Game Theory Lecture 5 | Game Theory

Chapter 1.

第一章。

Nash Equilibrium: Definition [00:00:00] Professor Ben Polak: Okay, so last time we came across a new idea, although it wasn't very new for a lot of you, and that was the idea of Nash Equilibrium.

纳什均衡：定义 [00:00:00] Ben Polak 教授：好的，上次我们遇到了一个新想法，尽管它对你们很多人来说并不是很新，这就是纳什均衡的想法。

What I want to do today is discuss Nash Equilibrium, see how we find that equilibrium into rather simple examples.

我今天想做的是讨论纳什均衡，看看我们如何通过相当简单的例子找到这种均衡。

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.

然后在后半天，我想看看一个应用程序，我们可以在其中真正享受一些乐趣并玩游戏。

At least I hope it's fun.

至少我希望这很有趣。

But let's start by putting down a formal definition.

但让我们首先给出一个正式的定义。

We only used a rather informal one last week, so here's a formal one.

上周我们只使用了一个相当非正式的，所以这里是一个正式的。

A strategy profile--remember a profile is one strategy for each player, so it's going to be S1*, S2*, all the way up to SM* if there are M players playing the game--so this profile is a Nash Equilibrium (and I'm 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*, i is part of that profile is a best response to the other players' choices.

策略配置文件 - 请记住，配置文件是每个玩家的一种策略，因此如果有 M 个玩家玩游戏，它将是 S1*，S2*，一直到 SM* - 所以这个配置文件是纳什均衡（从现在起我将在纳什均衡的班级中写 NE）如果，对于每个 i – 所以对于每个玩家 i，她的选择 – 所以她在这里的选择是 Si*，i 是该配置文件的一部分是最好的回应其他玩家的选择。

Of course, the other players' choices here are S--i* so everyone is playing a best response to everyone else.

当然，这里其他玩家的选择是 S--i*，所以每个人都在对其他人做出最好的反应。

Now, this is by far the most commonly used solution concept in Game Theory.

现在，这是迄今为止博弈论中最常用的解决方案概念。

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.

因此，那些正在面试麦肯齐或其他公司的人，你会发现他们会期望你知道这是什么。

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.

所以知道它是什么的原因之一是因为它在教科书中，它会在很多应用程序中使用，它会在你的麦肯齐面试中使用。

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.

这不是一个很好的理由，我当然不希望你得出这样的结论：现在我们已经达到了纳什均衡，我们所做的一切都知道在某种意义上是无关紧要的。

That's not the case.

事实并非如此。

It's not always going to be the case that people always play a Nash Equilibrium.

人们并不总是遵循纳什均衡。

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.

比如说我们玩数字游戏的时候，选择一个数字的游戏，我们上周或者上次已经讨论过，那个游戏的均衡是每个人都选一个，但是当我们真正玩这个游戏的时候，平均值比这个要高得多：平均值大约是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.

确实，当我们反复玩时，它似乎收敛于 1，但是当我们第一次玩一杆时，游戏的玩法并不是纳什均衡。

So we shouldn't form the mistake of thinking people always play Nash Equilibrium or people, "if they're rational," play Nash Equilibrium.

因此，我们不应该错误地认为人们总是玩纳什均衡，或者人们“如果他们是理性的”，就会玩纳什均衡。

Neither of those statements are true.

这些说法都不正确。

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.

尽管如此，除了其他人使用纳什均衡这一事实之外，还有一些很好的理由来考虑纳什均衡，让我们稍微讨论一下这些。

So I want to put down some motivations here--the first motivation we already discussed last time.

所以我想在这里写下一些动机——我们上次已经讨论过的第一个动机。

In fact, somebody in the audience mentioned it, and it's the idea of "no regrets." So what is this idea?

事实上，有观众提到过，那就是“不后悔”。那么这个想法是什么？

It says, suppose we're looking at a Nash Equilibrium.

它说，假设我们正在研究纳什均衡。

If we hold the strategies of everyone else fixed, no individual i has an incentive to deviate, to move away.

如果我们保持其他所有人的策略固定，那么任何人都没有动力去偏离、离开。

Alright, I'll say it again.

好吧，我再说一遍。

Holding everyone else's actions fixed, no individual has any incentive to move away.

如果其他人的行为固定不变，那么没有人有任何动力离开。

Let me be a little more careful here; no individual has any strict incentive to move away.

让我在这里更加小心一点；没有人有任何严格的动机离开。

We'll see if that actually matters.

我们会看看这是否真的重要。

So no individual can do strictly better by moving away.

因此，没有人可以通过搬走来做得更好。

No individual can do strictly better by deviating, holding everyone else's actions.

严格意义上来说，没有人可以通过偏离其他人的行动来做得更好。

So why I call that "no regret"?

那么为什么我称之为“不后悔”呢？

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.

这意味着，玩完游戏后，假设你确实玩了纳什均衡，然后你回顾自己所做的事情，现在你知道其他人都做了什么，你会说：“我对自己的行为感到后悔吗？”答案是：“不，我不后悔我的行为，因为我已经尽力了，就像他们所做的那样。”因此，这似乎是我们为什么应该关心纳什均衡的一个相当重要的中心思想。

Here's a second idea, and we'll see others arise in the course of today.

这是第二个想法，我们将在今天看到其他想法的出现。

A second idea is that a Nash Equilibrium can be thought of as self-fulfilling beliefs.

第二个想法是纳什均衡可以被认为是自我实现的信念。

So, in the last week or so we've talked a fair amount about beliefs.

所以，在过去一周左右的时间里，我们已经谈论了很多关于信仰的话题。

If I believe the goal keeper's going to dive this way I should shoot that way and so on.

如果我相信守门员会以这种方式扑球，我就应该以这种方式射门，依此类推。

But of course we didn't talk about any beliefs in particular.

但当然我们没有特别谈论任何信仰。

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.

这些信念，如果我相信——如果游戏中的每个人都相信其他人都会在特定的纳什均衡中发挥自己的作用，那么每个人实际上都会在纳什均衡中发挥自己的作用。

Now, why?

现在，为什么？

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?

如果每个人都相信其他人都在这个特定的纳什均衡中发挥自己的作用，那么为什么会出现这样的情况，这是如此令人满足并且人们实际上会这样做呢？

Why is that the case?

为什么会这样呢？

Anybody?

有人吗？

Can we get this guy in red?

我们能把这个穿红衣服的人抓起来吗？

Student: Because your Nash Equilibrium matches the best response against both.

学生：因为你的纳什均衡与针对两者的最佳反应相匹配。

Professor Ben Polak: Exactly, so it's really--it's almost a repeat of the first thing.

本·波拉克教授：确实如此，这几乎是第一件事的重复。

If I think everyone else is going to play their particular--if I think players 2 through N are going to play S2* through SN*--then by definition my best response is to play S1* so I will in fact play my part in the Nash Equilibrium.

如果我认为其他人都会玩他们的特定游戏——如果我认为玩家 2 到 N 会玩 S2* 到 SN*——那么根据定义，我最好的反应就是玩 S1*，所以我实际上会在纳什均衡中扮演我的角色。

Good, so as part of the definition, we can see these are self-fulfilling beliefs.

很好，作为定义的一部分，我们可以看到这些是自我实现的信念。

Let's just remind ourselves how that arose in the example we looked at the end last time.

让我们提醒自己，在我们上次看到的例子中，这是如何出现的。

I'm not going to go back and re-analyze it, but I just want to sort of make sure that we followed it.

我不会回去重新分析它，但我只是想确保我们遵循了它。

So, we had this picture last time in the partnership game in which people were choosing effort levels.

所以，我们上次在伙伴关系游戏中看到了这样的画面，人们在其中选择努力水平。

And this line was the best response for Player 1 as a function of Player 2's choice.

根据玩家 2 的选择，这条线是玩家 1 的最佳响应。

And this line was the best response of Player 2 as a function of Player 1's choice.

这条线是玩家 2 根据玩家 1 的选择做出的最佳反应。

This is the picture we saw last time.

这是我们上次看到的照片。

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.

让我们看看这些——纳什均衡是什么已经不是什么秘密了：纳什均衡是两条线的交叉点——但让我们看看它是如何映射到我们刚才所说的这两个动机的。

So, how about self-fulfilling beliefs?

那么，自我实现的信念又如何呢？

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.

好吧，如果玩家——抱歉，我输入了 1，那应该是 2——如果玩家 1 相信玩家 2 将选择这个策略，那么玩家 1 应该选择这个策略。

If Player 1 thinks Player 2 should take this strategy, then Player 1 should choose this strategy.

如果玩家 1 认为玩家 2 应该采取这个策略，那么玩家 1 应该选择这个策略。

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.

如果玩家1认为玩家2正在选择这个策略，那么玩家I应该选择这个策略，依此类推；这就是最佳回应的含义。

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.

但如果玩家 1 认为玩家 2 正在执行她的纳什策略，那么玩家 1 的最佳反应就是执行他的纳什策略。

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.

相反，如果玩家 2 认为玩家 1 正在采用他的纳什策略，那么玩家 2 的最佳反应确实是采用她的纳什策略。

So, you can that's a self-fulfilling belief.

所以，你可以这是一个自我实现的信念。

If both people think that's what's going to happen, that is indeed what's going to happen.

如果两个人都认为这就是将要发生的事情，那么这确实就是将要发生的事情。

How about the idea of no regrets?

不后悔的想法怎么样？

So here's Player 1; she wakes up the next morning--oh I'm sorry it was a he wasn't it?

这是玩家 1；第二天早上她醒来——哦，对不起，那是他，不是吗？

He wakes up the next morning and he says, "I chose S1*, do I regret this?" Well, now he knows what Player 2 chose; Player 2 chose S2* and he says, "no that's the best I could have done.

第二天早上他醒来后说：“我选择了 S1*，我会后悔吗？”好吧，现在他知道玩家 2 选择了什么；玩家 2 选择了 S2*，他说：“不，这是我能做到的最好结果。

Given that Player 2 did in fact choose S2*, I have no regrets about choosing S1*; that in fact was my best response." Notice that wouldn't be true at the other outcome.

鉴于玩家 2 事实上选择了 S2*，我对选择 S1* 并不后悔；这实际上是我最好的回应。”请注意，在其他结果中情况并非如此。

So, for example, if Player 1 had chosen S1* but Player 2 had chosen some other strategy, let's say S2 prime, then Player I would have regrets.

因此，举例来说，如果玩家 1 选择了 S1*，但玩家 2 选择了其他策略，比如说 S2 prime，那么玩家 I 就会后悔。

Player I would wake up the next morning and say, "oh I thought Player 1 was going to play S2*; in fact, she chose S2 prime.

玩家 I 会在第二天早上醒来并说：“哦，我以为玩家 1 会玩 S2*；事实上，她选择了 S2 prime。

I regret having chosen S1*; I would have rather chosen S1 prime.

我后悔选择了S1*；我宁愿选择S1 prime。

So, only at the Nash Equilibrium are there no regrets.

所以，只有纳什均衡才没有遗憾。

Everyone okay with that?

大家都同意吗？

This is just revisiting really what we did last time and underlining these points.

这只是回顾我们上次所做的事情并强调这些要点。

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.

所以，我今天想花很多时间来适应纳什均衡的想法并试图找到纳什均衡。

(I got to turn off that projector that's in the way there.

（我必须关掉挡在路上的投影仪。

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.

这会让灯光变得很乱吗？）好吧，所以我想做的是我想看一些非常简单的游戏，从少量的玩家开始，以及少量的策略，我希望我们习惯如何在这些简单的游戏中找到纳什均衡。

We'll start slowly and then we'll get a little faster.

我们会慢慢开始，然后会加快一点。

So, let's start with this game, very simple game with two players.

那么，让我们从这个游戏开始，这是一个只有两个玩家的非常简单的游戏。

Each player has three strategies and I'm not going to motivate this game.

每个玩家都有三种策略，我不会激励这个游戏。

It's just some random game.

这只是一些随机游戏。

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).

玩家 1 可以选择上、中、下，玩家 2 可以选择左、中、右，收益如下： (0,4) (4,0) (5,3) (4,0) (0,4) (5,3) 再次 (3,5) (3,5) 和 (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.

所以，我们可以讨论——如果我们有更多时间，我们实际上可以玩这个游戏——但这不是一个非常令人兴奋的游戏，所以让我们稍后再玩，相反，让我们尝试找出这个游戏中的纳什均衡是什么以及我们将如何找到它。

The way we're going to go about finding them is going to mimic what we did last time.

我们寻找它们的方式将模仿我们上次所做的。

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.

上次，我们有一个更复杂的游戏，其中两个玩家具有连续的策略，我们所做的是找出玩家 1 的最佳反应和玩家 2 的最佳反应：玩家 1 对玩家 2 所做的事情的最佳反应以及玩家 2 对玩家 1 所做的事情的最佳反应；然后我们看看它们重合的地方，那就是纳什均衡。

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.

我们将在这个简单的游戏中执行完全相同的操作，因此我们首先要弄清楚玩家 1 的最佳响应是什么样的。

So, in particular, what would be Player 1's best response if Player 2 chooses left?

那么，特别是，如果玩家 2 选择左边，玩家 1 的最佳反应是什么？

Let's get the mikes up so I can sort of challenge people.

让我们拿起麦克风，这样我就可以挑战别人了。

Anybody?

有人吗？

Not such a hard question.

不是一个很难的问题。

Do you want to try the woman in the middle?

你想尝试一下中间的女人吗？

Who's closest to the woman in the middle?

谁离中间的女人最近？

Yeah.

是的。

Professor Ben Polak: Okay, so Player 1's best response in this case is middle, because 4 is bigger than 0, and it's bigger than 3.

Ben Polak 教授：好的，所以在这种情况下，玩家 1 的最佳反应是中间，因为 4 大于 0，而且又大于 3。

So, to mark that fact what we can do is--let's put a circle--let's make it green--let's put a circle around that 3.

因此，为了标记这一事实，我们可以做的是——让我们画一个圆圈——让我们把它变成绿色——让我们在 3 周围画一个圆圈。

Not hard, so let's do it again.

不难，所以我们再做一次。

What is Player 1's best response if Player 2 chooses center?

如果玩家 2 选择中锋，玩家 1 的最佳反应是什么？

Let's get somebody on the other side.

让我们在另一边找人吧。

(Somebody should feel free to cold call somebody here.) How about cold calling the guy with the Yale football shirt on?

（有人应该随意给这里的某人打电话。）给穿着耶鲁大学足球衫的家伙打电话怎么样？

There we go.

我们开始吧。

Professor Ben Polak: All right, so up is the correct answer.

Ben Polak 教授：好的，向上就是正确答案。

(So, one triumph for Yale football).

（所以，这是耶鲁橄榄球队的一场胜利）。

So 4 is bigger than 3, bigger than 0, so good, thank you.

所以4比3大，比0大，很好，谢谢。

Ale why don't you do the same?

艾尔你为什么不做同样的事情呢？

Why don't you cold call somebody who's going to tell me what's the best response for Player 1 to right.

你为什么不打电话给某人，让他告诉我玩家 1 的最佳应对方式是什么。

Shout it out.

大声喊出来。

Professor Ben Polak: Down, okay so best response is down because 6 is bigger than 5, which is bigger than 5; I mean 6 is bigger than 5.

Ben Polak 教授：向下，好吧，所以最好的反应是向下，因为 6 比 5 大，而 5 又比 5 大；我的意思是6比5大。

So what we've done here is we've found Player 1's best response to left, best response to center, and best response to right and in passing notice that each of Player 1 strategies is the 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 1.

所以我们在这里所做的是，我们找到了玩家 1 对左侧的最佳响应、对中心的最佳响应和对右侧的最佳响应，并顺便注意到玩家 1 的每个策略都是对某些事物的最佳响应，因此我们在这里的统治论点不会消除任何内容，并且我们在这里对玩家 1 的永远不是最佳响应论点也不会消除任何内容。

Let's do the same for Player 2; so why don't I keep the mikes doing some cold calling, so why don't we--you want to cold call somebody at the back to tell me what is Player 2's best response against up?

让我们对玩家 2 做同样的事情；那么我为什么不让麦克风做一些冷叫，那么我们为什么不——你想冷叫后面的人告诉我玩家 2 对 up 的最佳反应是什么？

Professor Ben Polak: So, the gentleman in blue says left because 4 is bigger 3, and 3 is bigger than 0.

Ben Polak教授：所以，蓝衣先生说左，因为4比3大，而3比0大。

Let's switch colors and switch polygons and put squares around these.

让我们切换颜色并切换多边形并在它们周围放置正方形。

I don't insist on the circles and the squares.

我不坚持圆形和方形。

If you have a thing for hexagons you can do that to0--whatever you want.

如果你喜欢六边形，你可以做任何你想要的东西。

What's Player 2's--let's write it in here--the answer, the answer was that the best response was left, and Player 2's best response to middle--so do you want to grab somebody over there?

玩家2的是什么——我们就写在这里吧——答案，答案是留下了最好的反应，而玩家2对中间的最佳反应——所以你想抓住那边的人吗？

Shout it out!

大声喊出来！

Professor Ben Polak: Because 4 is bigger than 3, and 3 is bigger than 0, so that's center.

Ben Polak 教授：因为 4 比 3 大，而 3 又比 0 大，所以这是中心。

So, in my color coding that puts me at--that gives me a square here.

所以，在我的颜色编码中，这给了我一个正方形。

And finally, Player 2's best response to down?

最后，玩家 2 对倒下的最佳反应是什么？

And your turn Ale, let's grab somebody.

轮到你了，我们来找个人吧。

Professor Ben Polak: Right, okay good.

Ben Polak 教授： 好的，好的。

Because 6 is bigger than 5 again, so here we go.

因为 6 又比 5 大，所以我们开始吧。

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.

我们现在所做的就是找到玩家 1 的最佳响应函数，这与我们在这里所做的寻找最佳响应线类似。

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.

在这里，我们将其绘制为白色的直线，但我们也可以将其绘制为一系列绿色的小圆圈；它看起来像这样。

The same idea, I'm not going to do the whole thing but there would be a whole bunch of circles looking like this.

同样的想法，我不会做整个事情，但会有一大堆看起来像这样的圆圈。

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.

然后我们找到了玩家 2 对玩家 1 的每个选择的最佳反应，我们使用了粉红色的矩形，这与我们在这里所做的想法相同。

Here we did it in continuous strategies in calculus, but it's the same idea.

这里我们在微积分的连续策略中做到了这一点，但它是相同的想法。

So, imagine I'm drawing lots of pink rectangles.

所以，想象一下我正在画很多粉红色的矩形。

And again, I'm not going to do it, but you can do it in your notes; same basic idea.

再说一次，我不会这样做，但你可以在笔记中这样做；基本思想相同。

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--do you want to cold call somebody?

正如纳什均衡必须是这些最佳响应线在这里重合的地方，因为这是每个玩家对彼此做出最佳响应的点，所以这里的纳什均衡是——你想给某人打电话吗？

Do you want to just grab somebody in the row behind you or something, wherever?

你想抓住你后面一排的某个人或者什么东西吗？

Anybody?

有人吗？

Yeah, I think you in the Italia soccer shirt; I think you're going to get picked on, so okay what's the Nash Equilibrium here?

是的，我想你穿着意大利足球衫；我认为你会被选中，那么纳什均衡是什么？

Professor Ben Polak: So the down-right square.

Ben Polak 教授：右下角的方块。

So, the Nash Equilibrium here is--no prizes--no World Cup for that one--is down right.

所以，这里的纳什均衡是——没有奖品——没有世界杯——是正确的。

So, why is that the Nash Equilibrium?

那么，为什么会出现纳什均衡呢？

Because at that point Player 1 is playing a best response to Player 2 and Player 2 is playing a best response to Player I.

因为此时玩家 1 正在对玩家 2 做出最佳响应，而玩家 2 正在对玩家 I 做出最佳响应。

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.

现在，我想尝试说服你们，尤其是那些担心家庭作业的人，这不是火箭科学。

It's not hard to find Nash Equilibria in games.

在游戏中找到纳什均衡并不难。

It didn't take us very long, and we went pretty slow actually.

我们并没有花很长时间，而且实际上我们走得很慢。

So let's look at another example.

让我们看另一个例子。

Oh, before I do, notice this--before I leave this game I'm just going to make one other remark.

哦，在我这样做之前，请注意这一点——在我离开这场游戏之前，我只想再说另一句话。

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.

请注意，在这个游戏中，玩家 1 的每个策略都是对某事的最佳响应，而玩家 2 的每个策略都是对某事的最佳响应。

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.

所以，如果我们使用课堂上前面的方法，也就是说，删除占主导地位的策略或删除永远不是最佳响应的策略，我们在这个游戏中将一事无成。

So, Nash Equilibrium goes a little further in narrowing down our predictions.

因此，纳什均衡进一步缩小了我们的预测范围。

But we also learned something from that.

但我们也从中学到了一些东西。

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.

上次，在过去的几周里，我们认为，理性，甚至理性的共同知识，甚至理性的常识，除了删除占主导地位的策略，或者如果你愿意的话，删除永远不是最佳反应的策略之外，并不能真正让我们走得更远。

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.

所以，在这里我们得出的结论是，这个游戏的纳什均衡是正确的，这是一个非常特殊的预测，但请注意，一个完全理性的玩家可以在这里选择中间。

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.

他们可以选择中间，玩家 1 可以选择中间的原因是——可能是这样——他们说（理性地）他们应该选择中间，因为他们认为玩家 2 选择了左边。

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.

然后你说：“那么，你为什么认为玩家 2 会选择左边呢？”玩家 1 可能会说：“我认为玩家 2 会选择左边，因为玩家 2 认为我会上场。”然后你说：“但是玩家 2 怎么可能认为你会参加比赛呢？”然后球员 1 会说：“我认为球员 2 认为我会打中锋，因为球员 2 认为我认为他会打中锋。”然后你可以说，“玩家 2 怎样玩……”等等，等等。你可以看到你可以在那里解决一个小循环。

Nobody would be irrational about anything: Everything would be perfectly well justified in terms of beliefs.

没有人会对任何事情变得非理性：就信仰而言，一切都将是完全合理的。

It's just we wouldn't have a nice fixed point.

只是我们没有一个好的固定点。

We wouldn't have a nice point where it's a simple argument.

如果这是一个简单的论证，我们不会有一个好的观点。

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.

在右下的情况下，玩家 1 认为可以向下打，因为他认为 2 会打正确，而玩家 2 认为他们会打正确，因为他认为玩家 1 会打向下。

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.

因此，只是为了强调我在那里说得相当混乱，理性和这些类型的论点不应该让我们得出这样的结论：人们必然会玩纳什均衡。

We need a little bit more; we need a little bit more than that.

我们还需要一点；我们需要的还不止于此。

Nevertheless, we are going to focus on Nash Equilibrium in the course.

尽管如此，我们将在课程中关注纳什均衡。

Let's have a look at another example.

让我们看另一个例子。

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).

再次强调，我们现在将保持简单，并保持两人三策略游戏；上、中、下、左、中、右，这次的收益如下：(0,2) (2,3) (4,3) (11,1) (3,2) (0,0) (0,3) (1,0) 和 (8,0)。

So, this is a slightly messier game.

所以，这是一个稍微混乱的游戏。

The numbers are really just whatever came into my head when I was writing it down.

这些数字实际上就是我写下来时脑子里想到的任何数字。

Once again, we want to find out what the Nash Equilibrium is in this game and our method is exactly the same.

再次，我们想找出这个博弈中的纳什均衡是什么，我们的方法是完全一样的。

We're going to, for each player, figure out their best responses for each possible choice of the other player.

我们将为每个玩家找出他们对其他玩家的每个可能选择的最佳反应。

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.

所以，与其把它写在上面——让我去我的绿色圆圈和红色方块，让我再次拿起我的麦克风，这样我们就可以给人们打电话。

Can we get the--where's the mike?

我们能找到——麦克风在哪里吗？

Thank you.

谢谢你。

So, Ale do you want to just grab somebody and ask them what's the best response against left?

那么，Ale，你想抓住某人并问他们对左派的最佳反应是什么吗？

Grab anybody.

抓住任何人。

What's the best one against left?

对抗左派最好的方法是什么？

Professor Ben Polak: Middle, okay.

Ben Polak 教授：中等，好吧。

Good, so middle is the best response against left, because 11 is bigger than 0.

很好，所以中间是对左边的最佳反应，因为 11 比 0 大。

Myto , do you want to grab somebody?

米托，你想抓人吗？

What's the best response against center?

针对中心的最佳回应是什么？

Professor Ben Polak: Middle again because 3 is bigger than 2 is bigger than 1.

Ben Polak 教授：又是中间，因为 3 大于 2 大于 1。

And grab somebody at the back and tell me what the best response is against right?

然后抓住后面的一个人，告诉我最好的回应是什么，对吗？

Anybody just dive in, yep.

任何人都可以潜入其中，是的。

Professor Ben Polak: Okay down, good.

Ben Polak 教授：好的，好的。

Let's do the same for the column player, so watch the column player's--Ale, find somebody; take the guy who is two rows behind you who is about to fall asleep and ask him what's the best response to up?

让我们对专栏玩家做同样的事情，所以观察专栏玩家的——Ale，找人；带着你后面两排的那个快要睡着的人问他最好的反应是什么？

Professor Ben Polak: For Player 2.

Ben Polak 教授：对于玩家 2。

What's Player 2's best response for up?

玩家 2 对 up 的最佳回应是什么？

Sorry that's unfair, pick on somebody else.

抱歉，这不公平，请选择其他人。

That's all right; get the guy right behind you.

没关系；让那个人就在你身后。

What's the best response for up?

对 up 的最佳回应是什么？

Professor Ben Polak: So, this is a slightly more tricky one.

Ben Polak 教授：所以，这是一个稍微棘手的问题。

The best response to up is either c or r.

对 up 的最佳响应是 c 或 r。

This is why we got you to sign those legal forms.

这就是我们让您签署这些法律表格的原因。

Best ones to up is either c or r.

最好的选择是 c 或 r。

The best response to middle?

对中间的最佳反应？

Professor Ben Polak: Is center, thank you.

Ben Polak 教授： 是中间，谢谢。

And the best response to down?

对下来的最佳反应是什么？

Professor Ben Polak: So, the best response to down is left.

本·波拉克教授：所以，对羽绒服的最佳反应就是留下来。

Here again, it didn't take us very long.

在这里，我们并没有花很长时间。

We're getting quicker at this.

我们在这方面做得越来越快。

The Nash Equilibrium in this case is--let's go back to the guy who was asleep and give him an easier question this time.

在这种情况下，纳什均衡是——让我们回到那个睡着的人，这次给他一个更简单的问题。

So the Nash Equilibrium in this case is?

那么这种情况下的纳什均衡是什么呢？

Professor Ben Polak: Exactly, so the middle of center.

Ben Polak 教授：没错，所以在中心的中间。

Notice that this is a Nash Equilibrium.

请注意，这是纳什均衡。

Why is it the Nash Equilibrium?

为什么是纳什均衡？

Because each player is playing a best response to each other.

因为每个球员都在对对方做出最好的回应。

If I'm Player 1 and I think that Player 2 is playing center, I should play middle.

如果我是球员 1，并且我认为球员 2 打中锋，那么我应该打中锋。

If I'm Player 2, I think Player 1 is playing middle, I should play center.

如果我是球员2，我认为球员1打中锋，我应该打中锋。

If, in fact, we play this way neither person has any regrets.

事实上，如果我们这样玩，任何人都不会后悔。

Notice they didn't do particularly well in this game.

请注意，他们在这场比赛中表现不佳。

In particular, Player 1 would have liked to get this 11 and this 8, but they don't regret their action because, given that Player 2 played center, the best they could have got was 3, which they got by playing middle.

特别是，玩家 1 希望得到这个 11 和这个 8，但他们并不后悔自己的行为，因为考虑到玩家 2 打中锋，他们最好得到的就是 3，这是他们通过打中锋得到的。

Notice in passing in this game, that best responses needn't be unique.

请注意，在玩这个游戏时，最佳反应不必是唯一的。

Sometimes they can be a tie in your best response.

有时，它们可能与您的最佳回应并列。

It could happen.

这可能会发生。

So, what have we seen?

那么，我们看到了什么？

We've seen how to find Nash Equilibrium.

我们已经了解了如何找到纳什均衡。

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.

显然，它与最佳响应的想法密切相关，这是我们在过去一周左右一直在开发的想法。

But let's go back earlier in the course, and ask how does it relate to the idea of dominance?

但让我们回到课程的前面，问一下它与统治的概念有何关系？

This will be our third concept in this course.

这将是本课程中我们的第三个概念。

We had a concept about dominance, we had a concept about best response, and now we're at Nash Equilibrium.

我们有一个关于支配地位的概念，我们有一个关于最佳反应的概念，现在我们处于纳什均衡。

It's, I think, obvious how it relates to best response: it's when best responses coincide.

我认为，它与最佳响应的关系是显而易见的：最佳响应同时发生。

How about how it relates to dominance?

它与统治力有何关系？

Well, to do that let's go back.

好吧，为了做到这一点，让我们回去吧。

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.

我们要做的就是将纳什均衡与我们的统治观念联系起来，要做到这一点，一个明显的起点就是回到我们以前见过的游戏。

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).

因此，在这个游戏中，玩家 1 和玩家 2 选择 ά 和 β，收益为 (0,0) (3,-1) (-1,3) 和 (1,1)。

So, this is the game we saw the first time.

所以，这是我们第一次看到这个游戏。

This is the Prisoner's Dilemma.

这就是囚徒困境。

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.

我们知道在这个游戏中——我不会费心去推销它——我们知道在这个游戏中β是主导的——严格是由ά主导的。

It's something that we learned the very first time.

这是我们第一次学到的东西。

Just to check: so against ά, choosing ά gets you 0, β gets you -1.

只是为了检查一下：所以针对 ά，选择 ά 会让你得到 0，β 会让你得到 -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.

对抗 β，选择 ά 会得到 3，β 会得到 1，无论哪种情况，ά 都绝对更好，因此 ά 严格支配 β，当然，对于列玩家来说也是如此，因为游戏是完全对称的。

So now, let's find the Nash Equilibrium in this game.

现在，我们来求这个博弈中的纳什均衡。

I think we know what it's going to be, but let's just do it in this sort of slow way.

我想我们知道会发生什么，但让我们以这种缓慢的方式来做吧。

So, the best response to ά must be ά.

因此，对 ά 的最佳响应必定是 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.

对 β 的最佳反应一定是 ά，对于列玩家来说，对 ά 的最佳反应一定是 ά，对 β 的最佳反应一定是 ά。

Everyone okay with that?

大家都同意吗？

I'm just kind of--I'm rushing it a bit because it's kind of obvious, is that right?

我只是有点——我有点仓促，因为这很明显，是吗？

So, the Nash Equilibrium in this game is (ά, ά).

所以，本博弈的纳什均衡为(ά,ά)。

In other words, it's what we would have arrived at had we just deleted strictly dominated strategies.

换句话说，如果我们删除严格占优策略，我们就会得到这样的结果。

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.

所以，这里有一个 ά 严格支配 β 的情况，果然纳什均衡重合，它给了我们相同的答案，两人在这场博弈中都选择了 ά。

So, there's nothing--there's no news here, I'm just checking that we're not getting anything weird going on.

所以，没有什么——这里没有新闻，我只是检查一下我们没有发现任何奇怪的事情。

So, let's just be a bit more careful.

所以，我们要小心一点。

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.

我们怎么知道情况是这样的——我要断言，没有严格支配的策略——在这种情况下是β——没有严格支配的策略可以在纳什均衡中发挥作用。

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.

我声称——这是一件好事，因为我们希望这些想法能够一致——我声称在纳什均衡中不可能出现严格占优的策略。

Why is that the case?

为什么会这样呢？

There's a guy up here, yeah.

上面有一个人，是的。

Student: The strictly dominated strategy isn't the best response of anything.

学生：严格占优策略并不是最好的应对策略。

Student: It should be the best response to find the Nash Equilibrium.

学生：这应该是找到纳什均衡的最佳反应。

Professor Ben Polak: Good, very good.

本·波拉克教授：好，非常好。

So a strictly dominated strategy is never a best response to anything.

因此，严格支配的策略从来都不是对任何事情的最佳反应。

In particular, the thing that dominates it always does better.

特别是，主导它的事物总是做得更好。

So, in particular, it can't be a best response to the thing being played in the Nash Equilibrium.

因此，特别是，这不可能是对纳什均衡中所发生的事情的最佳反应。

So that's actually a very good proof that proves that no strictly dominated strategy could ever be played in a Nash Equilibrium.

因此，这实际上是一个非常好的证明，证明在纳什均衡中不可能使用严​​格占优的策略。

But now we have, unfortunately, a little wrinkle, and the wrinkle, unfortunately, is weakly dominated--is weak domination.

但不幸的是，现在我们有一点皱纹，不幸的是，这个皱纹是弱支配的——是弱支配的。

So we've argued, it was fairly easy to argue, that no strictly dominated strategy is ever going to reappear annoyingly in a Nash Equilibrium.

因此，我们认为，很容易争论，没有任何严格支配的策略会在纳什均衡中令人烦恼地重新出现。

But unfortunately, the same is not true about weakly dominated strategies.

但不幸的是，对于弱占优策略来说情况并非如此。

And in some sense, you had a foreshadowing of this problem a little bit on the homework assignment, where you saw on one of the problems (I think it was the second problem on the homework assignment) that deleting weakly dominated strategies can lead you to do things that might make you feel a little bit uneasy.

从某种意义上说，你在作业中对这个问题有一点预兆，你在其中一个问题（我认为这是作业中的第二个问题）上看到删除弱支配策略可能会导致你做一些可能让你感到有点不安的事情。

So weak domination is really not such a secure notion as strict domination, and we'll see here as a trivial example of that.

因此，弱统治实际上并不像严格统治那样安全，我们将在这里看到一个简单的例子。

And again, so here's the trivial example, not an interesting example, but it just makes the point.

再说一次，这是一个简单的例子，不是一个有趣的例子，但它只是说明了要点。

So here's a 2 x 2 game.

这是一个 2 x 2 游戏。

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).

玩家 1 可以选择向上或向下，玩家 2 可以选择向左或向右，收益非常微不足道：(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.

所以，让我们弄清楚这个游戏中的纳什均衡是什么，我不会打扰推销电话，因为这太简单了。

So the best response for Player 1, if Player 2 plays left is clear to choose up.

因此，如果玩家 2 向左玩，玩家 1 的最佳反应就是选择向上。

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.

如果玩家 2 选择正确，玩家 1 的最佳反应是——好吧，向上或向下都可以，因为无论哪种方式他都会得到 0。

So these are both best responses.

所以这些都是最好的回应。

Is that correct?

这是正确的吗？

They're both best responses; they both did equally well.

它们都是最好的回应；他们都做得同样好。

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.

相反，如果玩家 1 选择向上，玩家 2 的最佳反应肯定是选择向左，这正是我们想要的答案，但不幸的是，当玩家 1 向下选择时，玩家 2 的最佳反应要么是向左，要么是向右。

It makes no difference.

这没有什么区别。

They get 0 either way.

无论哪种方式，他们都会得到 0。

So, what are the Nash Equilibria in this game?

那么，这个博弈中的纳什均衡是什么呢？

So, notice the first observation is that there's more than one Nash Equilibrium in this game.

因此，请注意第一个观察结果是，该游戏中存在多个纳什均衡。

We haven't seen that before.

我们以前没见过这样的情况。

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.

我认为，房间里的每个人都存在纳什均衡，我希望，认为这是这场比赛中的明智预测。

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.

在这个游戏中，我想你们所有人，我希望你们所有人，如果你是玩家1，都会选择向上，而你们所有人，如果你是玩家2，都会选择左边。

Is that right?

是这样吗？

Is that correct?

这是正确的吗？

It's hard to imagine coming up with an argument that wouldn't lead you to choose up and left in this game.

很难想象提出一个不会导致你在这场游戏中选择离开的论点。

However, unfortunately, that is--this isn't unfortunate, up left is a Nash Equilibrium but so is down right.

然而，不幸的是，这并不不幸，左上是纳什均衡，右下也是。

If Player 2 is choosing right, your best response weakly is to choose down.

如果玩家 2 选择正确，你最好的弱反应就是选择向下。

If Player 1 is choosing down, Player 2's best response weakly is to choose right.

如果玩家 1 选择向下，那么玩家 2 的最佳弱反应就是选择右侧。

Here, this is arriving because of the definition of Nash; it's a very definite definition.

在这里，这是由于纳什的定义而得出的；这是一个非常明确的定义。

I deleted it now.

我现在把它删除了。

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.

当我们查看我们所说的定义时，每个人都在对彼此做出最佳反应，这就是纳什均衡；换句话说，没有玩家有严格的偏离动机。

No player can do strictly better by moving away.

严格来说，没有球员可以通过离开而做得更好。

So here at down right Player 1 doesn't do strictly better; it's just a tie if she moves away.

所以在右下方，玩家 1 并没有表现得更好；如果她搬走，那只是平局。

And Player 2 doesn't do strictly better if he moves away.

如果玩家 2 离开，严格来说他的表现也不会更好。

It's a tie.

这是一条领带。

He gets 0 either way.

无论哪种方式他都会得到 0。

So, here we have something which is going to worry us going on in the course.

所以，这里有一些事情会让我们在课程中感到担心。

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.

有时我们不仅会得到许多纳什均衡，这不应该让我们担心，这是生活的事实。

But in this case one of the Nash Equilibria seems silly.

但在这种情况下，纳什均衡之一似乎很愚蠢。

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.

如果你试图向你的室友解释并说：“我在这场比赛中预测了这两种结果”，他们会嘲笑你。

It's obvious in some sense that this has to be the sensible prediction.

从某种意义上说，这显然是明智的预测。

So, just a sort of worrying note before we move on.

所以，在我们继续之前，只是一个令人担忧的说明。

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.

所以，这非常正式，到目前为止还不是很令人兴奋，所以让我们尝试继续做一些更有趣的事情。

So, what I want to do now is I want to look at a different game.

所以，我现在想做的是我想看看不同的游戏。

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.

再次，我们将尝试在这个游戏中找到纳什均衡，但我们要做的不止于此，我们要稍微讨论一下这个游戏，这个游戏的一个特点是——为了与我们迄今为止所做的事情区分开来——我们将要看到的游戏涉及许多玩家，尽管每个玩家只有一些策略。

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.

所以，我想做的是说服你如何找到——讨论如何在游戏中找到纳什均衡，与这些游戏不同，这个游戏不只有两个玩家——它有很多玩家——但幸运的是，每个玩家的策略并不多。

So let me use this board.

那么让我使用这个板吧。

So this is going to be called The Investment Game and we're going to play this game, although not for real.

所以这将被称为投资游戏，我们将玩这个游戏，尽管不是真的。

So, the players in this game, as I've just suggested, the players are going to be you.

所以，这个游戏的玩家，正如我刚才所建议的，玩家将是你。

So, everyone who is getting sleepy just looking at this kind of analysis should wake up now, you have to play.

所以，看到这样的分析就犯困的各位现在该醒醒了，你们得玩了。

The strategies in this game are very simple, the strategy sets, or the strategy alternatives.

这个游戏的策略非常简单，就是策略集，或者策略选择。

Each of you can choose between investing nothing in a class project, $0, or invest $10.

你们每个人都可以选择在课程项目中不投资、0 美元或投资 10 美元。

So, I'm sometimes going to refer to investing nothing as not investing, is that okay?

所以，我有时会把不投资称为不投资，可以吗？

That seems like a natural to do.

这似乎是很自然的事。

You're either going to invest $10 or nothing, you're not going to invest.

你要么投资 10 美元，要么什么都不投资，你就不会投资。

So that's the players and those are the strategies, so as usual we're missing something.

这就是玩家和策略，所以像往常一样我们错过了一些东西。

What we're missing are the payoffs.

我们缺少的是回报。

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.

所以这是回报；所以收益如下：如果你不投资，如果你不投资，你什么都不投资，那么你的收益就是 0 美元。

So nothing ventured nothing gained: natural thing.

所以不冒险就没有收获：自然的事情。

But if you do invest $10, remember each of you is going to invest $10 then your individual payoffs are as follows.

但如果您确实投资 10 美元，请记住你们每个人都会投资 10 美元，那么您的个人收益如下。

Here's the good news.

这是好消息。

You're going to get a profit of $5.

您将获得 5 美元的利润。

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.

其运作方式是，您将投资 10 美元，这样您将获得 15 美元的毛利润，减去您最初投资的 10 美元，净额为 5 美元。

So a net profit--so $5 net profit, that's the good news.

净利润——5 美元净利润，这是个好消息。

But that requires more than 90% of the class to invest, greater than or equal to 90% of the class to invest.

但这需要90%以上的班级进行投资，大于或等于90%的班级进行投资。

If more than 90% of the class invests, you're going to make essentially 50% profit.

如果班级中有超过 90% 的人进行投资，那么您基本上将获得 50% 的利润。

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.

不幸的是，坏消息是你将损失 10 美元，什么也拿不回来，所以如果班级中投资的人少于 90%，这就是净损失。

I mean a key rule here; you're not allowed to talk to each other: no communication in the class.

我在这里指的是一条关键规则；你们不被允许互相交谈：课堂上不能交流。

No hand signals, no secret winks, nothing else.

没有手势，没有秘密眨眼，没有别的。

So, everyone understand the game?

那么，大家都了解这个游戏了吗？

Including up in the balcony, everyone understand the game?

包括在阳台上，大家都懂这个游戏吗？

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.

所以，我想让你们做的——我首先应该说，我们不能真正玩这个游戏，因为你们有大约 250 个人，而我手头没有那么多现金。

So we're not--pretend we're playing this for real.

所以我们不是——假装我们是真的在玩这个。

So, without communicating I want each of you to write on the corner of your notepad whether you're going to invest or not.

因此，在没有沟通的情况下，我希望你们每个人都在记事本的一角上写下是否要投资。

You can write Y if you're going to and N if you're not going to invest.

如果您打算投资，则可以写 Y；如果您不打算投资，则可以写 N。

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.

不要互相讨论；只需在记事本的一角写下 Y（如果您打算投资）和 N（如果您不打算投资）。

Don't discuss it guys.

别讨论这个了，伙计们。

Now, show your neighbor what you did, just so you can--your neighbor can make you honest.

现在，让你的邻居看看你做了什么，这样你的邻居就能让你诚实。

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.

现在，让我们举手，所以我想做的是，我想让所有投资的人举手。

Don't look around; just raise your hands, everyone who invested?

不要东张西望；投资的大家举手吧？

Everyone who didn't invest!

没有投资的大家！

Oh that's more than 10%.

哦，超过10%了。

Let's do that again.

让我们再做一次。

So everyone who invested raised their hands …

于是所有投资的人都举手了……

and everyone who didn't invest raise their hands.

没有投资的人都举手了。

So I don't know what that is, maybe that's about half.

所以我不知道那是什么，也许大约是一半。

So now I'm thinking we should have played this game for real.

所以现在我想我们应该真正玩这个游戏。

I want to get some discussion going about this.

我想就这个问题进行一些讨论。

I'm going to discuss this for a while; there's a lot to be said about this game.

我将讨论这个问题一段时间；关于这款游戏有很多话要说。

Let me borrow that, can I borrow this?

借我一下，可以借一下吗？

So this guy; so what did you do?

所以这个家伙；那么你做了什么？

Professor Ben Polak: All right, so he's rich, that's okay.

本·波拉克教授：好吧，所以他很有钱，那没关系。

You can pay for lunch.

您可以支付午餐费用。

Who didn't invest, non-investors?

谁没有投资，非投资者？

Yeah, here's one, so why didn't you invest?

是的，这是一个，那你为什么不投资呢？

Shout it out so everyone can hear.

大声喊出来，让每个人都能听到。

Student: I didn't invest because to make a profit there needs to be at least a 2:1 chance that everyone else--that 90% invest.

学生：我没有投资，因为要盈利，其他人至少有 2:1 的机会——即 90% 的人进行投资。

Student: Yeah, you only get half back but you would lose the whole thing.

学生：是的，你只能得到一半，但你会失去全部。

Professor Ben Polak: I see, okay so you're doing some kind of expected calculation.

Ben Polak 教授：我明白了，好吧，所以你正在做某种预期的计算。

Other reasons out there?

还有其他原因吗？

What did you do?

你做了什么？

Professor Ben Polak: I'm finding the suckers in the room.

本·波拉克教授：我发现房间里有傻瓜。

Okay, so you invested and why?

好的，那么你投资了，为什么？

Student: You usually stand to gain something.

学生：你通常会有所收获。

I don't see why anybody would just not invest because they would never gain anything.

我不明白为什么有人不投资，因为他们永远不会获得任何收益。

Professor Ben Polak: So Clayton's saying only by investing can I gain something here, not investing seems kind of--it doesn't seem brave in some sense.

本·波拉克教授：所以克莱顿说只有通过投资我才能在这里有所收获，不投资似乎有点——从某种意义上来说，这似乎并不勇敢。

Anyone else?

还有其他人吗？

Student: It's basically the same game as the (1,1) (0,0) game in terms they're both Nash Equilibrium, but the payoffs aren't the same scale and you have to really be risk adverse not to invest, so I thought it would be--

学生：这与 (1,1) (0,0) 游戏基本上是相同的游戏，它们都是纳什均衡，但回报的规模不同，你必须真正规避风险才能不投资，所以我认为会是——

Professor Ben Polak: All right, so let me give this to Ale before I screw up the sound system here.

Ben Polak 教授：好吧，在我搞砸这里的音响系统之前，让我把这个交给 Ale。

Okay, so we got different answers out there.

好的，所以我们得到了不同的答案。

Could people hear each other's answer a bit?

人们能听到彼此的回答吗？

Yeah.

是的。

So, we have lots of different views out here.

所以，我们这里有很多不同的观点。

We have half the people investing and half the people not investing roughly, and I think you can make arguments either way.

我们有一半的人进行投资，一半的人没有粗略地进行投资，我认为无论哪种方式你都可以提出论据。

So we'll come back to whether it's exactly the same as the game we just saw.

所以我们会回过头来看看它是否与我们刚刚看到的游戏完全相同。

So the argument that-- I'm sorry your name--that Patrick made is it looks a lot like the game we saw before.

所以帕特里克提出的论点——对不起你的名字——看起来很像我们之前看到的游戏。

We'll see it is related, clearly.

我们会清楚地看到它是相关的。

It's related in one sense which we'll discuss now.

它在某种意义上是相关的，我们现在将讨论这一点。

So, what are the Nash Equilibria in this game?

那么，这个博弈中的纳什均衡是什么呢？

Let me get the woman up here?

让我把那个女人弄到这里来吗？

Student: No one invests and everyone's happy they didn't lose anything; or everyone invests and nobody's happy.

学生：没有人投资，每个人都很高兴他们没有损失任何东西；或者每个人都投资但没有人高兴。

Professor Ben Polak: So Kate's saying that there are two Nash Equilibria and (with apologies to Jude) I'm going to put this on the board.

本·波拉克教授：所以凯特说有两个纳什均衡，（向裘德道歉）我要把它放在黑板上。

There are two Nash Equilibria here, one is all invest and another one is no one invest.

这里有两种纳什均衡，一种是全部投资，另一种是无人投资。

These are both Nash Equilibria in this game.

这些都是本博弈中的纳什均衡。

And let's just check that they are exactly the argument that Kate said.

让我们检查一下它们是否正是凯特所说的论点。

That if everyone invests then no one would have any regrets, everyone's best response would be to invest.

如果每个人都投资，那么就没有人会后悔，每个人最好的反应就是投资。

If nobody invests, then everyone would be happy not to have invested, that would be a best response.

如果没人投资，那么大家都乐意不投资，这就是最好的回应。

It's just--in terms of what Patrick said, it is a game with two equilibria like the previous game and there were other similarities to the previous game, but it's a little bit--the equilibria in this case are not quite the same as the other game.

只是——按照帕特里克的说法，这是一个像之前的游戏一样有两个均衡的游戏，与之前的游戏还有其他相似之处，但有一点——这种情况下的均衡与另一个游戏不太一样。

In the other game that other equilibrium, the (0,0) equilibrium seemed like a silly equilibrium.

在另一个平衡的游戏中，(0,0) 平衡似乎是一个愚蠢的平衡。

It isn't like we'd ever predict it happening.Whereas here, the equilibrium with nobody investing actually is quite a plausible equilibrium.

这不像我们预测的那样会发生。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。

If I think no one else is investing then I strictly prefer not to invest, is that right?

如果我认为没有人在投资，那么我宁愿不投资，对吗？

So, two remarks about this.

因此，对此有两点评论。

Do you want to do more before I do two remarks?

在我发表两句话之前，您想再做点什么吗？

Well, let's have one remark at least.

好吧，至少让我们说一说。

How did we find those Nash Equilibria?

我们如何找到纳什均衡？

What was our sophisticated mathematical technique for finding the Nash Equilibria on this game?

我们在这个游戏中寻找纳什均衡的复杂数学技术是什么？

We should - can you get the mike on - is it Kate, is that right?

我们应该 - 你能打开麦克风吗 - 是凯特，对吗？

So how do you find the Nash Equilibria?

那么如何找到纳什均衡呢？

Professor Ben Polak: All right, so in principle you could--I mean that works but in principle, you could have looked at every possible combination and there's lots of possible combinations.

本·波拉克教授：好吧，所以原则上你可以——我的意思是，这是可行的，但原则上，你可以考虑每一种可能的组合，而且有很多可能的组合。

It could have been a combination where 1% invested and 99% didn't, and 2% invested and 98% didn't and so on and so forth.

它可能是 1% 投资而 99% 没有投资，2% 投资而 98% 没有投资等等的组合。

We could have checked rigorously what everyone's best response was in each case, but what did we actually end up doing in this game?

我们本可以严格检查每个人在每种情况下的最佳反应是什么，但我们最终在这款游戏中做了什么？

What's the method?

有什么方法呢？

The guy in--yeah.

那个家伙——是的。

Professor Ben Polak: That's true, so that certainly makes it easier.

Ben Polak 教授：确实如此，所以这肯定会让事情变得更容易。

I claim, however--I mean you're being--both of you are being more rigorous and more mathematical than I'm tempted to be here.

然而，我声称——我的意思是你们——你们俩都比我在这里想的更严谨、更数学化。

I think the easy method here--the easy sophisticated math here is "to guess." My guess is the easy thing to do is to guess what flight would be the equilibrium here and then what?

我认为这里最简单的方法——这里简单复杂的数学就是“猜测”。我的猜测是，最容易做的事情就是猜测什么飞行将是这里的平衡，然后呢？

Then check; so a good method here in these games is to guess and check.

然后检查；因此，在这些游戏中，一个好的方法是猜测和检查。

And guess and check is really not a bad way to try and find Nash Equilibria.

猜测和检查确实是尝试找到纳什均衡的不错方法。

The reason it's not a bad way is because checking is fairly easy.

这不是一个坏方法的原因是因为检查相当容易。

Guessing is hard; you might miss something.

猜测很难；你可能会错过一些东西。

There might be a Nash Equilibrium hidden under a stone somewhere.

纳什均衡可能隐藏在某处的石头下面。

In America it's a "rock." It may hidden under a rock somewhere.

在美国，它是一块“岩石”。它可能隐藏在某个地方的岩石下面。

But checking with something that you--some putative 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, nobody wants to deviate.

但是用一些你认为的均衡、一些坦率的均衡来检查它是否是一个均衡很容易，因为你所要做的就是检查没有人想要移动，没有人想要偏离。

So again, 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.

再说一次，实际上这就是你在这个游戏中最终要做的事情，而且事实证明它很容易猜测和检查，这就是你能够找到它的原因。

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, and it works pretty well.

因此，猜测和检查在这些游戏中是一种非常有用的方法，其中有很多很多玩家，但每个玩家的策略并不多，而且效果很好。

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.

好的，现在我们已经把这个游戏放在了板上，我想花一些时间讨论它，因为它很重要。

So, what I want to do now is I want to remind us what happened just now.

所以，我现在想做的就是提醒我们刚才发生的事情。

So, what happened just now?

那么，刚才到底发生了什么？

Can we raise the yeses again, the invest again.

我们可以再次提出“是”，再次进行投资吗？

Raise the not invested, not invest.

筹集不投资的，不投资的。

And I want to remind you guys you all owe me $10.

我想提醒你们，你们都欠我 10 美元。

What I want to do is I want to play it again.

我想做的是我想再玩一次。

No communication, write it down again on the corner of your notepad what you're going to do.

没有沟通，在记事本的一角再次写下你要做什么。

Don't communicate you guys; show your neighbor.

不要和你们交流；向你的邻居展示。

And now we're going to poll again, so ready.

现在我们要再次投票，做好准备。

Without cheating, without looking around you, if you invested--let Jude get a good view of you--if you invested raise your hand now.

不作弊，不环顾四周，如果你投资了——让裘德好好看看你——如果你投资了，现在就举手。

If you didn't invest--okay.

如果你不投资——好吧。

All right, can I look at the investors again?

好吧，我可以再看看投资者吗？

Raise your hands honestly; we've got a few investors still, so these guys really owe me money now, that's good.

诚实地举起手；我们还有一些投资者，所以这些人现在真的欠我钱了，这很好。

Let's do it again, third time, hang on a second.

让我们再做一次，第三次，稍等一下。

So third time, write it down, and pretend this is real cash.

所以第三次，把它写下来，假装这是真正的现金。

Now, if you invested the third time raise your hand.

现在，如果您第三次投资，请举手。

There's a few suckers born everyday but basically.

每天都会有一些傻瓜出生，但基本上都是这样。

So, where are we heading here?

那么，我们要去哪里？

Where are we heading pretty rapidly?

我们正快速走向何方？

We're heading towards an equilibrium; let's just make sure we confirm that.

我们正在走向平衡；让我们确保我们确认这一点。

So everyone who didn't invest that third time raise your hands.

所以第三次没有投资的人请举手。

That's pretty close; that show of hands is pretty close to a Nash Equilibrium strategy, is that right?

非常接近了；举手示意非常接近纳什均衡策略，对吗？

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.

因此，这是我们上次提到的第三个原因的示例，也是我们可能对纳什均衡感兴趣的第三个原因。

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.

在某些情况下，游戏在自然意义上——不是在形式意义上而是在自然意义上——趋于平衡。

With the exception of a few dogged people who want to pay for my lunch, almost everyone else was converging to an equilibrium.

除了少数顽固的人愿意为我的午餐付钱之外，几乎所有其他人都趋于平衡。

So play converged fairly rapidly to the Nash Equilibrium.

因此，博弈相当快地收敛到纳什均衡。

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?

但我们讨论了这个博弈中有两个纳什均衡。这些纳什均衡中的一个，忽略我一秒钟，这些纳什均衡中的一个比另一个更好吗？

Yeah, clearly the "everyone investing" Nash Equilibrium is the better one, is that right?

是的，显然“每个人都投资”纳什均衡是更好的，对吗？

Everyone agree?

大家都同意吗？

Everyone investing is a better Nash Equilibrium for everyone in the class, than everyone not investing, is that correct?

对于班上的每个人来说，每个人都投资是一个比每个人不投资更好的纳什均衡，对吗？

Nevertheless, where we were converging in this case was what?

然而，在这种情况下我们的共同点是什么？

Where we're converging was the bad equilibrium.

我们的趋同点是不良均衡。

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.

我们正在迅速收敛到一种非常糟糕的均衡，一种没有人得到任何东西的均衡，所有的钱都留在桌子上。

So how can that be?

那怎么可能呢？

How did we converge to this bad equilibrium?

我们是如何收敛到这种不良均衡的？

To be a bit more formal, the bad equilibrium and no invest equilibrium here, is pareto dominated by the good equilibrium.

更正式地说，这里的坏均衡和无投资均衡是由好均衡主导的帕累托。

Everybody is strictly better off at the good equilibrium than the bad equilibrium.

严格来说，每个人在好的均衡状态下都比在坏的均衡状态下过得更好。

It pareto dominates, to use an expression you probably learned in 150 or 115.

用你可能在 150 或 115 中学到的表达方式来说，帕累托占主导地位。

Nevertheless, we're going to the bad one; we're heading to the bad equilibrium.

尽管如此，我们还是要走向坏的一面。我们正在走向不良平衡。

Why did we end up going to the bad equilibrium rather than the good equilibrium?

为什么我们最终会走向坏均衡而不是好均衡？

Can we get the guy in the gray?

我们能找到那个穿灰衣服的人吗？

Professor Ben Polak: Just now you mean?

Ben Polak 教授：你的意思是？

Say what you mean a bit more, yeah that's good.

多说一点你的意思，是的，这样很好。

Just say a bit more.

就多说一点吧。

Student: So it seemed like people didn't have a lot of confidence that other people were going to invest.

学生：看来人们对于其他人会投资没有太多信心。

Professor Ben Polak: So one 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 and then--so we started out at half/half which was below that critical threshold of 90%, is that right?

本·波拉克教授：所以一种说法是，当我们开始时，我们大致持平，大约一半/一半，但这对于投资的人来说已经很糟糕了——所以我们开始时是一半/一半，低于 90% 的临界阈值，对吗？

From then on in, we just tumbled down.

从那时起，我们就跌倒了。

So one way to say this--one way to think about that is it may matter, in this case, where we started.

因此，一种说法——一种思考方式是，在这种情况下，我们从哪里开始可能很重要。

Suppose the first time we played the game in this class this morning, suppose that 93% of the class had invested.

假设今天早上我们第一次在这堂课上玩这个游戏，假设全班 93% 的人都投入了。

In which case, those 93% would all have made money.

那样的话，那93%的人都会赚钱。

Now I'm--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.

现在我——我的猜测是——我无法证明这一点，我的猜测是，我们可能会以另一种方式收敛并收敛到良好的均衡。

Does that make sense?

这有道理吗？

So people figured out that they--people who didn't invest the first time--actually they played the best response to the class, so they stayed put.

于是人们发现，他们——那些第一次没有投入的人——实际上在课堂上做出了最好的反应，所以他们留在原地。

And those of you did invest, a lot of you started not investing as you caught up in this spiral downward and we ended up not investing.

你们中的一些人确实投资了，很多人开始不投资，因为你们陷入了这种螺旋式下降，我们最终没有投资。

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 that choice and they might have switched into investing, and we might have--I'm not saying necessarily, but we might have gone the other way.

但是，如果我们一开始就高于临界阈值，这里的阈值是 90%，如果你第一次就赚钱了，那么非投资者就会后悔这个选择，他们可能会转向投资，我们可能会——我不是说一定，但我们可能会走另一条路。

Yeah, can we get a mike on?

是的，我们可以打开麦克风吗？

Student: What if it had been like a 30/70 thing or [inaudible]

学生：如果是 30/70 的事情或者[听不清]怎么办？

Professor Ben Polak: Yes, that's a good question.

本·波拉克教授：是的，这是一个很好的问题。

Suppose we had been close to the threshold but below, so I don't know is the answer.

假设我们已经接近阈值但低于阈值，所以我不知道答案是什么。

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 in going up.

我们没有做实验，但似乎越高——我们越接近阈值，上升的机会就越大。

My guess is--and this is a guess--my guess is if we started below the threshold we probably have come down, and if was from above the threshold, we would probably have gone up, but that's not a theorem.

我的猜测是——这是一个猜测——我的猜测是，如果我们从阈值以下开始，我们可能会下降，如果从阈值以上开始，我们可能会上升，但这不是定理。

I'm just speculating on what might have happened; speculating on your speculations.

我只是猜测可能发生的事情；猜测你的猜测。

So, here we have a game with two equilibria, one is good, one is bad; one is really quite bad, its pareto dominated.

所以，这里我们有一个有两个均衡的博弈，一个是好的，一个是坏的；一个确实很糟糕，它是帕累托主导的。

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.

请注意，这里发生的事情，我们螺旋式下降的方式与我们已经讨论过的纳什均衡相一致，它与自我实现预测的想法相一致。

Provided you think other people are not going to invest, you're not going to invest.

如果你认为其他人不会投资，你就不会投资。

So, it's a self-fulfilling prediction to take you down to not investing.

所以，这是一个自我实现的预测，让你不再投资。

Conversely, provided everyone thinks everyone else is going to invest, then you're going to go up to the good equilibrium.

相反，如果每个人都认为其他人都会投资，那么你就会达到良好的均衡。

I think that corresponds to what the gentleman said in the middle about a bare market versus a bull market.

我认为这与中间这位先生所说的裸市与牛市相对应。

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.

如果这是一个裸露的市场，那么看起来其他人都对其投资没有信心，那么这就是一个自我实现的预言，我们最终没有投资。

Now, we've seen bad outcomes in the class before.

现在，我们以前在课堂上看到过不好的结果。

For example, the very first day we saw a Prisoner's Dilemma.

例如，第一天我们看到了囚徒困境。

But I claim that though we're getting a bad outcome here in the class, this is not a Prisoner's Dilemma.

但我声称，尽管我们在课堂上得到了不好的结果，但这并不是囚徒困境。

Why is this not a Prisoner's Dilemma?

为什么这不是囚徒困境？

What's different between--I mean both games have an equilibrium which is bad.

两者之间有什么不同——我的意思是这两款游戏都有一个很糟糕的平衡。

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.

当没有人收拾房间或者两个人都进监狱时，囚徒困境的平衡很差，但我声称这不是囚徒困境。

Get the guy behind you.

把那个家伙拉到你身后。

Professor Ben Polak: Okay, so maybe the outcome isn't quite so bad.

本·波拉克教授：好吧，也许结果并没有那么糟糕。

That's fair enough, I could have made it worse, I could have made it sort of--I could have made that--I could have lowered the payoffs until they were pretty bad.

这很公平，我本可以让事情变得更糟，我本可以让事情变得更糟——我本可以做到那样——我本可以降低回报，直到它们变得非常糟糕。

Why else is this not a Prisoner's Dilemma?

否则为什么这不是囚徒困境呢？

The woman who's behind you.

那个在你身后的女人。

Professor Ben Polak: Good; so in Prisoner's Dilemma playing ά was always a best response.

Ben Polak 教授： 好；所以在囚徒困境中扮演ά始终是最好的回应。

What led us to the bad outcome in Prisoner's Dilemma was that ά, the defense strategy, the non-cooperative strategy, the not helping tidy your room strategy, was always the best thing to do.

导致我们在囚徒困境中遭遇糟糕结果的原因是，ά、防御策略、不合作策略、不帮助整理房间的策略，始终是最好的选择。

Here, in some sense the "good thing," the "moral thing" in some sense, is to invest but it's not the case that not investing dominates investing.

在这里，从某种意义上说，“好事”，从某种意义上说，“道德的事”是投资，但情况并非是不投资主导投资。

In fact, if all the people invest in the room you ought to invest, is that right?

事实上，如果所有人都投资你应该投资的房间，对吗？

So this is a social problem, but it's not a social problem of the form of a Prisoner's Dilemma.

所以这是一个社会问题，但不是囚徒困境形式的社会问题。

So what kind of problem is this?

那么这到底是一个什么样的问题呢？

What kind of social problem is this?

这是一个什么样的社会问题？

The guy in front of you.

你面前的那个人。

Professor Ben Polak: It's one of--okay.

Ben Polak 教授：这是……好吧。

So it's--it would help if people cooperated here but I'm looking for a different term.

所以，如果人们在这里合作，将会有所帮助，但我正在寻找一个不同的术语。

The term that came up the first day-- coordination , this is a coordination game.

第一天就出现了这个词——协调，这是一个协调游戏。

For those people that read the New Yorker , I'll put an umlaut over the second "o." Why is it a coordination game?

对于那些阅读《纽约客》的人，我会在第二个“o”上加一个元音变音。为什么说它是协调游戏？

Because you'd like everyone in the class to coordinate their responses on invest.

因为您希望班上的每个人都协调他们对投资的反应。

In fact, if they did that, they all would be happy and no one would have an incentive to defect and there would in fact be an equilibrium.

事实上，如果他们这样做，他们都会很高兴，没有人会有背叛的动机，事实上就会存在一种平衡。

But unfortunately, quite often, we fail to have coordination.

但不幸的是，我们常常无法协调。

Either everyone plays non-invest or, as happened the first time in class, we get some split with people losing money.

要么每个人都玩非投资游戏，要么就像课堂上第一次发生的那样，我们会与赔钱的人产生分歧。

So, I claim that actually this is not a rare thing in society at all.

所以我想说，其实这在社会上根本不是什么罕见的事情。

There are lots of coordination problems in society.

社会上存在很多协调问题。

There are lots of things that look like coordination games.

有很多东西看起来像协调游戏。

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.

通常，在协调博弈中会产生不好的结果，我想用今天剩下的大部分时间来讨论这个问题，因为我认为这很重要，无论你是经济学家还是其他什么，所以让我们稍微讨论一下。

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?

还有什么具有协调博弈的结构，因此会导致人们不协调或在错误的地方进行协调，从而导致不良均衡的结果？

What else looks like that?

还有什么看起来像这样？

Let's collect some ideas.

让我们收集一些想法。

I got a hand way at the back.

我在后面有一只手。

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.

你能找到那个在后面的家伙，正好对抗——是的，就是这样，非常感谢。

Wait until the mike gets to you and then yell.

等到麦克风传到你身边，然后大喊大叫。

Professor Ben Polak: Yeah, good okay.

Ben Polak 教授： 是的，很好。

So a party on campus is a coordination game because what--because you have to coordinate being at the same place, is that right?

所以校园聚会是一场协调游戏，因为你必须在同一个地方进行协调，对吗？

That's the idea you had?

这就是你的想法？

Go ahead.

前进。

Professor Ben Polak: Good, okay that's good.

Ben Polak 教授： 好，好的，那很好。

So that's another in which--there's two ways in which a party can be a coordination problem.

这是另一个问题——有两种方式可以使一方成为协调问题。

One is the problem that if people don't show up it's a lousy party, so you don't want to show up.

其中一个问题是，如果人们不出现，那就是一个糟糕的聚会，所以你不想出现。

Conversely, if everyone is showing up, it's great, it's a lot of fun, it's the place to be and everyone wants to show up.

相反，如果每个人都出现，那就太好了，很有趣，这是一个值得去的地方，每个人都想出现。

Second--so there's two equilibria there, showing up and--everyone not showing up or everyone showing up.

其次，这里有两个均衡，即每个人都出现，或者每个人都没有出现。

Similar idea, the location of parties which is what I thought you were driving at, but this similar idea can occur.

类似的想法，聚会的地点，这就是我认为你正在开车的地方，但这种类似的想法可能会发生。

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.

所以纽黑文过去的情况是有不同的——实际上已经不多了——但校园周围曾经有不同的酒吧（你都不被允许去，所以你不知道）但无论如何，校园周围有很多不同的酒吧。

And there's a coordination game where people coordinate on Friday night--or to be more honest, the graduate students typically Thursday night.

还有一个协调游戏，人们在周五晚上进行协调——或者更诚实地说，研究生通常在周四晚上进行协调。

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.

所以以前的情况是，市中心的一间酒吧是戏剧学院的人协调的，另一家是经济学家协调的，他们不在同一个地方协调，这确实是很好的平衡。

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.

因此，当您去一个新城镇时，您必须了解的一件事是我想去的那种聚会的集合点在哪里。

Again, you're going to have a failure of coordination, everyone's wandering around the town getting mugged.

再次，你会遇到协调失败，每个人都在镇上闲逛，遭到抢劫。

What other things look like coordination problems like that?

还有哪些事情看起来像这样的协调问题？

Again, way back in the corner there, right behind you, there you go.

再一次，回到那个角落，就在你身后，就在那里。

Student: Maybe warring parties in the Civil War signing a treaty.

学生：也许内战中的交战双方签署了一项条约。

Professor Ben Polak: Okay, that could be a--that could be a coordination problem.

本·波拉克教授：好的，这可能是一个协调问题。

It has a feeling of being a bit Prisoner's Dilemmerish and in some sense, it's my disarming, my putting down my arms before you putting down your arms, that kind of thing.

它有一种有点囚徒困境的感觉，从某种意义上说，这是我解除武装，我在你放下武器之前放下武器，诸如此类的事情。

So it could be a coordination problem, but it has a little bit of a flavor of both.

所以这可能是一个协调问题，但两者都有一点。

Go ahead, go on.

继续，继续。

Okay, other examples?

好吧，还有其他例子吗？

There's a guy there.

那里有一个人。

While you're there why don't you get the guy who is behind you right there by the door, great.

当你在那里的时候，为什么不去找那个在你身后就在门口的人呢，太好了。

Student: Big sports arena, people deciding whether or not they want to start a chant or [inaudible]

学生：大型运动场，人们决定是否要开始喊口号或[听不清]

Professor Ben Polak: Yeah, okay.

本·波拉克教授：是的，好的。

I'm not quite sure which is the good outcome or the bad outcome.

我不太确定哪个是好结果，哪个是坏结果。

So there's this thing called, The Wave.

所以有一个东西叫做“波浪”。

There's this thing called The Wave that Americans insist on doing, and I guess they think that's the good outcome.

美国人坚持做一个叫做“波浪”的事情，我想他们认为这是一个好的结果。

Other things?

其他的事情？

Professor Ben Polak: Let's come back to that one.

Ben Polak 教授：让我们回到那个问题。

Hold that thought and we'll come back to it next time.

保留这个想法，我们下次再讨论这个问题。

You're right that's a good--but let's come back to it next time.

你说得对，这很好——但我们下次再讨论这个问题。

Anything else?

还要别的吗？

Let me try and expand on some of these meeting place ideas.

让我尝试扩展其中一些聚会场所的想法。

We talked about pubs to meet at, or parties to meet at, but think about online sites.

我们讨论了聚会的酒吧或聚会，但想想在线网站。

Online sites which are chat sites or dating sites, or whatever.

聊天网站或约会网站等在线网站。

Those are--those online sites clearly have the same feature of a party.

这些在线网站显然具有与聚会相同的特征。

You want people to coordinate on the same site.

您希望人们在同一站点上进行协调。

What about some other economic ideas?

还有其他一些经济理念吗？

What about some other ideas from economics?

经济学中的其他一些想法又如何呢？

What else has that kind of externality like a meeting place?

还有什么地方像聚会场所一样具有外部性呢？

Student: I mean it's excluding some people, but things like newspapers or something, like we might want only one like global news site.

学生：我的意思是它排除了一些人，但像报纸之类的东西，就像我们可能只想要一个像全球新闻网站一样的东西。

Professor Ben Polak: So, that's an interesting thought, because it can go both ways.

本·波拉克教授：所以，这是一个有趣的想法，因为它可以是双向的。

It could be a bad thing 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 that everyone's read the same thing.

出于显而易见的原因，拥有一份报纸可能是一件坏事，但就在午餐时就昨天报纸上的内容进行良好的对话而言，每个人都阅读相同的内容会有所帮助。

Certainly, there's a bandwagon effect to this with TV shows.

当然，电视节目会产生跟风效应。

If everybody in America watches the same TV show, which apparently is American Idol these days, then you can also talk about it over lunch.

如果美国人都看同一个电视节目（现在显然是《美国偶像》），那么你也可以在午餐时谈论它。

Notice that's a really horrible place to coordinate.

请注意，这是一个非常糟糕的协调地方。

There are similar examples to the American Idol example.

还有与《美国偶像》类似的例子。

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.

当我在英国长大时，我将再次透露我的年龄；每个人都认为，在英国，要想成为一个“in”人，就必须穿喇叭裤。

This was--and so to be in you had to wear flared trousers.

这是——所以要进去你必须穿喇叭裤。

This is a horrible coordination problem, right?

这是一个可怕的协调问题，对吗？

So for people who don't believe that could ever have happened in England that you could ever these sort of fashion goods that you end up at a horrible equilibrium at the wrong place, if you don't believe that could ever happen think about the entirety of the Midwest.

因此，对于那些不相信这种情况可能发生在英国的人来说，如果你不相信这种情况可能发生，那么你可能会在错误的地方最终处于可怕的平衡状态，想想整个中西部。

I didn't say that, we're going to cut that out of the film later.

我没这么说，我们稍后会把它从电影中删掉。

What else is like this?

还有什么是这样的？

I'm going to get a few ideas now, this gentleman here.

这位先生，我现在要得到一些想法。

Student: The establishment of monopolies, because a lot of people use Microsoft, say then everything is compatible with Microsoft so more people would use it.

学生：垄断的建立，因为很多人用微软，所以说所有的东西都兼容微软，所以更多的人会用它。

Professor Ben Polak: So, Steven's pointing out that certain software can act this way by being a network good.

本·波拉克教授：所以，史蒂文指出，某些软件可以通过成为网络产品来发挥这种作用。

The more people who use Microsoft and Microsoft programs, the bigger the advantage to me using Microsoft, and therefore--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.

使用微软和微软程序的人越多，我使用微软的优势就越大，因此，因为我可以交换程序，如果我与我的合著者等一起工作，我可以交换文件，所以你可以在不同的软件上协调不同的平衡，同样，你可能最终会得到错误的平衡。

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.

我想很多人会争论——但我会对此保持中立——很多人会认为微软不一定是世界最终的最佳去处。

There are other technological network goods like this.

还有其他类似的科技网络商品。

These are called network externalities.

这些被称为网络外部性。

An example here would be high definition television.

这里的一个例子是高清电视。

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.

对于高清电视之类的东西，你希望有一个每个人都同意的技术标准，因为这样每个人都可以生产符合该标准的电视和符合该标准的产品，当然，每个生产电视并拥有标准生产线的公司都希望他们的产品被选为标准。

Again, you could end up at the wrong place.

同样，您可能会到达错误的地方。

You could end up with a bad equilibrium.

你最终可能会得到一个糟糕的平衡。

How about political bandwagons?

政治潮流怎么样？

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.

在政治上，特别是在初选中，民主党或共和党可能有优势，让你们在初选中投票给同一个候选人，这样他们就会得到很大的推动，而且看起来不像你们的政党分裂等等。

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.

这最终可能会导致——我再次对此保持中立——最终可能会导致错误的候选人获胜。

There's a political bandwagon effect, the person who wins New Hampshire and Iowa tends then to win everything, so that's another example.

有一种政治潮流效应，赢得新罕布什尔州和爱荷华州的人往往会赢得一切，所以这是另一个例子。

Any other economic examples?

还有其他经济例子吗？

Can we get this guy in here?

我们能把这个人弄到这里来吗？

Professor Ben Polak: Yeah, okay, so in particular which stock exchange to list on.

本·波拉克教授：是的，好的，特别是在哪个证券交易所上市。

So there's a huge advantage having lots of stocks in the same stock exchange.

因此，在同一证券交易所拥有大量股票具有巨大的优势。

There are shared fixed costs; there's also liquidity issues and lots of issues of that form but mostly the form of fixed costs.

共享固定成本；还有流动性问题和许多这种形式的问题，但主要是固定成本的形式。

So there's a tendency to end up with one stock exchange.

因此，最终的趋势是只有一个证券交易所。

We're not there yet but we do seem to be going that way quite rapidly.

我们还没有达到那个目标，但我们似乎正在快速地朝着这个方向前进。

The problem of course being, that might not be the best stock exchange or it might give that stock exchange monopoly power.

当然，问题是，这可能不是最好的证券交易所，或者它可能赋予该证券交易所垄断权。

Let me give one--let me try one more example.

让我再举一个例子。

What about bank runs?

银行挤兑怎么办？

What's a bank run?

什么是银行挤兑？

Somebody--what's a bank run?

有人——什么是银行挤兑？

Student: It's when the public loses confidence in--because their security of their money in banks, then they rush to withdraw their deposits.

学生：当公众对银行里的钱的安全性失去信心时，他们就会急于提取存款。

Professor Ben Polak: Good.

本·波拉克教授： 很好。

So you can imagine a bank as a natural case where there's two equilibria.

因此，您可以将银行想象为存在两个均衡的自然情况。

There's a good equilibrium, everyone has confidence in the bank, everyone leaves their deposits in the bank.

有一个很好的均衡，每个人都对银行有信心，每个人都把存款留在银行。

The bank is then able to lend some of that money out on a higher rate of interest on it.

然后，银行可以以更高的利率贷出其中的一部分资金。

The bank doesn't want to keep all that money locked up in the vault.

银行不想把所有的钱都锁在金库里。

It wants to lend it out to lenders who can pay interest.

它希望将其借给能够支付利息的贷方。

That's a good equilibrium for everybody.

这对每个人来说都是一个很好的平衡。

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.

然而，如果人们对银行失去信心并开始提取存款，那么银行金库中就没有足够的现金来支付这些存款，银行就会破产。

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.

现在，我过去常常在课堂上说，你们中没有人见过银行挤兑，因为这种情况在美国大约在 30 年代中期就不再发生了。

There were lots and lots of bank runs in America before the 1930s, but since federal deposit insurance came in, there's far fewer.

20 世纪 30 年代之前，美国发生过很多次银行挤兑，但自从联邦存款保险推出后，这种情况就少得多了。

However, I really can't say that today because there's a bank run going on right now.

然而，我今天真的不能这么说，因为现在正在发生银行挤兑。

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.

实际上，在英格兰，一家名为北方安全公司（不，是北岩银行）的公司正在发生银行挤兑，正如我们所说，它被称为北岩银行，这确实是一次银行挤兑。

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.

我的意思是，如果你昨天看《纽约时报》的报纸，你会看到储户在这家银行位于伦敦的办事处外排队，试图提取存款。

And you see the Bank of England trying to intervene to restore confidence.

你会看到英格兰银行试图进行干预以恢复信心。

Just be clear, this isn't simple--this isn't a simple case of being about the mortgage crisis.

需要明确的是，这并不简单——这不是一个关于抵押贷款危机的简单案例。

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.

这家银行确实提供抵押贷款，但它似乎并没有特别参与那种吸引了所有公众关注的抵押贷款业务。

It really seems to be a shift in confidence.

这似乎确实是信心的转变。

A move from the good equilibrium of everyone remaining invested, to the bad equilibrium of everyone taking their money out.

从每个人都继续投资的良好均衡，转向每个人都把钱拿出来的不良均衡。

Now, there are famous bank runs in American culture, in the movies anyway.

现在，美国文化中存在着著名的银行挤兑事件，至少在电影中也是如此。

What is the famous bank run in the movies, in American movies?

美国电影中著名的银行挤兑是什么？

Professor Ben Polak: It's a Wonderful Life ; there's actually--there's one in Mary Poppins as well, but we'll do It's a Wonderful Life .

本·波拉克教授：生活真是美好；事实上，《欢乐满人间》里也有这样一个，但我们会拍《生活多美好》。

How many of you have seen It's A Wonderful Life ?

有多少人看过《生活多美好》？

How many have you not seen It's a Wonderful Life ?

有多少人没看过《人生多美好》？

Let me get a poll here.

让我在这里进行民意调查。

How many people have not seen--keep your hands up a second, keep your hands up.

有多少人没见过——举起手来，举起手来。

You need to know that if you're on a green card, you can lose your green card if you haven't sent It's a Wonderful Life .

您需要知道，如果您拥有绿卡，如果您没有发送“It's a Wonderful Life”，您可能会失去绿卡。

So, in It's a Wonderful Life there's a run on the bank--actually it's a savings and loan, but never mind.

所以，在《生活多美好》中，有银行挤兑——实际上是储蓄和贷款，但没关系。

We'll think of it as a bank.

我们会把它想象成一家银行。

Luckily, it doesn't end up with the savings or loan, or bank, going under.

幸运的是，最终并没有导致储蓄、贷款或银行破产。

Why doesn't the bank go under in It's a Wonderful Life ?

为什么《生活多美好》中的银行没有倒闭？

Why doesn't it go under?

为什么它不沉下去？

Yeah, the guy in green?

是啊，那个绿衣人？

Can we get the guy in green?

我们能找到那个穿绿衣服的人吗？

Student: Everyone agrees to only take as much as they need [inaudible]

学生：每个人都同意只拿他们需要的东西[听不清]

Professor Ben Polak: For the people who didn't hear it, everyone agrees only to take out a small amount, perhaps even nothing and therefore the bank run ends.

本·波拉克教授：对于那些没有听到的人来说，每个人都同意只取出少量资金，甚至可能什么都不取出，因此银行挤兑就结束了。

Everyone realizes the bank isn't going to collapse, and they're happy to leave their money in the bank.

每个人都意识到银行不会倒闭，他们很高兴把钱留在银行。

Now, it's true everyone agrees but what do they agree?

现在，确实每个人都同意，但他们同意什么？

What makes them agree?

是什么让他们同意？

What makes them agree is Jimmy Stewart, right?

让他们达成一致的是吉米·斯图尔特，对吗？

Everyone remember the movie?

大家还记得电影吗？

So Jimmy Stewart gets up there and he says--he gives a speech, and he says, look, more or less,--I mean he doesn't say it in these words but he would have done it if he had taken the class--he says, look there are two equilibria in this game.

所以吉米·斯图尔特站起来，他说——他做了一次演讲，他说，看，或多或少，——我的意思是他没有用这些话说出来，但如果他上过课，他就会这么做——他说，看，这个游戏中有两个均衡。

(I can't do the--whatever it is, the West Pennsylvania accent, is that what it is, or whatever it is.) But anyway; there are two equilibria 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 in.

（我做不到——不管它是什么，西宾夕法尼亚口音，就是这样，或者无论它是什么。） 但无论如何；这个博弈中有两个均衡；有一种坏的情况，我们都把钱取出来，最终我们都失去了家园；有一种好的情况，我们都把钱留在里面，这对每个人都更好。所以，让我们都把钱留在里面。

But he gives this--he's a bit more motivationally stimulating than me--but he leads people leaving their money in.

但他给出了这一点——他比我更具激励性——但他带领人们把钱留下来。

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.

所以，我想做的是，我现在想在班上挑选一个人——每个人都明白这个游戏，每个人都明白有两个均衡，每个人都明白一个均衡更好。

Let's play the game again.

我们再玩一次游戏吧。

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.

让我们再次选择游戏，但在我选择之前，我要把麦克风交给帕特里克，帕特里克将有五秒钟的时间来说服你。

Stand up.

起来。

Patrick's going to have five seconds to persuade you to tell you whatever he likes starting now.

从现在开始，帕特里克将有五秒钟的时间说服您告诉您他喜欢告诉您的任何事情。

Student: Okay, so clearly if we all invest we're always better off, so everybody should invest.

学生：好的，很明显，如果我们都投资，我们的境况总是会更好，所以每个人都应该投资。

Professor Ben Polak: All right, now let's see if this is going work.

Ben Polak 教授：好吧，现在让我们看看这是否有效。

Okay, so let's see what happens now.

好吧，让我们看看现在会发生什么。

Everybody who is going to invest raise their hands and everyone who's not investing raise their hands.

每个要投资的人都举手，每个不投资的人都举手。

Oh we almost made it.

哦，我们差一点就成功了。

We must have almost made it.

我们一定快成功了。

So notice what happened here.

所以请注意这里发生了什么。

Give another round of applause for Patrick.

请再次为帕特里克鼓掌。

I think he did a good job there.

我认为他在那里做得很好。

But there's a lesson here; the lesson here is the game didn't change.

但这里有一个教训：这里的教训是游戏没有改变。

It's the same game that we've played three times already.

这是我们已经玩了三遍的同一个游戏。

This was the fourth time we've played it.

这是我们第四次玩这个游戏了。

We had a totally different response in playing this time.

这次我们在比赛中得到了完全不同的反应。

Almost all of you, the vast majority of you, perhaps even 90% of you invested this time and you did so in response to Patrick.

几乎你们所有人，你们中的绝大多数人，甚至可能是 90% 的人这次都投资了，你们这样做是为了回应帕特里克。

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.

但帕特里克并没有付任何钱，他没有贿赂你，他没有与你签订合同，他没有威胁要打断你的腿，他只是指出这是一个好主意。

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.

现在，请记住囚徒困境，在囚徒困境中，如果帕特里克帕特里克能够在囚徒困境中站起来并发表相同的演讲并说，看，伙计们，如果我们在囚徒困境中选择 β ，我们都会比选择 ά 更好；大致相同的讲话。

What will you have done in the Prisoner's Dilemma?

陷入囚徒困境时你会做什么？

You would have all chosen ά anyway.

无论如何，你们都会选择 ά。

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.

所以帕特里克试图说服你，或者帕特里克告诉你，在囚徒困境中选择β会做得更好，但在这里——先别走。

Here it does work.

在这里它确实有效。

Why does Patrick--why is Patrick persuasive in this game but he isn't persuasive in the Prisoner's Dilemma?

为什么帕特里克——为什么帕特里克在这场游戏中很有说服力，但在囚徒困境中却没有说服力？

Can we get the mike on Katie again?

我们可以再给凯蒂拿麦克风吗？

Why is Patrick persuasive in this game and not before?

为什么帕特里克在这场比赛中而不是之前有说服力？

Student: He's not trying to get you to play a strictly dominated strategy.

学生：他并不是想让你采取严格的占优策略。

Professor Ben Polak: He's not trying to get you play a strictly dominated strategy and more than that, he's trying to persuade you to play what?

Ben Polak 教授：他并不是想让你玩严格占优的策略，更重要的是，他试图说服你玩什么？

To play a Nash Equilibrium.

发挥纳什均衡。

So, there's a lesson here, in coordination problems, unlike Prisoner's Dilemma, communication--just communication, no contracts--communication can help.

所以，这里有一个教训，在协调问题上，与囚徒困境不同，沟通——只有沟通，没有合同——沟通可以提供帮助。

And in particular, what we can persuade each other to do is to play the other Nash Equilibrium.

特别是，我们可以说服对方做的是发挥另一个纳什均衡。

Now, this gives us one more motivation for a Nash Equilibrium.

现在，这给了我们纳什均衡的更多动力。

In a Prisoner's Dilemma, to get out of it we needed a contract, we needed side payments, we needed to change the payoffs of the game.

在囚徒困境中，为了摆脱困境，我们需要一份合同，我们需要附带付款，我们需要改变游戏的收益。

But a Nash Equilibrium can be a self-enforcing agreement.

但纳什均衡可以是一个自我执行的协议。

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.

我们可以同意，我们将在这个游戏中进行投资，事实上，我们将在没有任何附带付款的情况下进行投资，没有任何人威胁要打断你的腿，没有任何合同，没有任何法规或法律。

I'm assuming Patrick isn't that violent.

我猜帕特里克没那么暴力。

We're going to end up doing the right thing here because it's in our own interest to do so.

我们最终将在这里做正确的事情，因为这样做符合我们自己的利益。

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.

所以我们一致认为的协调问题是整个社会的问题，无论是银行挤兑还是市场泡沫，还是中西部的时尚，它们都是整个社会的问题。

Communication can make a difference and we'll pick that theme up on Monday.

沟通可以带来改变，我们将在周一讨论这个主题。