的预言这一概念相符，一个自我实现的预言。只要你认为其他人不会投资，你也不会投资。所以这是一个自我实现的预言，让你走向不投资的状态。相反，只要每个人都认为其他人会投资，你就会走向好的均衡。我认为这与那位先生之前说的关于空头市场与牛市的内容相对应。那是一个空头市场，看起来其他人对彼此投资都没有信心，然后这是一个自我实现的预言，我们最终没有投资。

[段 33]

All right. Okay. 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 where nobody tidies to their room or both guys go to jail. But I claim this is not a prisoner’s dilemma. And I get the guy, it’s two behind you. No one suffers, but no one gets any fun in this. Okay, so maybe the outcome isn’t quite so bad. That’s fair enough. I could have made it worse, right? I could have made it sort of, you know, I could have made that, I could have lowered the payoffs until they were pretty bad. What, why else isn’t this not a prisoner’s not? The woman who’s behind you? Because there’s no strictly dominant strategy. Good, good. So in Prisoner’s dilemma, playing Alpha was always a best response. What led us to the bad outcome in Prisoner’s dilemma, was that alpha, the defect strategy, the non-cooperative strategy, the not helping tidy your room strategy, was always the best thing to do. Here, in some sense, the good thing, moral thing in some sense, is to invest, but it’s not the case that not investing dominates investing.

[译文 33]

好的。我们以前在课堂上见过不好的结果。例如，第一天，我们看到了囚徒困境。但我声称，虽然我们在课堂上得到了不好的结果，但这不是囚徒困境。为什么这不是囚徒困境？两者之间有什么不同？嗯，两个游戏都有一个不好的均衡？囚徒困境中不好的均衡是没有人整理房间或者两人都进监狱。但我声称这不是囚徒困境。我找到那个人了，就是你后面两个。没有人受苦，但也没有人得到任何乐趣。好的，也许结果没有那么糟糕。这是合理的。我本可以让它更糟，对吧？我本可以让它，你知道，我可以降低收益直到它们相当糟糕。什么，为什么这不是囚徒困境？你后面的那位女士？因为没有严格占优策略。好的，好的。所以在囚徒困境中，玩Alpha永远是最佳反应。导致我们在囚徒困境中得到不好结果的原因是，Alpha，即背叛策略、不合作策略、不帮忙整理房间的策略，永远是最佳选择。这里，在某种意义上，好的事情，在某种意义上是道德的事情，是投资，但不是不投资就主导投资。

[段 34]

In fact, if other people invests in the room, you want to invest. Is that right? So this is a social problem, but it’s not a social problem of the form of a prisoner’s dilemma. So what kind of problem is this? What kind of social problem is this? The guy in front of you are. Perhaps it’s one of cooperation? It’s one of, okay, so it would help if people cooperated here, but I’m looking for a different term. A term that came up the first day. Coordination. This is a coordination game. Those people who read the New Yorker, of the second, no, it’s a coordination game. Okay? All right. So, why is it a coordination game? Because you’d like everyone in the class to coordinate their responses on invest. And in fact, if they did that, they’d everyone would be happy. And no one would have an incentive to defect. That would, in fact, be an equilibrium. But unfortunately, quite often, we fail to have coordination, either everyone of, well, this is a kind of form of coordination, either everyone plays not invest, or has happened the first time in the class. But unfortunately, quite often we fail to have coordination. Either everyone, well, this is a kind of form of coordination, either everyone plays not invest, or has happened the first time in the class, we get some split with people losing money.

[译文 34]

实际上，如果其他人投资，你也想投资。是这样吗？所以这是一个社会问题，但不是囚徒困境形式的社会问题。那这是什么类型的问题？这是一种什么类型的社会问题？前面那位男士说的是。可能是合作问题？它是合作，嗯，我正在寻找一个不同的术语。第一天出现的一个术语。协调。这是一个协调游戏。那些阅读《纽约客》的人，不对，这是一个协调游戏。好的？因为你希望班上的每个人都协调他们的回应——投资。事实上，如果他们这样做了，他们每个人都会很高兴。没有一个人会有动机去背叛。那实际上会是一个均衡。但不幸的是，我们经常无法实现协调。每个人要么都玩不投资，或者就像第一次在课堂上发生的那样。但不幸的是，我们经常无法实现协调。每个人要么都玩不投资，或者我们已经得到的分裂，有人赔钱。

[段 35]

All right. 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, right, 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 in a bad equilibrium? What else looks like this? Let’s collect some ideas here. I’ve got a hand way at the back. Can you get the guy who’s just way, way, way at the back, way, way at the back, right up against the… There you go, great, thank you. Wait till the mic gets to you, Danielle. Yeah. Like a party on campus can be a coordination game. Yeah, good, good, okay. So a party on campus is a coordination game because what? Because you have to coordinate at being at the same place. Is that right? That’s the idea you had… Go ahead, go ahead. The thing is, like, if not very many people are coming, the people that did come are not going to enjoy it, but if a lot of people do come, then it will be good for everybody. be good for everybody.

[译文 35]

好的。所以我声称实际上这在社会中并不是什么罕见的事情。社会上有许多协调问题。有很多事情看起来像协调游戏，而且经常在协调游戏中，不好的结果会出现。我今天剩下的时间大部分都要讨论这个问题，因为我认为这很重要，对吧，无论你是经济学家还是什么。所以，让我们讨论一下。还有什么具有协调游戏的结构，因此可能产生人们不协调或协调到错误的地方，你最终陷入不好均衡的结果？还有什么看起来像这样？让我们收集一些想法。我看到后面有人举手。你能让那个在后面很远、很远、很远的人，就是那个靠在…那边的人，好，谢谢。等麦克风传到你那里，Danielle。是的。比如校园派对可以是一个协调游戏。是的，好，好。所以校园派对是一个协调游戏，因为什么？因为你必须协调在同一个地方。是这样吗？这是你有的想法…继续，继续。问题是，如果来的人不多，那些来了的人不会享受，但如果很多人来了，那么对每个人都有好处。

[段 36]

Good, good. That’s good. So there’s another way in which… There’s two ways in which a party can be a coordination problem. One is the problem that people don’t show up. It’s a lousy party, so you don’t want to show up. Conversely, if everyone’s showing up, it’s a lot of fun, it’s the place to be, and everyone wants to show up. And second, so there’s two equilibrium there showing up and everyone not showing up or everyone’s showing up. And similar idea, the location of parties, which I thought you were driving up, but is the similar idea can occur. So it used to be 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’re 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, for graduate students, typically Thursday night. All right? 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. All right. All right. So one of things you have to learn when you go to a new town is where is where is the meeting point for the kind of party I want to go to.

[译文 36]

好的，好的。这很好。所以还有另一种方式…派对可能是一个协调问题的两种方式之一。一种问题是人们不出现。这是一个糟糕的派对，所以你不想出现。相反，如果每个人都出现，它会很有趣，是值得去的地方，每个人都想出现。第二，所以有两个均衡，出现和每个人都不出现，或者每个人都出现。类似的想法，派对的位置，我认为你在开车上来的，但类似的想法可以发生。所以过去在纽黑文是这样的，实际上现在不多了，但过去校园周围有不同的酒吧，你不被允许去，所以你不了解，但无论如何，校园周围有很多不同的酒吧，有一个协调游戏，人们在周五晚上协调，或者更诚实地说，对于研究生来说，通常是周四晚上。好的。所以过去其中一家市中心的酒吧是戏剧学院的人协调的地方，另一个是经济学家协调的地方，他们不在同一个地方协调，这是一个很好的均衡。好的。好的。所以你去一个新城镇时必须学习的事情之一是，我想去的那种派对的聚会点在哪里。

[段 37]

And again, you can have a failure of coordination, everyone’s wandering around the town getting mugged. What other things look like coordination problems like that? So again, way back in the corner there, there’s somebody right behind you, there you go. You have to really shout now. Maybe warring parties in a civil war or signing a treaty? Okay, that could be, so I’m, that could be a coordination problem. It has a feeling of being. It has a feeling of being a bit prisoner’s delemish. In some sense, sometimes my disarming, my putting down my arms before you putting down your arms, that kind of thing. So it could be a coordination problem, but it has a little bit of a flavor of both. Go ahead, go ahead, do you want? Okay, okay, okay, okay. Other examples. There’s a guy there, while you’re there, when you get the guy who’s behind you. There, on the get by the door, there you go, great. At a sports arena, people deciding whether or not they want to start a chant for whatever team. Yeah, okay, okay. I’m not quite sure which is the good outcome or the bad outcome. So there’s this thing called the wave, there’s this thing called the wave that Americans insist on doing, and I guess they think that’s the good outcome. All right, all right, other things, other things.

[译文 37]

再次强调，协调可能会失败，每个人都在城里游荡然后被抢劫。还有什么其他事情看起来像这样的协调问题？再次，在后面的角落里，有个人就在你身后，你来了。你现在必须大声喊出来。也许是内战中的交战国或签署条约？好吧，那可能是，那可能是一个协调问题。它有一种……它有一种有点像囚徒困境的感觉。在某种意义上，有时候我放下武器，我在你放下武器之前放下我的武器，诸如此类。所以它可能是一个协调问题，但它有一点两者兼具的味道。说吧，说吧，你想说吗？好吧，好吧，好吧，好吧。其他例子。那边有个人，当你在这儿的时候，当你找到你身后那个人时。在门那边的，好了，很好。在体育场馆，人们决定是否要为他们支持的球队开始齐声呐喊。是的，好吧，好吧。我不太确定哪个是好结果，哪个是坏结果。有一种叫做“人浪”的东西，有一种美国人坚持要做的人浪，我想他们认为那是好结果。好吧，好吧，其他事情，其他事情。

[段 38]

There’s a, wait until they get to see, yeah, good. Battle of the sexes? Let’s come back to that one. Let’s hold that thought and we’ll come back to it next time. You’re right, that’s a good, that’s a coordination one, but let’s come back to it next time. All right, anything else, anything else. Let me try and expand on some of these meeting place ideas. We talked about pubs to meet at or parties to meet at, but think about online sites, online sites which are chat sites or dating sites or whatever, right? Those online sites clearly have the same feature of a party. You want people to coordinate on the same site. All right? What about some other economic ideas? What about some other ideas from economics? What else has that kind of externality? that kind of externality, like a meeting place. Yeah, can we get him? Patrick? I mean, it’s excluding some people, but things like newspapers or something, like we might want only one, like, global news source. So that’s an interesting thought, because it can go both ways. It could be a bad thing only to have one newspaper, for obvious reasons. But in terms of having a good conversation about what was in the newspaper yesterday around the, over lunch, it helps everyone’s read the same thing. And certainly, there’s a bandwagon effect to this with TV. effect with TV shows.

[译文 38]

等他们看到再说，是的，很好。“性别之战”？让我们回到那个话题。让我们先记下这个想法，下次再回来讨论。你说得对，那是一个好的，那是一个协调问题，但我们下次再回来讨论。好吧，还有别的吗，还有别的吗？让我尝试扩展一下这些聚会场所的想法。我们讨论过酒吧聚会或派对聚会，但想想那些在线网站、聊天网站或约会网站或其他什么的，对吧？那些在线网站显然具有派对的相同特征。你希望人们在同一个网站上协调。好吧？还有什么其他经济学想法？还有什么其他经济学想法？还有什么具有那种外部性的东西？那种像聚会场所一样的外部性。是的，能叫他吗？帕特里克？我的意思是，它排斥了一些人，但像报纸之类的东西，也许我们只需要一个全球新闻源。所以这是一个有趣的想法，因为它可以双向发展。只拥有一家报纸可能是一件坏事，原因显而易见。但就大家在午餐时对昨天报纸内容的良好讨论而言，它有助于每个人阅读相同的内容。当然，电视节目也有这种从众效应。

[段 39]

If everybody in America watches the same TV show, which apparently is American Idol these days, then you can all talk about the same thing. And certainly, there’s a bandwagon effect to this with TV shows. If everybody in America watches the same TV show, which apparently is American Idol these days, then you can all talk about it over lunch. Notice that’s a really horrible place to coordinate. Right. Right. There are similar examples to the American Idol example. When I was growing up in England, again, I’m going to reveal my age, everybody decided that to be an in-person in England, you had to wear flared trousers, right? This was, and so to be in, you had to wear flared trousers. This is a horrible coordination problem, right? So for people who don’t believe that could ever have happened in England, you could ever have these sort of fashion goods that you end up at a horrible equilibrium at the wrong place, you don’t believe that could ever happen. Think about the entirety of the Midwest. I didn’t say that. We’re going to cut that off of the film then. All right? What else is like? this? What else is like this? I’m getting a few ideas out now. Let’s get this gentleman here. The establishment of monopolies, say like a lot of people use Microsoft, say, then everything is compatible with Microsoft so more people want to use it.

[译文 39]

如果美国每个人都看同一个电视节目，现在看来是《美国偶像》，那么你们都可以讨论同一件事。当然，电视节目也有这种从众效应。如果美国每个人都看同一个电视节目，现在看来是《美国偶像》，那么你们午餐时就可以讨论它。注意那是一个非常糟糕的协调场所。对的。对的。《美国偶像》的例子有类似的例子。当我在英国长大的时候，我又要暴露我的年龄了，每个人都认为在英国要成为一个潮人，你必须穿喇叭裤，对吧？这是，而且要成为一个潮人，你必须穿喇叭裤。这是一个糟糕的协调问题，对吧？所以对于那些不相信这种事在英国曾经发生过的人，不相信你可能会有这种时尚单品，最终在错误的地方达到糟糕的均衡，你不认为那曾经发生过。想想整个中西部地区。我没说过那个。我们要把它从录像中剪掉。好吧？还有什么是像这样的？还有什么是像这样的？现在我有了一些想法。让我们找这位先生。垄断的建立，比如说很多人使用微软，那么一切都与微软兼容，所以更多人想要使用它。

[段 40]

Good. So that’s gotten your name. Steven. So Steven’s pointing out that certain software can act this way by being a network good. The more people who use Microsoft and Microsoft programs, the bigger the advantage to me using Microsoft. All right. because I can exchange programs, I can exchange files if I’m working with my co-authors and so on. And so you can have different equilibria coordinating on different software. And again, you could end up at the wrong one. I think a lot of people would argue, but I’m going to stay neutral on this, a lot of people would argue that Microsoft wasn’t necessarily the best place for the world to end up. All right? There are other technological network goods like this. These are called Network Exanalysis. An example here would be high-definition television. You want to have one technological standard that everyone agrees on, such things like high-definition. televisions because then everyone can produce TV to that standard and goods that go along with that standard. And of course, each company who’s producing a TV and has a standard mind would like theirs to be chosen as the standard. And again, you could end up at the wrong place. You could end up at a bad equilibrium. How about political bandwagons? In politics, particularly in primaries, there may be an 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 booze and it doesn’t seem like your pot is split and so on.

[译文 40]

很好。所以那让你留名了。史蒂文。所以史蒂文指出某些软件可以通过作为网络商品来起到这种作用。使用微软和微软程序的人越多，我使用微软的优势就越大。好的。因为我可以交换程序，如果我和我的合著者一起工作等等。所以你可以有不同的均衡， coordi在不同的软件上。再次，你可能会在错误的地方结束。我认为很多人会争论，但我在这件事上保持中立，很多人会争论说微软不一定是世界最终落脚的最佳选择。好吧？还有其他类似的技术网络商品。这些被称为网络效应分析。一个例子是高清电视。你希望有一个每个人都同意的单一技术标准，比如高清电视之类的东西，这样每个人都可以按照那个标准生产电视和符合该标准的商品。当然，每个生产电视并有自己的标准想法的公司都希望自己的标准被选为标准。再次，你可能会在错误的地方结束。你可能会处于一个糟糕的均衡。政治从众效应怎么样？在政治中，特别是在初选中，在民主党或共和党一方，投票给同一个候选人可能是有优势的，这样他们就能获得大量捐款，看起来你的选票没有分散等等。

[段 41]

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. All right. So that’s another example. Any other economic examples? Yeah, there’s, can we get this guy in here? Listing on a stock exchange? Yeah, okay, so in particular which stock exchange? particular which stock exchange to list on, right? So there’s a huge advantage of having lots of stocks on the same, stock exchange, there are shared fixed costs, there’s also liquidity issues, all right, and lots of issues of that form, but mostly of the form of the form of fixed costs. So there’s a tendency to end up with one stock exchange. We’re not there yet, but we do seem to be going that way quite rapidly. The problem, of course, being, that might not be the best stock exchange, or it might give that stock exchange monopoly power. Let me get one more, let me try out one more example. What about bank run? What’s a bank run? What’s a bank run? Somebody? Yeah, can we get this? What’s a bank run? It’s when… It’s when the public loses confidence in their security of their money in banks, then they rush to withdraw the deposits.

[译文 41]

这可能会导致，再次我要在这件事上保持中立，它最终可能导致错误的候选人获胜。有一个政治从众效应。在新罕布什尔州和爱荷华州获胜的人往往会赢得一切。好吧。所以那是另一个例子。还有其他经济例子吗？是的，有，我们能让这边这位先生参与吗？在证券交易所上市？是的，好吧，特别是选择在哪个证券交易所上市，对吧？在同一个证券交易所有很多股票是有巨大优势的，有共同固定成本，也有流动性问题，好吧，还有很多这类问题，但主要是固定成本形式的问题。所以有一种趋势，最终只剩下一个证券交易所。我们还没有到那一步，但我们似乎正在快速朝那个方向发展。当然，问题是，那可能不是最好的证券交易所，或者它可能给那个证券交易所垄断权力。让我再举一个例子，让我试试另一个例子。银行挤兑怎么样？什么是银行挤兑？什么是银行挤兑？有人吗？是的，能说说吗？什么是银行挤兑？就是当……就是当公众对他们在银行资金的安全性失去信心时，他们赶紧去提款。

[段 42]

So you imagine a bank has a natural case where there’s two equilibria. There’s a good. Everyone has confidence in the bank. Everyone leaves their deposits in the bank. The bank is then able to lend some of that money out and earn a higher rate of interest on it. The bank doesn’t want to keep all that money locked up in the vault. It wants to lend it out to lenders who can pay interest. That’s a good equilibrium for everybody. However, if people lose confidence in the bank and start drawing their deposits out, then the bank hasn’t got enough cash in its vault to cover those deposits, and the bank goes under. All right? Now, I used to say at this point, in the class, none of you would have seen a bank run because they stopped happening in America, more or less around 19, 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 a bank going on actually in England where the company called Northern Northern Rock, it’s called, 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 the news, New York Times, you’ll see a line of depositors lined up outside the offices in London of this bank trying to get I mean, if you looked at the newspaper yesterday on the New York Times, you’ll see a line of depositors lined up outside the offices in London of this bank trying to get their deposits out and you see the Bank of England trying to intervene to restore confidence.

[译文 42]

所以想象一家银行有一个自然的情况，有两个均衡。有一个好的。每个人对银行都有信心。每个人都把存款留在银行。然后银行能够借出一些钱并赚取更高的利息。银行不想把所有的钱都锁在金库里。它想把它借给能支付利息的借款人。这对每个人来说都是一个好的均衡。然而，如果人们对该银行失去信心并开始提取存款，那么银行的保险库里就没有足够的现金来支付这些存款，银行就会倒闭。好吧？现在，我过去常在这个时候说，在课堂上，你们谁都没有见过银行挤兑，因为它们在美国停止发生了，大概是在19世纪30年代中期。在20世纪30年代之前，美国有很多很多银行挤兑，但自从联邦存款保险制度出台后，就少得多了。然而，我今天真的不能那么说了，因为现在正有一场银行挤兑正在发生。实际上在英国正有一场银行挤兑正在进行，一家公司叫Northern Rock，叫Northern Rock，就在我们说话的时候。它真的就是一次银行挤兑。我的意思是，如果你昨天看报纸上的新闻，《纽约时报》，你会看到在伦敦这家银行办公室外排着一列存款人，试图拿到他们的存款，你看到英格兰银行正试图干预以恢复信心。

[段 43]

And just to be clear, this isn’t a simple case of being about the mortgage crisis. This bank does do mortgages, but it doesn’t seem to be particularly involved in the kind of mortgages that have been attracting all the publicity. It really seems to be a shift in confidence, a move from the good equilibrium of everyone remaining invested to the bad equilibrium of everyone taking their money out. Hang a second. Now, there are famous bank runs in American culture. In the movies, anyway. What is the famous bank run in the movies, in American movies? It’s a wonderful life, all right? There’s actually one in Mary Poppins as well, but we’ll do it to a wonderful life. How many of you have seen it’s a wonderful life? How many of you not seen it’s a wonderful life? Can you get a poll here? How many people have not seen a moment? Keep your hands up a second. Keep your hands up. You need to know that if you’re on a green card, you can lose your green card if you haven’t seen it’s a one, okay? All right? So in It’s a Wonderful Life, there’s a run on the bank. Actually, it’s a saving and loan, but never mind. We’ll think of it as a bank. All right. And luckily, it doesn’t end up with the saving and loan or bank going under.

[译文 43]

需要明确的是，这不是一个简单的房贷危机案例。这家银行确实做抵押贷款业务，但似乎并没有特别卷入那些吸引所有关注的贷款类型。这似乎真的是信心的转移，从每个人都继续投资的良好均衡，转移到每个人都取出资金的糟糕均衡。等一下。在美国文化中有著名的银行挤兑事件。至少在电影里是这样。在美国电影中，著名的银行挤兑是什么？《美好人生》，对吧？实际上在《欢乐满人间》里也有一个，但我们以《美好人生》为例。你们有多少人看过《美好人生》？有多少人没看过《美好人生》？我们来做个调查好吗？有多少人连一刻都没看过？举手示意一下。举手。各位需要知道，如果你是持绿卡的，如果你没看过这部电影，你可能会失去你的绿卡，明白吗？所以在《美好人生》中，发生了银行挤兑。实际上那是一家储蓄和贷款机构，但没关系，我们就把它当作银行来想。好在最后储蓄贷款机构或银行并没有倒闭。

[段 44]

Why doesn’t the bank go under in It’s a Wonderful Life? Why doesn’t it go under? Yeah, the guy in Britain. Can we get the guy in? Green? Yeah. Everyone agrees to only take as much as they need and not to take out their entire deposit. All right. So if people didn’t hear it, everyone agrees only to take out a small amount, perhaps even nothing, and therefore the bank runs and everyone realizes the bank isn’t going to collapse and they’re happy to leave their money in the bank. Now it’s true everyone agrees, but why do they agree? What makes them agree? What makes them agree is Jimmy Stewart, right? It’s Jimmy Stewart, right? Everyone remember the movie? Right? So Jimmy Stewart gets up there and he says, he gives a speech, and he says, look, more or less, he doesn’t say in these words, but he would have done to have taken the class, he says, look, there are two equilibrium in this game. I can’t do the, whatever it is, West Pennsylvania accent, whatever it is. Is that where it’s from? Anyway, but there are two equilibrium in this game, there’s a bad one where we all draw our money out and we all lose our homes eventually, and there’s a good one where we all leave our money in, and that’s better for everyone, so let’s all leave our money out.

[译文 44]

为什么在《美好人生》中这家银行没有倒闭？为什么没有倒闭？是的，那位英国来的先生。我们能把那位先生请上来吗？绿卡？是的。每个人都同意只取出自己需要的部分，而不是把所有存款都提出来。所以如果有人没听清，每个人都同意只取出少量，甚至什么都不取，因此银行挤兑停止了，每个人都意识到银行不会倒闭，他们愿意把钱留在银行里。现在虽然每个人都同意了，但他们为什么同意？是什么让他们同意？让他们同意的是吉米·斯图尔特，对吧？是吉米·斯图尔特，对吧？大家都记得这部电影吧？所以吉米·斯图尔特站起来发表了一番演讲，他说的内容大致是，虽然他不会用这些原话，但如果有上过这门课的话，他会说，看，这个博弈中有两个均衡。我学不来他那种西宾夕法尼亚口音，不管那是什么口音。反正这个游戏中有两个均衡，一个是坏的均衡，我们所有人都把钱取出来，最后我们都失去房子，还有一个好的均衡，我们所有人都把钱留在里面，这对每个人都更好，所以让我们都把钱留在里面吧。

[段 45]

But he gives this, He’s a bit more motivational-stimulating than me, right? But he leads to people not leaving their money in. So what I want to do is, I want to pick on somebody in the class. Now, everyone understands this game, everyone understands this two equilibrium, 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 mic to Patrick here, and Patrick is going to have exactly five seconds to persuade you. Stand up, stand up, set up, Patrick’s going to have five seconds to persuade you, well, whatever he likes. You can figure what he’d like, starting now. Okay, so clearly if we all invest, we’ll all be better off, so everyone should invest. All right, all right. Now let’s see this is going to work. Let’s have a round of him from Patrick. So let’s see what happens now. Everybody, everybody, oh, we haven’t got time to write down. Everyone who’s going to invest, raise their hands. Everyone’s going to invest, raise their hands. And everyone is not investing, raise their hands. Oh, we almost make. We must have almost made it. All right? So notice what happened here. Give another round of applause of Patrick. I think you did a good job there. But there’s a lesson here. The lesson here is the game didn’t change.

[译文 45]

但他发表的这个演讲，他比我更有激励性，对吧？但他让人们没有把钱取出来。所以我想做的是，我想找班里的一个人来演示一下。现在大家都理解这个游戏了，都理解这两个均衡，都理解其中一个均衡更好。让我们再玩一次这个游戏。让我们重新选择这个游戏，但在开始之前，我要把话筒递给Patrick，Patrick将有整整五秒钟的时间来说服你们。站起来，站起来，做好准备，Patrick将有五秒钟来说服你们，不管他想说什么。你们可以猜猜他会说什么，开始。好吧，显然如果我们所有人都投资，我们都会更好，所以每个人都应该投资。好，好。现在让我们看看这会不会有效。让我们为Patrick鼓掌。我觉得你做得很好。但这里有一个教训。这个教训是游戏本身没有改变。

[段 46]

It’s the same game that we played three times already. This was the fourth time we played it. We had a totally different response in playing this time, right? Almost all of you, the vast majority of you, perhaps even 90% of you, invested this time. Right? And you did so in response to Patrick, but Patrick wasn’t putting any money down. He wasn’t bribing you. He wasn’t writing a contract with you. He wasn’t threatening to break your legs. He just was pointing out it’s a good idea. 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 beta in the prisoner’s dilemma than if we choose alpha. Roughly the same speech. And what will you have done in the prisoner’s dilemma? You’d have all chosen alpha anyway. So Patrick trying to persuade you or Patrick communicating to you that you do better by choosing beta in the prisoner’s dilemma doesn’t work. But here, don’t go yet, here it does work. Why is Patrick persuasive in this game, but he isn’t persuasive in the prisoner’s dilemma? Yeah, can we get the mic on Katie again? Why is Patrick persuasive in this game? Why is Patrick persuasive in this? game and not before.

[译文 46]

这是我们之前玩过三次的同一个游戏。这是我们第四次玩它。我们这次的反应完全不同，对吧？几乎你们所有人，可能高达90%的你们，这次都投资了。对吧？你们这样做是对Patrick的回应，但Patrick没有投入任何钱。他没有贿赂你们。他没有和你们签订合同。他没有威胁要打断你们的腿。他只是在指出这是一个好主意。现在回想一下囚徒困境。在囚徒困境中，如果Patrick，Patrick可以站起来发表同样的演讲，说，看，如果我们所有人都选择贝塔而不是阿尔法，我们都会更好。大致是同样的演讲。在囚徒困境中你们会怎么做？你们还是会选择阿尔法。所以Patrick试图说服你们，或者Patrick告诉你们在囚徒困境中选择贝塔会做得更好，这在囚徒困境中是不起作用的。但在这里，别急着走，在这里它确实起作用了。为什么Patrick在这个游戏中具有说服力，但在囚徒困境中却不具有说服力？我们能把话筒递给Katie吗？为什么Patrick在这个游戏中有说服力，但在之前没有？

[段 47]

He’s not trying to persuade us to play as strictly yeah can we get the mic on Katie again yeah why is Patrick persuasive in this game and not before he’s not trying to persuade us to play a strictly dominated strategy he’s not trying to get you to play a strictly dominated strategy and more than that he’s trying to persuade you to play what to play a Nash equilibrium all right so there’s a lesson here in coordination problems unlike prisoner’s dilemma unlike prisoner’s dilemma communication just communication no contract, communication can help. And in particular, what we can persuade each other to do is to play the other Nash equilibrium. And this gives us one more motivation for a Nash equilibrium. In a president’s lemma to get out of it, we needed a contract, we needed side payments, we needed to change the payoffs of the game. But a Nash equilibrium can be a self-enforcing agreement. The Nash equilibrium can be self-enforcing agreements. 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, all right? We’re going to end up doing the right thing here because it’s in our own interest to do so.

[译文 47]

他并不是试图说服我们玩一个严格被支配的策略，是的，我们能把话筒递给Katie吗？是的，为什么Patrick在这个游戏中有说服力，但在之前没有？他并不是试图让你们玩一个严格被支配的策略，不仅如此，他试图说服你们去玩——去玩什么——一个纳什均衡，好吧。所以在协调问题中有一个教训，与囚徒困境不同，与囚徒困境不同，仅仅是沟通——没有合同——沟通是有帮助的。特别是，我们能互相说服去做的是去玩另一个纳什均衡。这给了我们另一个研究纳什均衡的动力。在谢林定理中，为了摆脱它，我们需要合同，需要侧向支付，需要改变游戏的收益。但纳什均衡可以是一个自我执行的协议。纳什均衡可以是自我执行的协议。我们可以同意我们将在这个游戏中选择投资，而且实际上我们会不经过任何侧向支付、不经过任何人威胁打断你的腿、不经过任何合同、不经过任何监管或法律的情况下就选择投资——我假设Patrick没有那么暴力，好吧？我们最终会做正确的事情，因为这样做符合我们自己的利益。

[段 48]

All right. So coordination problems, we’ve agreed, all over society, whether it comes to bank runs or bubbles, we can talk about that, bubbles in the market, or fashion in the Midwest, all over society, communication can make a difference. And we’ll pick that theme up on Monday.

[译文 48]

好的。协调问题，我们已经达成共识，遍布整个社会，无论是银行挤兑还是泡沫——我们可以谈谈泡沫，市场泡沫——还是中西部的时尚，遍布整个社会，沟通可以产生差异。我们将在周一继续探讨这个主题。