Game Theory Lecture 6 | Game Theory
Chapter 1.
第一章。
Coordination Games: Scope for Leadership and Strategic Complements [00:00:00] Professor Ben Polak: All right, so last time we were talking about The Investor Game and this was a coordination game, and we learned some things.
协调博弈：领导力和战略互补的范围 [00:00:00] Ben Polak 教授：好的，上次我们谈论投资者博弈，这是一个协调博弈，我们学到了一些东西。
I just want to recall some of the things we learned so I can highlight them a bit.
我只是想回忆一下我们学到的一些东西，这样我就可以重点强调它们。
One thing we learned was that communication can help in a coordination game.
我们学到的一件事是，沟通有助于协调游戏。
So I forget who it was, but someone down here who has disappeared, was our Jimmy Stewart character and helped coordinate you on a better equilibrium simply by suggesting what you should do.
所以我忘记了是谁，但下面有人失踪了，他是我们的吉米·斯图尔特角色，他通过建议你应该做什么来帮助你协调更好的平衡。
There are two lessons here.
这里有两个教训。
One is this is very different from the Prisoner's Dilemma.
一是这与囚徒困境有很大不同。
So we learned the very first time that in the Prisoner's Dilemma communication per se won't help, but in the coordination problem, which could be just as serious socially as a Prisoner's Dilemma, in a coordination problem it may well help.
因此，我们第一次了解到，在囚徒困境中，沟通本身没有帮助，但在协调问题中，这在社会上可能与囚徒困境一样严重，在协调问题中，沟通可能会有所帮助。
The reason it helps is you're trying to coordinate onto a Nash Equilibrium.
它有帮助的原因是你正在尝试协调纳什均衡。
One way to think about Nash Equilibria is that they are self-enforcing agreements, so provided that everyone believes that everyone is going to go along with this agreement, then everyone in fact will.
思考纳什均衡的一种方式是，它们是自我执行的协议，因此，如果每个人都相信每个人都会遵守该协议，那么每个人实际上都会这样做。
I want to make another, slightly more philosophical remark associated with this and it's to do with the idea of "leadership." So leadership is kind of a big word that you see written probably too often these days, in too many newspaper articles, and it probably comes up in too many Yale classes, and I don't claim to know anything about leadership.
我想提出另一个与此相关的、稍微更具哲学性的评论，它与“领导力”的概念有关。因此，领导力是一个很大的词，你现在可能经常在太多的报纸文章中看到这个词，并且可能在太多的耶鲁课程中出现，而我并不声称对领导力一无所知。
And I don't think Game Theory is going to contribute to anything to understanding about leadership.
我认为博弈论不会对理解领导力做出任何贡献。
But one thing we can do is tell you where leadership may help.
但我们能做的一件事就是告诉您领导力可以在哪些方面提供帮助。
In the coordination game, where the idea is to try and get people to coordinate on a particular equilibria rather than on another equilibria, or worse still, to be uncoordinated entirely.
在协调博弈中，其想法是尝试让人们在特定的均衡上进行协调，而不是在另一个均衡上进行协调，或者更糟糕的是，完全不协调。
In those kind of games, leadership can help tremendously.
在这类游戏中，领导力可以发挥巨大作用。
A little bit of leadership can help tremendously.
一点点的领导力可以带来巨大的帮助。
So these games, these coordination games, are games where there is a "scope for leadership."
所以这些游戏，这些协调游戏，是有“领导空间”的游戏。
Just to see that in a very simple example, again, we don't use such a complicated example as the one we looked at last time, you could imagine a game, a really trivial coordination game, which looked like this (1,1) (0,0) (0,0) (1,1).
再次，在一个非常简单的例子中，我们不使用像我们上次看到的那样复杂的例子，你可以想象一个游戏，一个非常简单的协调游戏，它看起来像这样 (1,1) (0,0) (0,0) (1,1)。
And clearly in this game what matters is coordinating.
显然，在这场比赛中最重要的是协调。
You either want to coordinate on up left or you want to coordinate on down right.
您要么想要在左上协调，要么想要在右下协调。
You don't want to end up uncoordinated on down left or up right.
你不想最终在左下或右上变得不协调。
Everyone see that?
大家看到了吗？
So in this game if you just played it, it's quite likely you're going to end up uncoordinated, but if you have a little bit of leadership can say okay let's make sure this is where we coordinate, or let's make sure this is where we coordinate.
所以在这个游戏中，如果你刚刚玩过，很可能你最终会不协调，但如果你有一点领导能力，可以说好吧，让我们确保这是我们协调的地方，或者让我们确保这是我们协调的地方。
So this matters a lot.
所以这很重要。
And I don't want to overplay the social importance of this, but go back a couple of years to what was happening in the aftermath of Katrina and realize how important--how bad things get when things fail to be coordinated.
我不想过分夸大这一点的社会重要性，但回顾几年卡特里娜飓风过后发生的事情，就会意识到当事情无法协调时，事情会变得多么重要，事情会变得多么糟糕。
One other remark before we leave this, in the game we played last time, in the investment game, one feature of that game was that the more you thought other people were going to invest, the more you wanted to invest.
在我们离开之前还有一点要说的是，在我们上次玩的游戏中，在投资游戏中，该游戏的一个特点是，你越认为别人会投资，你就越想投资。
The more you thought other people were going to invest, the more likely that you were going to invest.
你越认为其他人会投资，你就越有可能投资。
If you go back to the time before that, we talked about this partnership game.
如果你回到之前的时间，我们讨论过这个合作游戏。
In the partnership game you were contributing effort to a joint project.
在伙伴关系游戏中，你们正在为一个联合项目做出贡献。
It could have been a law firm; it could have been working in the study group on a homework assignment.
它可能是一家律师事务所；它可能正在学习小组中完成家庭作业。
In that game, if you remember what the best responses looked like, they looked like this where this was the effort of Player 1; this was the effort of Player 2.
在那场比赛中，如果你还记得最佳反应是什么样的，那么它们看起来就像这样，这是玩家 1 的努力；这是玩家2的努力。
This was the best response of Player 1 and this was the best response of Player 2.
这是玩家 1 的最佳响应，这是玩家 2 的最佳响应。
This game also has the feature that the more effort the other person--the more the other person does--the more you want to do.
这个游戏还有一个特点，对方越努力——对方做得越多——你就越想做。
The more effort your partner provides into this project the more effort you want to provide in this project.
您的合作伙伴为此项目付出的努力越多，您希望在此项目中付出的努力也就越多。
I just want to introduce a bit of jargon here.
我只是想在这里介绍一些行话。
These games in which the more the other person does the more I want to do, these are called games of strategic complements.
这种别人做的越多我就越想做的游戏，称为战略互补游戏。
These are games of strategic complements.
这些是战略互补的游戏。
So both the investment game and the game with--the partnership firm game are games with strategic complements.
因此，投资博弈和合伙企业博弈都是具有战略互补性的博弈。
We could call the strategies strategic complements.
我们可以将这些战略称为战略补充。
We'll come back to this later on today.
我们今天晚些时候会再讨论这个问题。
So before we leave coordination games, I want to look at another one, a little bit more complicated one perhaps, that we mentioned briefly last time.
因此，在我们离开协调游戏之前，我想看一下我们上次简要提到的另一个游戏，也许更复杂一点。
So we'll look at and play another game, and we'll call this game, "Going to the Movies." So I always regard one purpose of this class to help hapless Yale students in their dating strategies.
因此，我们将看并玩另一个游戏，我们将这个游戏称为“去看电影”。所以我一直认为这门课的目的之一就是帮助不幸的耶鲁学生制定约会策略。
That seems like a good thing to do.
这似乎是一件好事。
How many of you are Econ majors?
你们中有多少人是经济学专业的？
There's a lot of people who probably need a lot of help with their dating strategies, right?
有很多人在约会策略上可能需要很多帮助，对吧？
Okay, so the idea of this game is a couple is going to meet up at the movies.
好吧，这个游戏的想法是一对情侣在电影中相遇。
And let's have a look at the movies concerned here and we'll draw--there's three possible movies.
让我们看看这里涉及的电影，然后我们画出三部可能的电影。
The movies we're going to look at are The Bourne Ultimatum , and the movie called Good Shepherd , and a movie called Snow White and I'll explain the game in more detail in a second.
我们要看的电影是《谍影重重》、《好牧人》和《白雪公主》，我稍后会更详细地解释这个游戏。
Now, it used to be in the old days before I had kids, I could list off 15 current movies and help you a bit more with your dating strategy by giving you instant movie reviews, but now I have kids, I get to see precisely two movies a year, and the two movies I got to see this year were The Bourne Ultimatum and the Good Shepherd.
现在，过去在我有孩子之前，我可以列出 15 部当前的电影，并通过给你即时电影评论来帮助你制定约会策略，但现在我有了孩子，我每年只能看两部电影，今年我要看的两部电影是《谍影重重》和《好牧人》。
And now I think about it, both of those have Matt Damon in it.
现在我想起来，这两部影片中都有马特·达蒙的身影。
My wife chose both so maybe I need to work out some more.
我的妻子选择了两者，所以也许我需要做更多的锻炼。
So just to give you some idea about these movies, how many of you saw Bourne Ultimatum ?
那么，为了让您对这些电影有一些了解，你们中有多少人看过《谍影重重》？
Quite a lot of you; this is a movie, it has pretty good action, virtually no plot.
你们中的很多人；这是一部电影，动作很好，几乎没有情节。
Basic lesson of this movie is--if you take home a lesson--it's that all spies are psychos or something like that.
这部电影的基本教训是——如果你吸取教训的话——那就是所有间谍都是精神病或类似的东西。
Then how many of you saw Good Shepherd ?
那么你们中有多少人看过《好牧人》呢？
A lot of you saw that as well.
你们很多人也看到了这一点。
It's actually pretty good.
其实还不错。
It has a lot of plot and no action, so it's the other way around.
它有很多情节但没有动作，所以情况正好相反。
The basic lesson of this movie is--and you probably knew this already--everyone at Yale is a spy …
这部电影的基本教训是——你可能已经知道了——耶鲁大学的每个人都是间谍……
and by the way also a psycho.
顺便说一句，他也是一个精神病患者。
The third movie is Snow White , which I haven't gone out to see but my four-year old daughter has seen on 24 of the last 27 nights on video.
第三部电影是《白雪公主》，我没有出去看过，但我四岁的女儿在过去 27 个晚上中的 24 个晚上通过视频观看了这部电影。
And this movie, I don't know if I would recommend it that much, it's--perhaps I'm being too PC--but I'm not convinced that for the modern woman, hanging around waiting for your prince to come is really a good strategy.
而这部电影，我不知道我是否会那么推荐它，它——也许我太电脑化了——但我不相信对于现代女性来说，闲逛等待你的王子到来真的是一个好的策略。
By the way, for those of you--those of you who are, if you are doing that strategy, got me in trouble.
顺便说一句，对于你们中的那些人来说，如果你们采用这种策略，就会给我带来麻烦。
Never mind, if you are doing that strategy, take it from a Brit, most princes are as dumb as toast, not worth waiting for.
没关系，如果你正在采取这种策略，请从英国人那里得到它，大多数王子都像吐司一样愚蠢，不值得等待。
So let's put the payoffs in here.
所以让我们把收益放在这里。
So the idea here is that these people are going to meet at the movie, they're going to go out to a movie.
所以这里的想法是这些人将在电影中见面，他们将出去看电影。
And they've decided to go to the Criterion [New Haven movie theatre], or the local movie house, and there were these three movies showing, and they're all excited about going to this movie except being Economics majors and not very good at dating, they have forgotten to tell each other which movie they're actually going to go to.
他们决定去 Criterion [纽黑文电影院]，或者当地的电影院，放映了这三部电影，他们都很兴奋去看这部电影，除了他们是经济学专业的学生，不太擅长约会，他们忘记告诉对方他们实际上要去哪部电影。
They're going to meet in there on the--in the back row probably and--but they're not telling us which movie.
他们将在那里见面——可能在后排——但他们不会告诉我们哪部电影。
So that's a problem and let's put in the payoffs, and we'll put in the payoffs that roughly I think would correspond--so my preferences and we'll talk about it--what these preferences mean in a second.
所以这是一个问题，让我们输入收益，我们将输入我认为大致对应的收益——所以我的偏好，我们将讨论它——这些偏好意味着什么。
So here we go so …
所以我们就这样……
-1,( -1, 0), (-1, 0), (-2, -2).
-1,(-1, 0), (-1, 0), (-2, -2)。
So here are the preferences for these movies of Player 1 and Player 2, and you can see from these preferences, from these payoffs, that the best thing for Player 1 is for both players, both people to meet and go to the Bourne Ultimatum ; this is the action movie.
所以这里是玩家1和玩家2对这些电影的偏好，从这些偏好、从这些回报中你可以看到，对于玩家1来说最好的事情就是对两个玩家来说，两个人都见面，一起去看谍影重重；这是动作片。
So it's not to be sexist--assume this is the she and this is the he, so she would like to go and see Matt Damon beat people up and coordinate on that, her favorite thing.
所以这并不是性别歧视——假设这是她，这是他，所以她想去看看马特·达蒙殴打别人，并在这件事上进行协调，这是她最喜欢的事情。
And she gets nothing if they fail to coordinate and so on and so forth.
如果他们不能协调等等，她就什么也得不到。
Her second choice is to manage to coordinate at Matt Damon being a Yale spy, and then she really doesn't want to go and see Snow White , and the worst thing of all, actually this is for both players, the worst thing of all is to coordinate with Snow White because then you've got to talk about it afterwards at Koffee [New Haven café].
她的第二个选择是设法在马特·达蒙那里协调成为一名耶鲁间谍，然后她真的不想去看白雪公主，而最糟糕的事情，实际上这对两个球员来说，最糟糕的事情是与白雪公主协调，因为然后你必须在咖啡[纽黑文咖啡馆]谈论这件事。
Same thing with the other person.
另一个人也同样如此。
Same thing exactly, except that he would rather meet at the Good Shepherd.
完全一样，只是他宁愿在好牧人会面。
Since he's a Yale guy, he probably thinks of himself as the Matt Damon character though perhaps not, and failing that, he'd like to coordinate at the Bourne Ultimatum .
由于他是耶鲁大学的学生，他可能认为自己是马特·达蒙的角色，尽管也许不是，如果做不到这一点，他想在《谍影重重》中进行协调。
But again, the disaster is to fail to coordinate and go to see different movies.
但同样，灾难是无法协调并去看不同的电影。
So these are the preferences.
这些是偏好。
What can we tell immediately, if you're stuck in this situation?
如果您陷入这种情况，我们可以立即告诉您什么？
What can you tell immediately about this game?
关于这款游戏，您能立即看出什么？
What's an easy first step?
简单的第一步是什么？
Let's get the guy in the red here.
让我们把那个穿红衣服的人抓到这里吧。
Professor Ben Polak: Good, so for both players Snow White is a dominated strategy.
Ben Polak 教授：很好，所以对于两位玩家来说，白雪公主都是占优策略。
So both players having taken this class--I told you it would help you with your dating.
所以两位球员都参加了这门课程——我告诉过你这会对你的约会有所帮助。
So both players will realize that they should at least not go to Snow White , is that right?
所以两个玩家都会意识到他们至少不应该去找白雪公主，对吗？
Great animation but not perhaps a good date movie, so it's gone.
很棒的动画，但可能不是一部好的约会电影，所以它消失了。
Everyone see that?
大家看到了吗？
So that leaves us just with these two options, the two Matt Damon movies, Bourne Ultimatum and Good Shepherd.
所以我们只剩下这两个选择，马特·达蒙的两部电影，《谍影重重》和《好牧人》。
And here are the remaining payoffs, and let's see how we play this out.
这是剩余的回报，让我们看看我们如何解决这个问题。
So let's pick on some people.
那么让我们挑选一些人吧。
Ale you want to pick on somebody?
你想挑衅某人吗？
I've got Kai here as well.
我这里也有凯。
Okay, so you've picked on somebody there.
好吧，所以你已经选择了那里的某个人。
The person Ale picked on, you want to stand up?
阿乐挑衅的人，你要站起来吗？
Okay, your name is?
好吧，你的名字是？
Professor Ben Polak: Nina, okay Nina I'm sorry.
本·波拉克教授：尼娜，好吧，尼娜，我很抱歉。
Nina and Kai get your guy to stand up there.
尼娜和凯让你的家伙站在那里。
And your name is?
你的名字是？
Professor Ben Polak: No you're--so you're about to go on a date.
本·波拉克教授：不，你——所以你要去约会。
So Nina's preferences are Player 1's preferences here.
所以这里 Nina 的偏好就是玩家 1 的偏好。
So she--her best thing now is to successfully meet David at The Bourne Ultimatum and David's preferences are Player 2's preferences, so his favorite thing is to successfully mette at The Good Shepherd .
所以她——她现在最好的事情就是在谍影重重中成功见到大卫，而大卫的喜好就是玩家2的喜好，所以他最喜欢的事情就是在好牧人成功见到大卫。
Why don't you write down a second on the corner of your notepad what it is you're going to choose to do with my T.A.'s watching so we can't cheat.
你为什么不在记事本的一角写下你要选择在我的助教观看时做什么，这样我们就不会作弊了。
Both have it written down?
两个都写了吗？
Should we have a good look at them?
我们应该好好看看他们吗？
Should we just embarrass them a bit?
我们应该让他们难堪一点吗？
We looked at them already I guess.
我想我们已经看过它们了。
So Nina, shout out to the crowd what it is you've--where it is you've chosen to go.
所以尼娜，向人群大声喊出你已经选择了什么——你选择去哪里。
Professor Ben Polak: Bourne Ultimatum ; and David where do you choose to go?
本·波拉克教授：谍影重重；大卫，你选择去哪里？
Professor Ben Polak: They're going to coordinate; that's very good.
Ben Polak 教授：他们将进行协调；那很好。
I don't know what this tells us about David and Nina, but don't let them off the hook quite yet.
我不知道这告诉我们关于大卫和尼娜的什么信息，但先别让他们摆脱困境。
So now, that was good, we managed to coordinate.
所以现在，这很好，我们成功地进行了协调。
I think we can all see that we might not have done.
我想我们都可以看到我们可能没有这样做。
Let's try some communication in this game.
让我们尝试在这个游戏中进行一些交流。
We said that coordination games are helped by communication.
我们说过，协调游戏是通过沟通来帮助的。
So let's imagine we're playing the game again, once again, you're going to the movies, once again the first one didn't happen so you didn't--for some reason it was cancelled that night because someone had a bad cold or something.
所以，让我们想象一下，我们再次玩游戏，再一次，你去看电影，再次，第一个没有发生，所以你没有——出于某种原因，那天晚上它被取消了，因为有人得了重感冒或其他什么原因。
You are about to go off on Friday night to see these movies and let's allow some communication ahead of time.
您将于周五晚上去看这些电影，让我们提前进行一些沟通。
So David, you're about to go, you realize you've got this coordination problem, so you phone Nina up and you can say whatever you like, so what would you say to Nina?
大卫，你要走了，你意识到你有这个协调问题，所以你给尼娜打电话，你可以说任何你喜欢的话，那么你会对尼娜说什么？
Student: Looks like you want to go to Bourne Ultimatum .
学生：看来你想去《谍影重重》。
I'd rather go and--if you're going to be stubborn I'd rather go see Bourne Ultimatum with you than not go on a date at all.
我宁愿去——如果你要固执的话，我宁愿和你一起去看《谍影重重》，也不愿根本不去约会。
Professor Ben Polak: So here's another clue.
本·波拉克教授：这是另一条线索。
Stubborn is not a good first date word, but okay.
固执不是一个好的第一次约会词，但没关系。
So Nina what would you say in response to that?
那么尼娜对此有何回应？
Professor Ben Polak: All right, so write down what you're going to do this time.
Ben Polak 教授：好吧，写下你这次要做什么。
Nina what did you do?
妮娜你做了什么？
Professor Ben Polak: So they're still managing to coordinate but you--okay, so thank you for this couple, let's give them a round of applause.
本·波拉克教授：所以他们仍在设法协调，但是你们——好吧，谢谢这对夫妇，让我们给他们热烈的掌声。
We may come back and pick on you later on in the course, but we'll leave it for now.
我们可能稍后会在课程中回来挑选您，但我们现在就先不谈了。
So in this case, the communication worked but am I right in thinking that the communication isn't such an instant solution as it was in the game we saw last time?
因此，在这种情况下，沟通有效，但我认为沟通并不是像我们上次在游戏中看到的那样即时解决方案，这样的想法正确吗？
This game's a little bit harder to get communication to work.
这个游戏的沟通有点困难。
Why?
为什么？
Is that right first of all?
首先这是对的吗？
So what's the problem here?
那么这里有什么问题呢？
Why is this a slightly more difficult game?
为什么这是一个稍微困难一点的游戏？
Let's keep the mikes handy a second.
让我们把麦克风放在手边。
Why is this a more difficult game to attain coordination in?
为什么这是一个更难达到协调性的游戏？
Student: Can I say the best response is the Nash Equilibrium?
学生：我可以说最好的反应是纳什均衡吗？
Professor Ben Polak: Well no, hang on a second.
本·波拉克教授：嗯，不，请稍等。
Just slow down a second, that's a good one.
放慢一点速度，这样很好。
Let's start with that.
让我们从那开始吧。
What are the Nash Equilibria in this game?
这个博弈中的纳什均衡是什么？
Somebody, let's just pick on somebody.
来人吧，我们就选一个人吧。
Just pick on anybody okay.
随便选一个就可以了。
Yeah, what are the Nash Equilibria in this game?
是啊，这个游戏的纳什均衡是什么？
Student: Both players doing Bourne Ultimatum and both players doing Good Shepherd .
学生：两个玩家都在玩《谍影重重》，两个玩家都在玩《好牧人》。
Professor Ben Polak: All right, so in fact, if we checked the Nash Equilibria in this game, the Nash Equilibria, and you can check that they are in fact best responses, are both people doing The Bourne Ultimatum or both people doing The Good Shepherd .
Ben Polak 教授：好吧，事实上，如果我们检查这个游戏中的纳什均衡，纳什均衡，你可以检查它们实际上是最佳响应，是两个人都在玩《谍影重重》，还是两个人都在玩《好牧人》。
And the reason for that is if the other person's going to go to Bourne Ultimatum I want to do that, and if the other person's going to go Good Shepherd I want to do that.
这样做的原因是，如果另一个人要去《谍影重重》，我想这么做，如果另一个人要去《好牧人》，我也想这么做。
So these are both Nash Equilibria.; That isn't so much the problem.
所以这些都是纳什均衡。这并不是什么大问题。
That was true last time as well.
上次也是如此。
There were two well coordinated Nash Equilibria although one was better than the other.
有两个协调良好的纳什均衡，尽管其中一个比另一个更好。
What's the tricky thing here?
这里有什么棘手的事情？
What's the extra trick here?
这里有什么额外的技巧吗？
Is there a mike on this side?
这边有麦克风吗？
There was a hand up there, yeah.
那里有一只手，是的。
Stand up.
起来。
Great.
伟大的。
Professor Ben Polak: All right, so unlike the other game, the two examples of coordination games we saw so far were really pure coordination problems.
Ben Polak 教授：好吧，与其他游戏不同，我们到目前为止看到的协调游戏的两个例子实际上是纯粹的协调问题。
Is that right?
是这样吗？
They were pure coordination problems.
它们纯粹是协调问题。
There was no conflict at all.
根本没有冲突。
In the case of the Investor Game last week, every player preferred one equilibrium to the other.
在上周的投资者博弈中，每个玩家都更喜欢一种均衡而不是另一种。
The game I just put up, that's a trivial example, it didn't really matter which equilibrium we played here, we just wanted to play an equilibrium, is that right?
我刚刚提出的游戏，这是一个微不足道的例子，我们在这里玩哪种均衡并不重要，我们只是想玩一个均衡，对吗？
But here, there's a potential source of conflict here.
但这里存在潜在的冲突根源。
Both people would rather be at an equilibrium than to be mal-coordinated or uncoordinated, but Player 1 wants to go to Bourne Ultimatum and Player 2 wants to go to Good Shepherd , and actually I thought Nina's strategy there was pretty good.
两个人都宁愿处于平衡状态，也不愿不协调或不协调，但是玩家1想要去谍影重重，玩家2想要去好牧人，实际上我认为尼娜的策略很好。
Nina's version of communication was, "I'm going to Bourne Ultimatum ." That basically fixed things.
尼娜的沟通版本是，“我要去谍影重重的最后通牒”。这基本上解决了问题。
But you could imagine that communication could break down here.
但你可以想象，这里的沟通可能会中断。
There could be a negotiation going on.
可能正在进行谈判。
So think about--I don't want to push this too hard but think about other games where people are communicating to fail--to avoid a failure of coordination.
所以想一想——我不想把这件事推得太难，但想一想其他游戏中人们沟通失败的情况——以避免协调失败。
There's a strike negotiation going on as we speak.
就在我们说话的时候，罢工谈判正在进行中。
In fact, there was a critical moment this morning up in Detroit between General Motors and the united autoworkers and I don't want to say that strikes are only about mis-coordination, but clearly, everyone's better off if they come to some agreement rather than strike.
事实上，今天早上在底特律，通用汽车公司和联合汽车工人之间存在着一个关键时刻，我不想说罢工只是因为协调不当，但显然，如果他们达成某种协议而不是罢工，每个人都会过得更好。
There's at least some agreement that's going to be better for everybody than a strike, and yet, because they're conflicting interests there, basically in that case conflicting interest about health and pension payments, it could well be that you end failing to coordinate.
至少有一些协议比罢工对每个人都更好，但是，因为他们之间存在利益冲突，基本上在这种情况下是关于健康和养老金支付的利益冲突，很可能最终无法协调。
So this game has a name, and actually somebody mentioned it last time.
所以这个游戏有一个名字，实际上上次有人提到过。
Who was the person who mentioned this last time?
上次提到这件事的人是谁？
Somebody mentioned this.
有人提到过这个。
What was this game called?
这个游戏叫什么名字？
Shout it out!
大声喊出来！
Battle of the Sexes.
性别之战。
That's good.
那挺好的。
So this game's called The Battle of the Sexes and we'll see it in various forms over the course of the semester.
所以这个游戏被称为“性别之战”，我们将在整个学期以各种形式看到它。
It's actually a very interesting game.
这实际上是一个非常有趣的游戏。
Games like it, they are coordination games but different people disagree about where you'd like to coordinate.
像这样的游戏，它们是协调游戏，但不同的人对于你想要协调的地方存在不同意见。
So much for talking about coordination games and helping you with your dating strategy.
关于协调游戏和帮助您制定约会策略的内容就这么多了。
This being a Game Theory class, there's at least one game we have to discuss and we've come to it now.
这是一门博弈论课，我们至少要讨论一个游戏，现在我们已经讨论了。
So we're going to spend most of the rest of today talking about Cournot Duopoly.
因此，我们将在今天剩下的大部分时间里讨论古诺双寡头。
Before I do that, let me just check.
在我这样做之前，让我先检查一下。
How many of you have seen Cournot Duopoly before?
你们中有多少人以前看过古诺双寡头？
Just raise your hands just for me.
只为我举起你的手。
All right, so maybe about half of you.
好吧，大概是你们一半的人。
So those of you who have, don't worry, I mean this will be a bit review, but we'll see it more through the eyes of Game Theory this time, and for those of you who haven't, don't worry we're going to go through it.
所以，那些已经了解过的人，别担心，我的意思是，这将是一个回顾，但这次我们会更多地通过博弈论的视角来看待它，而对于那些还没有了解过的人，别担心，我们将详细介绍它。
So this is a classic game, perhaps it's one of the most famous games, and therefore worth studying in the class.
所以这是一款经典游戏，也许是最著名的游戏之一，因此值得在课堂上学习。
Now, as a purely Game Theory exercise, one reason for studying Cournot Duopoly, is that so far we've discussed how to find Nash Equilibrium when there are few players, each of whom has few strategies, and we've discussed how to find Nash Equilibrium where there are many players, each of whom has few strategies, and this is a game where there are few players, maybe two, but they have many strategies.
现在，作为纯粹的博弈论练习，研究古诺双寡头的一个原因是，到目前为止，我们已经讨论了如何在参与者很少、每个人都没有策略的情况下找到纳什均衡，并且我们已经讨论了如何在参与者很多、每个人都没有策略的情况下找到纳什均衡，而这是一个参与者很少（也许是两个，但他们有很多策略）的博弈。
They actually have a continuum of strategies.
他们实际上有一系列的策略。
For those people who aren't familiar with this and are worried about the economics of it in particular, it's gone over in considerable detail in chapter 6 of the textbook.
对于那些不熟悉这一点并且特别担心其经济性的人，教科书的第 6 章对此进行了相当详细的介绍。
So just to motivate this a little bit, so there's two reasons why this game is interesting.
所以只是为了稍微激励一下，所以这个游戏有趣的原因有两个。
This is a game in which there are two firms who are competing in the same market, and we'll give a bit more detail in a second.
这是一个有两家公司在同一市场竞争的博弈，我们稍后会提供更多细节。
One reason this game is interesting from the point of view of economics, is this game lies between the two extreme cases that you learn about in your Intro Economics class.
从经济学的角度来看，这个游戏有趣的原因之一是，这个游戏位于您在经济学入门课程中学到的两种极端情况之间。
One extreme case is perfect competition and the other extreme case is monopoly.
一种极端情况是完全竞争，另一种极端情况是垄断。
So this is really the first attempt, way back in the nineteenth century to study a market that's somewhere in the middle, where it happens most markets are--there are two firms.
因此，这实际上是第一次尝试，早在十九世纪就研究了一个处于中间位置的市场，大多数市场都在那里——有两家公司。
We're interested in two things here.
我们对这里的两件事感兴趣。
We're interested in what's going to happen in these markets.
我们对这些市场将发生的事情感兴趣。
And then from a welfare point of view, from a policy point of view, we're interested about whether this is good for consumers or good for producers or what.
然后从福利的角度来看，从政策的角度来看，我们感兴趣的是这对消费者有利还是对生产者有利还是什么。
How this relates to profits and consumer surplus.
这与利润和消费者剩余有何关系。
So with that in mind, let's just set the game up.
考虑到这一点，让我们来设置游戏。
So the players in this game are two firms and the strategies in this game for the firms--and this is going to turn out to be important--the strategies are the quantities that they produce of an identical product.
因此，这个游戏中的参与者是两家公司，而这个游戏中的策略对公司来说很重要——策略是它们生产相同产品的数量。
So they are the quantities they produce, each of them produces, of an identical product.
因此，它们是他们生产的相同产品的数量，每个人生产的数量。
So as far as the consumers are concerned, these two products are perfect substitutes.
所以对于消费者来说，这两种产品是完美的替代品。
You could think of these as two companies producing bottled water--and now we're going to get hundreds of letters saying not all bottled waters are the same, especially from Italians and the French, but never mind.
你可以把它们想象成两家生产瓶装水的公司——现在我们会收到数百封信，说并非所有瓶装水都是一样的，尤其是来自意大利和法国的，但没关系。
Let's just pretend that they are.
让我们假装他们是。
So just to emphasize that the strategies are quantities, rather than using S let me use q today to be the strategies.
因此，只是为了强调策略是数量，而不是使用 S，让我今天使用 q 作为策略。
So qi and q-i or q1 and q2 will be the strategies.
因此 qi 和 q-i 或 q1 和 q2 将是策略。
We need to give a little bit more structure on the payoff before I get to the payoffs.
在我开始讨论收益之前，我们需要对收益给出更多的结构。
So in particular, I need to tell you what is the cost of production.
因此，我特别需要告诉您生产成本是多少。
And the cost of production in this game is simply going to be cq.
而这款游戏的制作成本就是 cq。
So if I produce one unit it costs me c; if I produce two units it costs me 2c; if I produce 100 units, it'll cost me 100c and if I produce .735 units that costs me .735c.
因此，如果我生产一单位，我的成本就是 c；如果我生产两个单位，则花费我 2c；如果我生产 100 个单位，则花费 100c，如果我生产 0.735 个单位，则花费 0.735c。
So for those people who took Intro Economics, which is most of you, this is a game--this a setting in which we have constant marginal costs.
因此，对于那些学过经济学导论的人（也就是你们中的大多数人）来说，这是一个游戏——在这个游戏中，我们有恒定的边际成本。
The constant marginal cost is c.
恒定边际成本为c。
I'll need to tell you about how prices are determined in this market.
我需要告诉您这个市场的价格是如何确定的。
So prices are determined as follows: prices depend on some parameters I'm just going to call a and b, and let me write the equation and then we'll see what it looks like.
所以价格确定如下：价格取决于一些参数，我将称之为 a 和 b，让我写下方程式，然后我们看看它是什么样子。
So basically the idea is that the more these firms produce, so the more the total quantity produced q1 + q2, the lower is the price in the marketplace for this product.
所以基本上这个想法是，这些公司生产的越多，那么生产的总量 q1 + q2 就越多，该产品的市场价格就越低。
Let's just draw a picture of that; we'll come back to this in a minute.
让我们画一张图；我们稍后再讨论这个问题。
Let's draw a picture which we can keep for later.
让我们画一张图，以便以后保存。
Actually, let's save myself some time and bring this down.
事实上，让我们为自己节省一些时间，把这件事解决掉。
So this equation I've just written, if you can imagine q1 + q2, total quantity on the horizontal axis, and you could imagine price on the vertical axis, and basically what we're saying is that prices depend on total quantities as follows: where the slope of this line is -b.
所以我刚刚写的这个方程，如果你可以想象 q1 + q2，水平轴上的总量，你可以想象垂直轴上的价格，基本上我们所说的是价格取决于总量，如下所示：这条线的斜率是 -b。
Now, for those of you who took Economics 115 or equivalent, what is the name of this line I've just drawn?
现在，对于学过经济学 115 或同等课程的人来说，我刚刚画的这条线的名称是什么？
That was way fewer responses than I wanted.
这比我想要的要少得多。
Let's try again; what's the name of this downward sloping (hint-hint) line that I've just drawn?
让我们再试一次；我刚刚画的这条向下倾斜（提示提示）线的名称是什么？
It's a demand curve.
这是一条需求曲线。
Thank you; it's a demand curve.
谢谢;这是一条需求曲线。
That was the demand.
这就是需求。
It tells me--the other way around--to look at how prices correspond to quantities, it tells me the quantity demanded at any given price.
它告诉我——相反——看看价格如何与数量相对应，它告诉我在任何给定价格下的需求数量。
We'll come back to that in a second.
我们稍后会回到这个话题。
Meanwhile, let's just finish up what we're doing here and put in payoffs.
与此同时，让我们完成我们正在做的事情并付出代价。
So payoffs for these firms are going to depend on profits, the payoffs.
因此，这些公司的回报将取决于利润、回报。
The firms' aim to maximize profit and profit is going to be given by P times q minus--sorry, let's do this for Firm 1.
公司的目标是利润最大化，利润将由 P 乘以 q 减去——抱歉，让我们为公司 1 这样做。
Let's be careful here; let's do this for Firm 1 and we'll do Firm 2 in a second.
让我们小心一点；让我们对公司 1 执行此操作，稍后我们将对公司 2 执行此操作。
So the payoff for Firm 1, as it depends on the quantity that she produces and the quantity that the other firm produces, is going to be prices times the quantity that Firm 1 produces minus costs times the quantity that she produces.
因此，公司 1 的收益取决于她生产的数量和其他公司生产的数量，因此将是价格乘以公司 1 生产的数量减去成本再乘以她生产的数量。
So this is--this term here is revenues and this term here is total costs.
所以，这个术语是收入，这个术语是总成本。
Revenues minus costs makes profits, and again, for those of you who are less familiar with economics, I'm hoping this is not really too hard but you can read up on it.
收入减去成本就产生利润，对于那些不太熟悉经济学的人来说，我希望这并不是太难，但你可以阅读一下。
What I'm going to do here is I'm going to substitute in for prices.
我在这里要做的是用价格来代替。
So I've got this expression for prices here, here it is, and I want to plug it into that P there.
所以我在这里得到了这个价格表达式，就在这里，我想将它插入到那里的 P 中。
And I'm going to rewrite it now with that P expanded out.
现在我将用 P 扩展来重写它。
So I'm going to get--I'm going to multiply it out at the same time, so I'm going to have aq1 - bq1² - bq1q2 - cq1.
所以我要同时将其相乘，所以我将得到 aq1 - bq1² - bq1q2 - cq1。
All I'm doing here, nothing particularly exciting, I'm simply plugging this expression in for P and then I multiplied the whole thing out because it was all multiplied by q.
我在这里所做的一切，没有什么特别令人兴奋的，我只是将这个表达式代入 P，然后我将整个结果相乘，因为它全部乘以 q。
I should warn you again that I'm very likely to make mistakes when I'm doing this kind of thing, so please catch me I do.
我应该再次警告你，当我做这种事情时，我很可能会犯错误，所以请抓住我。
So here I have a new expression for Firm 1's profit and I could do the same for Firm 2, but I'm not going too because it's--I'm getting bored.
所以在这里我对公司 1 的利润有一个新的表达方式，我可以对公司 2 做同样的事情，但我不会也这样做，因为它——我感到无聊了。
So this is just Firm 1's profit.
所以这只是公司 1 的利润。
Now, with this in hand, what I want to do is, and in Firm 2 I have a similar expression, what I want to do is, I want to figure out the Nash Equilibrium of this game.
现在，有了这个，我想做的是，在公司 2 中我有一个类似的表达，我想做的是，我想找出这个博弈的纳什均衡。
Now, I will need the other board; I want to figure out the Nash Equilibrium on this game.
现在，我需要另一块板；我想找出这个游戏的纳什均衡。
Both firms are producing quantities; both firms are trying to maximize profit, and I want to find out the Nash Equilibrium.
两家公司都在批量生产；两家公司都试图实现利润最大化，我想找出纳什均衡。
How do I go about that exercise?
我该如何进行这项练习？
What's the--what do I need to do find each firm's Nash Equilibrium?
我需要做什么才能找到每个公司的纳什均衡？
How do we always find Nash Equilibrium when we're not guessing?
当我们不猜测时，如何才能找到纳什均衡？
What do we do?
我们该怎么办？
Anybody?
有人吗？
Somebody way over there who's going to be way off camera but we can actually get a mike in there.
那边有人远离镜头，但我们实际上可以在那里放一个麦克风。
Can we get a--he's way in the corner there.
我们能找到——他就在角落里吗？
Come this way, a little closer to the aisle, there you go.
这边走，离过道近一点，就到了。
Student: Well, we would just delete the--we would iteratively delete dominated strategies.
学生：嗯，我们会删除——我们会迭代地删除主导策略。
Professor Ben Polak: Okay, we could do that.
Ben Polak 教授：好的，我们可以做到。
We could do that; we could try iteratively deleting dominated strategies and see if that process converged.
我们可以这样做；我们可以尝试迭代删除主导策略，看看该过程是否收敛。
I had something else in mind here, something else more straightforward.
我在这里想到了别的事情，一些更直接的事情。
What else?
还有什么？
The guy in red.
那个红衣人。
Student: Identify the best responses of each player as a function of the others and find out where they intersect.
学生：根据其他玩家的函数确定每个玩家的最佳反应，并找出它们的交叉点。
Professor Ben Polak: Say that loud--more--that was correct, say it more loudly, shout.
本·波拉克教授：大声说——更多——这是正确的，大声说，喊。
Student: Identify the best responses of each player as a function of the others and find out where they intersect.
学生：根据其他玩家的函数确定每个玩家的最佳反应，并找出它们的交叉点。
Professor Ben Polak: Okay good.
本·波拉克教授： 好的，很好。
So what we're going to do is we're going to figure out Player 1's best response quantity to each possible choice of Player 2, and then we're going to flip it around and figure out Player 2's best response quantity to each possible choice of Player 1, and then we're going to see where they--where those coincide, where they cross.
所以我们要做的就是找出玩家 1 对玩家 2 的每个可能选择的最佳响应量，然后我们将翻转它并找出玩家 2 对玩家 1 的每个可能选择的最佳响应量，然后我们将看到它们在哪里 - 它们在哪里重合，在哪里交叉。
So, just like we've done several times before.
所以，就像我们之前做过几次一样。
So what I need to do then is I need to figure out what is Player 1's best response for each possible choice q2 of Player 2.
那么我需要做的是找出玩家 1 对于玩家 2 的每个可能选择 q2 的最佳反应是什么。
So how do I do that?
那么我该怎么做呢？
I want to find the best response.
我想找到最好的回应。
How do I do that?
我该怎么做？
Everyone is looking like this is--I bet you all know really.
每个人看起来都是这样的——我敢打赌你们都知道。
Anybody?
有人吗？
Cold call somebody?
冷冰冰地打电话给某人？
Athletic day for you.
适合你的运动日。
Somebody way at the back there; stand up and shout.
后面有人；站起来喊。
Student: Find the best response function by differentiating this and maximizing the function for every q2, so we could just--
学生：通过对每个 q2 求微分并最大化该函数来找到最佳响应函数，这样我们就可以——
Professor Ben Polak: Good, so what we're going to do is--all right good, we're going to--we're trying to maximize--the best response is going to maximize these profits.
本·波拉克教授：很好，所以我们要做的是——好吧，我们将——我们正在努力最大化——最好的反应就是最大化这些利润。
So, in particular, what we're going to do to find out what quantity q1maximizes this profits for each choice of q2.
因此，特别是，我们将如何找出 q1 的数量可以使 q2 的每种选择的利润最大化。
We're going to differentiate this with respect to q1 and then what?
我们将针对 q1 对它进行微分，然后呢？
And then set it equal to 0.
然后将其设置为等于0。
So again, let me just take a look out there.
那么，让我再去看看那里。
How many of you remember this?
你们中有多少人还记得这个？
We did this once before in this class.
我们以前在这堂课上做过一次。
How many of you remember this from when you were--high school calculus days or from 112?
你们中有多少人还记得高中微积分时代或 112 时代的这一点？
Quite a number of you actually.
你们中实际上有相当多的人。
Okay, good, so what we're going to do is we're going to differentiate this thing to find a first order condition.
好的，很好，所以我们要做的就是对这个东西进行微分以找到一阶条件。
We're going to differentiate with respect to q1, the thing we're trying--our control variable, the thing we're trying to maximize the thing with respect to and set it equal to 0.
我们将对 q1 进行微分，我们正在尝试的东西——我们的控制变量，我们试图最大化的东西并将其设置为等于 0。
So what are we going to get?
那么我们会得到什么呢？
So this term here aq1 is going to become an a and this term here -bq² is going to become a 2bq1 and this term here, -b q1q2 is going to become a -bq2, and the last term -cq1 is going to become a -c.
因此，这里的项 aq1 将变为 a，这里的项 -bq² 将变为 2bq1，这里的项 -b q1q2 将变为 -bq2，最后一项 -cq1 将变为 -c。
Everyone happy with that?
大家对此满意吗？
What I did was I differentiated this fairly simple function with respect to q1 and since I want to find a maximum, what I'm going to do is I'm going to set this thing equal to 0.
我所做的就是对这个相当简单的函数对 q1 进行微分，因为我想找到最大值，所以我要做的就是将这个值设置为 0。
At my maximum, I'll put a hat over it to indicate this is the argmax; at my maximum I'm going to set this thing equal to 0.
在我的最大值下，我会在它上面戴上一顶帽子来表明这是 argmax；在我的最大范围内，我会将这个值设置为 0。
Now, since we're being nerdy in this class, despite our attempts to go dating, we're being nerdy, let's actually be a little bit careful.
现在，既然我们在这堂课上很书呆子，尽管我们尝试去约会，但我们很书呆子，让我们实际上要小心一点。
This was a first order condition or a first order necessary condition.
这是一阶条件或一阶必要条件。
I actually need to check the second order condition.
我实际上需要检查二阶条件。
So how do I check the second order condition?
那么如何检查二阶条件呢？
I differentiate again, right?
我再区分一下吧？
I differentiate a second time and check the sign, so the second order condition, I differentiate this expression again with respect to q1.
我第二次微分并检查符号，因此在二阶条件下，我再次对 q1 对该表达式进行微分。
The only place q1 appears here is here, so when I differentiate again I'm going to get -2b and sure enough that's negative, which is what I wanted to know, just to check that when I'm finding this thing, I'm finding a maximum and not a minimum.
q1 出现在这里的唯一地方是这里，所以当我再次微分时，我将得到 -2b ，果然这是负数，这就是我想知道的，只是为了检查当我找到这个东西时，我找到的是最大值而不是最小值。
Good, so this is our key expression and I'm going to use this expression; I'm going to solve it for q1.
很好，这就是我们的关键表达方式，我将使用这个表达方式；我要解决 q1 的问题。
So the best response for Player 1, as a function of what Player 2 chooses, q2, is just equal to the q1 hat in this expression and if I solve that out carefully, I will no doubt make a mistake, but let's try it.
因此，作为玩家 2 选择的函数 q2，玩家 1 的最佳响应正好等于此表达式中的 q1 帽子，如果我仔细解决这个问题，我无疑会犯错误，但让我们尝试一下。
I got to have a - c over 2b - q2 over 2.
我必须有 a - c 超过 2b - q2 超过 2。
So try that at home, I think I did that right.
所以在家里尝试一下，我认为我做得对。
So I took this to the other side and I divided through by 2b and the b here cancels.
所以我把它带到另一边，然后除以 2b，这里的 b 被取消。
Everyone just stare at that a second, make sure I got it right.
每个人都盯着看一秒钟，确保我做对了。
I'm very capable of getting these things wrong.
我很容易把这些事情搞错。
Good, so what I have here is an equation that tells me Player 1's best response for each possible choice of Player 2.
很好，所以我这里有一个方程，它告诉我玩家 1 对玩家 2 的每个可能选择的最佳反应。
I could do the same thing for Player 2 to find Player 2's best response for every possible choice of Player 1.
我可以对玩家 2 做同样的事情，找到玩家 2 对玩家 1 的每个可能选择的最佳响应。
On the other hand, we know it's--the math is going to be the same, so let's cheat.
另一方面，我们知道数学是一样的，所以让我们作弊吧。
I know that Player 2's best response for every possible choice of Player 1, which if we had done it would be q2 hat is going to a - c over 2b--q1 over 2, right?
我知道玩家 2 对玩家 1 的每个可能选择的最佳反应，如果我们这样做的话，这将是 q2 帽子将是 a - c 超过 2b--q1 超过 2，对吗？
I'm just flipping around the 2's and the 1's.
我只是翻转 2 和 1。
So at this point I've found Player 1's best response as a function of q2.
所以此时我已经找到了玩家 1 的最佳响应作为 q2 的函数。
I've found Player 2's best response as a function of q1, and the way I did it, just remember, the way I did it was I applied a little bit of 112 and/or high school calculus, so that's your single variable calculus.
我发现玩家 2 的最佳响应是 q1 的函数，我的做法是，记住，我的做法是应用了一点 112 和/或高中微积分，所以这就是你的单变量微积分。
Now, we could just solve at this point but let's not.
现在，我们可以在这一点上解决，但我们不这样做。
Let's draw these.
我们来画这些吧。
So what I'm going to do is I'm going to go back to my picture and draw these functions.
所以我要做的就是回到我的图片并画出这些函数。
I'll just remind us of what these functions are; it's a - c over 2b - q2 over 2 and accordingly for Player 2.
我只是提醒我们这些功能是什么；它是 a - c 超过 2b - q2 超过 2，因此对于玩家 2 来说。
That's the thing; it was hidden by the board.
就是这样；它被董事会隐藏了。
What I want to do is I want to draw a picture, a little bit like we did for the partnership game.
我想做的是画一幅画，有点像我们为合作游戏所做的那样。
So in the partnership game we put efforts on these axis and now I'm going to put quantities on these axis.
因此，在合作游戏中，我们在这些轴上投入了精力，现在我将在这些轴上投入数量。
So this is going to be the choice of Player 1, and this is going to be the choice of Player 2, and what I want to do is I want to figure out what this looks like.
所以这将是玩家 1 的选择，这将是玩家 2 的选择，我想做的是弄清楚这是什么样的。
For each q2 that you give me or that Player 2 chooses, I want to find out and draw what is Player 1's best response.
对于你给我的或玩家 2 选择的每个 q2，我想找出并画出玩家 1 的最佳响应是什么。
Everyone happy with what I'm doing here?
大家对我在这里所做的事情感到满意吗？
So let's start somewhere; what we're going to do is we'll refer back to this other picture, which is why I left it here.
那么让我们从某个地方开始吧；我们要做的是回顾另一张图片，这就是我把它留在这里的原因。
So, in particular, what would be Player 1's best response if Player 2 didn't produce at all?
那么，特别是，如果球员 2 根本没有表现，球员 1 的最佳反应是什么？
How do we find that?
我们如何找到它？
Without worrying about the economics of it a second, how would we find that just as a math exercise?
不用担心它的经济性，我们怎么会发现它只是一个数学练习呢？
So suppose Player 2 doesn't produce at all.
所以假设玩家 2 根本没有产出。
What is Player 1's best response?
玩家 1 的最佳反应是什么？
Someone read it off for me.
有人给我读了一遍。
Why don't we cold call somebody out, you can--
为什么我们不冷酷地叫某人出来，你可以——
Professor Ben Polak: Good, so if I plug q2 = 0 into here, this term disappears and I just get a - c over 2b.
Ben Polak 教授：很好，所以如果我将 q2 = 0 代入这里，这项就消失了，我只得到 a - c over 2b。
What's that telling me?
这告诉我什么？
Let me put the 45º line in here.
让我把 45° 线放在这里。
What's that telling me is that if Player 2 chooses not to produce then Player 1's best response is a - c over 2b.
这告诉我的是，如果玩家 2 选择不产出，那么玩家 1 的最佳反应是 a - c 超过 2b。
Now, I claim that that quantity, a - c over 2b actually has another name.
现在，我声称 a - c 除以 2b 的量实际上有另一个名称。
What's the name of that quantity?
这个数量的名称是什么？
What's the name of the quantity a - c over 2b?
2b 上的 a - c 量的名称是什么？
Once we escape the algebra just think about it in terms of economics.
一旦我们摆脱了代数，就从经济学的角度来思考它。
Let's think about it a bit, let's go back to the previous picture.
我们想一下，我们回到上一张图片。
If Player 2 is producing nothing, then what is Player 1 effectively?
如果玩家 2 没有做出任何贡献，那么玩家 1 的实际意义是什么？
He's a monopoly; so she's a monopolist, so we know how to figure out monopoly quantities from what we did in 115 or equivalent courses.
他是一个垄断者；所以她是垄断者，所以我们知道如何从我们在 115 或同等课程中所做的事情中计算出垄断数量。
Let me finish the picture here; here's my demand curve, here's my constant marginal cost at c, and I want to use this picture on the left now to figure out what the monopoly quantity is.
让我把这幅图画完吧；这是我的需求曲线，这是我在 c 处的恒定边际成本，我现在想用左边的这张图来计算垄断数量是多少。
Can anyone tell me--let's cold call somebody again.
谁能告诉我——我们再给某人打电话吧。
Raise your hand if you took 115, 110 or 150.
如果你拿了 115、110 或 150，请举手。
No, no, I know more of you took it than that.
不，不，我知道你们中更多人拿过它。
It's a pre-req for the class, right?
这是课程的先决条件，对吧？
Raise your hands if you didn't take any of those things.
如果你没有拿走这些东西，请举手。
Ale, keep your hands up.
艾尔，举起你的手。
Cold call somebody who hasn't got their hand up.
冷酷地呼叫那些还没有举手的人。
Anybody, go ahead.
任何人，都来吧。
Do you want to tell me what the--where's the monopoly quantity on this picture?
你想告诉我这张照片上的垄断数量在哪里吗？
The woman--where you are--the woman here.
那个女人——你在哪里——这里的女人。
Professor Ben Polak: Who else doesn't remember?
本·波拉克教授：还有谁不记得了？
Somebody must--don't remember is a good reply if you're auditioning to be the Attorney General, but it's not such a good reply--anybody?
如果你正在试镜司法部长，必须有人——不记得这是一个好的答复，但这不是一个很好的答复——有人吗？
Somebody help me out here, where's the monopoly quantity on this picture?
谁来帮帮我，这张图上的垄断数量在哪里？
It's a good review exercise, yeah.
这是一个很好的复习练习，是的。
Student: It's where the marginal revenue is equal to the marginal costs.
学生：边际收益等于边际成本。
Professor Ben Polak: It's where marginal revenue equals marginal cost.
本·波拉克教授：这是边际收益等于边际成本的地方。
I should have picked on some of the SOM people by the way.
顺便说一句，我应该选择 SOM 的一些人。
It's where marginal revenue equals marginal cost, right?
边际收益等于边际成本，对吗？
The reason I should pick on the SOM people, is their ambition in life is to run a monopoly, right.
我之所以应该选择 SOM 的人，是因为他们的人生志向就是经营垄断，对吧。
Trouble is I haven't drawn the marginal revenue curve yet.
问题是我还没有画出边际收益曲线。
Right, you can't actually see the marginal revenue here.
是的，你实际上看不到这里的边际收益。
What does the marginal revenue look like in this picture?
这张图中的边际收益是什么样的？
Why don't we go to the same guy, the guy in brown.
我们为什么不去找同一个人，那个穿棕色衣服的人。
Where's the marginal revenue--what's the marginal revenue look like in this picture on the left?
边际收益在哪里——左图中的边际收益是什么样的？
Professor Ben Polak: Yeah, or it's--I guess it's twice the slope but that's fair enough.
本·波拉克教授：是的，或者是——我想它是斜率的两倍，但这很公平。
I know what you mean.
我知道你的意思。
So the marginal revenue here, let's put it in a different color, the marginal revenue looks something like this and as--I don't know what your name is--as the guy said, the monopoly quantity is when marginal revenue equals marginal costs.
所以这里的边际收益，让我们用不同的颜色来表示，边际收益看起来像这样——我不知道你叫什么名字——正如那家伙所说，垄断数量是指边际收益等于边际成本。
As we know, this line here has twice the slope of the original line of the demand curve, so the slope of this thing is -2b.
我们知道，这里的这条线的斜率是需求曲线原来的线的两倍，所以这个东西的斜率是-2b。
Now, I'm going to claim that this monopoly quantity I claimed before is going to--our intuition says if the other firm isn't producing, my best response must be to produce monopoly quantity which I can see on this picture, and I also claim that the math is telling me, just a kind of nerdy math is telling me, that that quantity is a - c over 2b and I claim that they're the same thing.
现在，我要断言我之前声称的这个垄断数量将会——我们的直觉告诉我们，如果另一家公司不生产，我最好的反应一定是生产我在这张图片上看到的垄断数量，我还声称数学告诉我，只是一种书呆子数学告诉我，这个数量是 a - c 超过 2b，我声称它们是同一件事。
How can I see they're the same thing?
我怎么能看出它们是同一件事？
Well look, here I have a line of slope -2.
好吧，看，这里有一条斜率为 -2 的线。
How far down does it have to go?
还要往下走多远？
It has to a - c down.
它必须 a - c 向下。
This pink line has to drop off from a all the way to c.
这条粉红色的线必须从 a 一直下降到 c。
How far along do I have to go drop off a - c when I have slope -2b?
当坡度为 -2b 时，我需要走多远才能从 a - c 下车？
Answer a - c over 2b.
回答 a - c 超过 2b。
Not even calculus - all you need is high school.
甚至连微积分都不需要——你所需要的只是高中。
So this monopoly quantity is indeed a - c over 2b.
所以这个垄断数量确实是 a - c 超过 2b。
I'm going to ask again, is some of this being--coming out of the fog?
我要再问一遍，其中有一些是从迷雾中走出来的吗？
I mean, you may not understand it with algebra before but some of these sorts of pictures have you seen before?
我的意思是，你以前可能不理解代数，但你以前见过一些这样的图片吗？
It's good review exercise for some of you who are--who have taken 115 or are about to take 150 or are there now.
对于已经考过 115 分、即将考取 150 分或现在已经考过 150 分的人来说，这是一次很好的复习练习。
So we found precisely one point on this best response picture, and there's a lot of points to find, and it's 20 past 12, so we better get going.
所以我们在这张最佳响应图片上准确地找到了一个点，而且还有很多点需要找到，而且现在是 12 点 20 分，所以我们最好开始行动。
So let's try and find another point.
那么让我们尝试找到另一个点。
Let's ask a different question.
让我们问一个不同的问题。
How much quantity would Firm 2 have to produce in order to induce Firm 1 not to produce at all?
为了促使公司 1 根本不生产，公司 2 必须生产多少数量？
Again, how much quantity would Firm 2 have to produce in order to induce Firm 1's best response to be 0?
同样，企业 2 必须生产多少数量才能使企业 1 的最佳响应为 0？
Help me out--it's Katie.
帮帮我——我是凯蒂。
Is that right?
是这样吗？
The woman in green, let's get a mike to Katie.
绿衣女人，我们给凯蒂拿个麦克风吧。
Or, there's a mike close by.
或者，附近有一个麦克风。
Professor Ben Polak: All right, so that's just solving out the algebra, so we're saying what's--what q solves, a - c over 2b - q2 over 2 = 0.
Ben Polak 教授：好吧，这只是解决代数问题，所以我们说的是 q 解决的问题，a - c over 2b - q2 over 2 = 0。
What q2 makes this equal to 0 and Katie's answer is solving out the algebra here is that q2 that solves this must be a - c over b.
q2 使这个等于 0，凯蒂的答案是解决这里的代数问题，解决这个问题的 q2 必须是 a - c over b。
That's right; where can I see that one on the picture though?
这是正确的;我在哪里可以看到图片上的那个？
Let's go back to the economics.
让我们回到经济学上来。
So I'm claiming that there's some quantity up here.
所以我声称这里有一些数量。
I claim this quantity is a - c over b such that if Firm 2 produces that much quantity, Firm 1 will just produce nothing.
我声称这个数量是 a - c 超过 b，这样如果企业 2 生产那么多数量，企业 1 将不会生产任何东西。
But that's just kind of algebra and math.
但这只是代数和数学。
Where can I see it on this picture?
在这张图片上哪里可以看到它？
What quantity, if produced by Firm 2, would cause Firm 1 to shut down on this picture?
如果由公司 2 生产，多少数量会导致公司 1 在这张图片中关闭？
Let's get a mike in here.
我们在这里拿个麦克风吧。
Student: That's where the marginal cost and the demand thing, demand lines intersect.
学生：这就是边际成本和需求、需求线相交的地方。
Professor Ben Polak: So it's here right, it's here.
Ben Polak 教授：所以它就在这里，就在这里。
It's where marginal--it's where the marginal cost and the demand curve intersects.
这是边际成本和需求曲线相交的地方。
What's the intuition?
直觉是什么？
Let's work it out.
让我们来解决一下。
Suppose Firm 2 has produced all of this quantity up to here.
假设到目前为止，公司 2 已经生产了所有这些数量。
So Firm 2 is already producing all of this quantity.
因此，公司 2 已经生产了所有这些数量。
So already, just from Firm 2's production the price has been driven all the way down to costs.
因此，仅从公司 2 的生产来看，价格就已一路下降至成本。
So if I--I'm Firm 1--if I produce any more quantity, what's going to happen to the price?
因此，如果我——我是第一家公司——如果我生产更多数量，价格会发生什么变化？
I produce any quantity at all in addition to what's out there already, what's going to happen to the price?
除了现有产品之外，我还生产任何数量，价格会发生什么变化？
It's going to be pushed below costs.
它将被压至成本以下。
So I'll be producing this stuff, this water at cost c and only getting p, which is not only less than c in return.
所以我将以成本 c 生产这些东西，这些水，并且只得到 p，这不仅低于 c 的回报。
So I'll be losing money on any product that I produce.
所以我生产的任何产品都会赔钱。
Does everyone see that?
大家都看到了吗？
Let me say it again.
我再说一遍。
So Firm 2--if Firm 2 produces all the way up to here then any product produced by Firm 1 is going to push prices even lower.
因此，企业 2——如果企业 2 的产量一直达到这里，那么企业 1 生产的任何产品都会将价格压得更低。
In particular, they'll be lower here than costs and so you'll make losses on that product.
特别是，它们的价格会低于成本，因此您会在该产品上蒙受损失。
What's the name--going back to Economics 115--what's the name for this quantity?
名字是什么——回到经济学115——这个量的名字是什么？
The quantity where demand and marginal costs equal--that's the competitive quantity.
需求和边际成本相等的数量——这就是竞争数量。
So this is the perfect competition quantity.
所以这就是完美竞争量。
In a perfectly competitive market that's exactly where prices are going to end up.
在完全竞争的市场中，这正是价格最终的结果。
This is not a perfectly competitive market, but if it were, that's where price is going to end up.
这不是一个完全竞争的市场，但如果是这样，价格就会最终达到这个水平。
So we have the monopoly quantity here, and we have the competitive here, and in between what does this best response curve look like?
所以我们这里有垄断数量，我们这里有竞争，在这两者之间，最佳响应曲线是什么样的？
Somebody?
有人吗？
It's a straight line, thank you.
这是一条直线，谢谢。
So in between--this is just a straight line.
所以在两者之间——这只是一条直线。
So here is the best response of Firm 1 to each possible choice of Firm 2.
因此，这是公司 1 对公司 2 的每个可能选择的最佳回应。
Everyone's looking really like this was hard, but it can't be that hard.
每个人都看起来真的很难，但其实并没有那么难。
Most of you have seen this before.
你们中的大多数人以前都见过这个。
If you haven't seen it before don't panic.
如果您以前没有见过，请不要惊慌。
All I did was, I did a little bit of calculus, a little bit of algebra, and then I drew the thing.
我所做的只是做了一点微积分、一点代数，然后我画了这个东西。
Okay, so this is Firm 1's best response as a function of q2.
好的，这是公司 1 作为 q2 函数的最佳响应。
What is Firm 2's best response as a function of q1?
作为 q1 的函数，企业 2 的最佳响应是什么？
Let's just--we'll get there, just to remind you, the way we read this is you give me a quantity of Firm 2, I find Firm 1's best response by going across to the pink line and dropping down.
让我们——我们会到达那里，只是提醒你，我们读这篇文章的方式是你给我一定数量的公司 2，我发现公司 1 的最佳反应是穿过粉红线并下降。
So if Firm 2 produces this amount then Firm 1's best response is this amount.
因此，如果公司 2 生产了这个数量，那么公司 1 的最佳反应就是这个数量。
If Firm 2 produces this amount then Firm 1's best response is this amount.
如果公司 2 生产了这个数量，那么公司 1 的最佳反应就是这个数量。
Now conversely, how do we find Firm 2's best response as a function of q1?
现在反过来，我们如何找到公司 2 作为 q1 函数的最佳响应？
What does that look like?
那看起来像什么？
Those two guys in front of you.
眼前的这两个家伙。
Professor Ben Polak: All right, it's reflected across the 45º line.
Ben Polak 教授：好吧，它是在 45° 线上反射的。
So let's reflect these two points.
那么我们来反思一下这两点。
This will be here; this will be--I've got to be a bit more careful.
这将在这里；这将是——我必须更加小心一点。
Missed by a mile, let me try again.
差了一英里，让我再试一次。
I missed by a mile, which is a problem in drawing my lines, but never mind.
我错过了一英里，这在画线时是一个问题，但没关系。
So this will be the monopoly quantity for Firm 2 and this is the competitive quantity of Firm 1.
因此，这将是企业 2 的垄断数量，这是企业 1 的竞争数量。
So if I had drawn that better it would look as if this was half of this distance, but I didn't draw it well.
所以如果我画得更好的话，看起来好像是这个距离的一半，但我画得不好。
Try and draw it better in your notes.
尝试在笔记中画得更好。
So this is a - c over b and this is a - c over 2b so this distance and this distance are meant to be the same.
所以这是 a - c over b ，这是 a - c over 2b ，所以这个距离和这个距离应该是相同的。
The way I've drawn it they're not the same at all.
我画的方式它们根本不一样。
The way we read this green graph is you give me a choice of Firm 1, q1.
我们阅读这个绿色图表的方式是你给我一个公司 1，q1 的选择。
I go up to the green line and go across and this tells me the best response for Firm 2.
我走到绿线并穿过，这告诉我公司 2 的最佳反应。
So at this point, how many of you have seen this picture before?
那么到目前为止，你们中有多少人曾经看过这张照片？
A good many of you have seen it before.
你们中的很多人以前都看过它。
So I think we can really cold call somebody for this one.
所以我认为我们真的可以为此打电话给某人。
So somebody tell me--pick somebody to cold--why don't you call a person, anybody that goes by.
所以有人告诉我——选一个冷场的人——为什么你不打电话给一个人，任何路过的人。
There we go, okay.
我们就这样吧，好吧。
So here's the tough question.
所以这是一个棘手的问题。
What's the Nash Equilibrium on this picture?
这张图上的纳什均衡是什么？
Professor Ben Polak: All right, where the green and the pink line intersect.
Ben Polak 教授：好的，就在绿线和粉红线相交的地方。
So this must be the Nash Equilibrium, that wasn't hard, right?
所以这一定是纳什均衡，这并不难，对吧？
Okay now--so why--let's go back again.
好吧——所以为什么——让我们再回去吧。
Why is this the Nash Equilibrium?
为什么这是纳什均衡？
Because at this point, as in the partnership game, which there was a similar thing, as in the partnership game where the best responses intersect is where Player 1 is playing a best response to Player 2, and Player 2 is playing a best response to Player 1.
因为在这一点上，就像在伙伴游戏中一样，也有类似的事情，在伙伴游戏中，最佳响应的交叉点是玩家 1 对玩家 2 做出最佳响应，而玩家 2 对玩家 1 做出最佳响应。
So this is the Nash Equilibrium in this Cournot game.
这就是古诺博弈中的纳什均衡。
Let's do a little bit of algebra just to make sure we can find this thing.
让我们做一些代数来确保我们能找到这个东西。
So what we're going to do is set these two things equal to each other, put in stars here.
所以我们要做的就是将这两件事设置为彼此相等，并在此处添加星星。
So at the Nash Equilibrium quantities I'm going to have q1* is equal to a - c over 2bq* and q2* is equal to a - c 2bq1* over 2 and now we're going to solve this out by setting q1 = q2 since I know the game is symmetric and they were on the 45º line.
因此，在纳什均衡数量下，我将让 q1* 等于 a - c 超过 2bq*，q2* 等于 a - c 2bq1* 超过 2，现在我们将通过设置 q1 = q2 来解决这个问题，因为我知道游戏是对称的，并且它们位于 45° 线上。
So what I have to do here to do this algebraically is to solve out these equations.
因此，我在这里要做的就是用代数方法求解这些方程。
So let's try and do that.
那么让我们尝试这样做吧。
So putting q1 in here--if I substitute q1 in here, what will that give me?
所以把 q1 放在这里——如果我在这里替换 q1，那会给我带来什么？
It'll give me q1* is equal to a - c over 2b - q1* over 2.
它会给我 q1* 等于 a - c 除以 2b - q1* 除以 2。
Let's multiply both sides by 2, I'll get 2q1* is equal to a - c over b - q1*.
让我们将两边都乘以 2，我将得到 2q1* 等于 a - c 除以 b - q1*。
Take that to the other side.
把它带到另一边。
I have 3 q1* is equal to a - c over b; and finally divide by 3 q1* is equal to a - c over 3b.
我有 3 q1* 等于 a - c 除以 b；最后除以 3 q1* 等于 a - c 除以 3b。
So that crossing point actually occurs at a - c over 3b.
因此该交叉点实际上出现在 3b 上的 a - c 处。
I'm going to look desperately at my T.A.'s to make sure I didn't screw that up.
我会拼命地查看我的助教，以确保我没有搞砸。
So this is something that's called the Cournot quantity.
这就是所谓的古诺量。
Now, this game, this game of imperfect competition between two firms competing in quantities, was thought up and studied by a French economist called Cournot almost a hundred years before Nash.
现在，这个博弈，即两个企业之间在数量上竞争的不完全竞争博弈，是由一位名叫古诺的法国经济学家提出并研究的，比纳什早了近一百年。
So a hundred years really before the invention of Game Theory, someone had figured out this answer for this game.
因此，早在博弈论发明的一百年前，就有人为这个游戏找到了答案。
Okay, so what do we know so far?
好的，那么到目前为止我们知道什么呢？
I'll leave the algebra there, transfer it up here, q1* = q2* = a - c over 3b.
我把代数留在那里，转移到这里，q1* = q2* = a - c over 3b。
So, so far, we've been working pretty hard and we haven't, I guess, learned a lot, we've just kind of solved the thing out.
所以，到目前为止，我们一直在努力工作，但我想我们并没有学到很多东西，我们只是解决了问题。
Now, we get to draw some lessons out of this thing, so everybody who's feeling a little bit shell shocked from having been doing algebra and calculus and drawing pictures and feeling like they've been cheated into taking a class that looks far too much like economics, calm down we're going to actually talk right now.
现在，我们要从这件事中吸取一些教训，所以每个因为做代数、微积分和画画而感到有点震惊的人，感觉自己被骗了，参加了一门看起来太像经济学的课程，冷静下来，我们现在要真正谈谈。
So, one thing to remark about this game, one thing that we've learned immediately, is that this game is different in a significant way.
因此，关于这款游戏需要注意的一件事，我们立即了解到的一件事是，这款游戏有很大的不同。
It's different from the partnership game.
这与伙伴关系游戏不同。
I mean, obviously it's different because it's about something different, but I mean in terms of the Game Theory it's different.
我的意思是，显然它是不同的，因为它涉及不同的东西，但我的意思是就博弈论而言它是不同的。
It's different from the partnership game, it's different from the investment game.
它不同于合伙游戏，也不同于投资游戏。
What is it that's different about this game from the--what's the obvious thing just looking at this picture that makes it different from the partnership game?
这款游戏与伙伴游戏有什么不同——只要看这张图片，它与伙伴游戏的明显区别是什么？
In the partnership game the best response lines sloped up.
在合作游戏中，最佳反应线向上倾斜。
The more I did of my strategy, the more the other player did as a best response.
我对自己的策略做得越多，其他玩家就越能做出最佳回应。
In the investment game, the more likely I was to invest, the more likely you--the more you wanted to invest.
在投资游戏中，我越有可能投资，你就越有可能——你就越想投资。
But in this game we have the exact opposites.
但在这款游戏中，我们的情况恰恰相反。
The more Player 1 produces, the less Player 2 wants to produce and the more Player 2 produces, the less Player 1 wants to produce.
玩家 1 生产的越多，玩家 2 想要生产的就越少，而玩家 2 生产的越多，玩家 1 想要生产的就越少。
So this game is a game, not of strategic complements, but of strategic substitutes.
所以这个博弈不是战略互补的博弈，而是战略替代的博弈。
I want to be careful here.
我想在这里小心一点。
It's not that these goods are substitutes.
并不是说这些商品是替代品。
I mean, clearly that's also the case, right?
我的意思是，显然情况也是如此，对吧？
If both these firms are producing bottled water and it's identical, then the goods themselves are substitutes.
如果这两家公司都生产瓶装水并且产品相同，那么产品本身就是替代品。
That's not the point I'm making here.
这不是我在这里要说的重点。
Strategic substitutes is a strategy--is a statement about the nature of the game.
战略替代是一种策略——是关于游戏本质的陈述。
So strategic substitutes is telling me that my strategy is a strategic substitute of your strategy if the more I do at my strategy, the less you want to do of yours and conversely, the more you want to do of your strategy, the less I want to do of mine.
因此，战略替代品告诉我，如果我对我的战略做的越多，你对你的战略的想做的就越少，那么我的战略就是你的战略的战略替代品，反之，你对你的战略的想做的越多，我对我的战略的想做的就越少。
Now, let's come back to the question we started with, which has to do with profits and so on in society.
现在，我们回到一开始的问题，这个问题涉及到社会上的利润等等。
We know that if these players play these games, at least if we believe in Nash Equilibrium, then they're going to produce these quantities, they're going to produce here.
我们知道，如果这些玩家玩这些游戏，至少如果我们相信纳什均衡，那么他们将生产这些数量，他们将在这里生产。
But let's ask a different question.; Each of these firms is trying to maximize profits, but how about the total profit in the industry?
但让我们问一个不同的问题。每家企业都在努力实现利润最大化，但行业的总利润又如何呢？
Each of these firms--we know the fact that they're playing best response--is maximizing their profits taking as giving what the other firm is doing.
这些公司中的每一个——我们知道他们正在做出最好的反应——正在最大化他们的利润，同时给予其他公司正在做的事情。
But how about total industry profits?
但行业总利润又如何呢？
Are they being maximized here?
它们在这里被最大化了吗？
Who thinks total industry profits are being maximized?
谁认为行业总利润正在最大化？
Who thinks total industry profits are not being maximized?
谁认为行业总利润没有最大化？
All right, good; shout out.
好吧，很好；喊出来。
Total industry profits are not being maximized.
行业总利润并未实现最大化。
Where on the picture--let me do a bit more cold calling here--where on the picture maximizes total industry profits?
图片中的哪个位置——让我在这里进行更多的推销——图片中的哪个位置使行业总利润最大化？
We had him before?
我们以前有过他吗？
No idea?
不知道吗？
You're taking the fifth here?
你在这里拿第五个吗？
The guy in there, yeah.
里面那个人，是的。
Professor Ben Polak: Monopoly, exactly.
本·波拉克教授：确切地说，是垄断。
So clearly, if we produce the monopoly quantity, by definition, the monopoly quantity maximizes total industry profits.
很明显，如果我们生产垄断数量，根据定义，垄断数量会使行业总利润最大化。
For example, if Firm 2 shut down and Firm 1 produced its monopoly profits, that is, a monopoly quantity, that would maximize firm profits.
例如，如果企业 2 关闭，而企业 1 产生垄断利润，即垄断数量，那么企业利润就会最大化。
Conversely, if Firm 1 shut down and Firm 2 produced its monopoly quantity that would maximize industry profits.
相反，如果企业 1 关闭，企业 2 生产其垄断数量，将使行业利润最大化。
Where else in this picture maximizes industry profits?
这张图中还有哪些地方可以实现行业利润最大化？
So this point maximized industry profits and this point maximizes industry profits.
所以这一点使行业利润最大化，这一点又使行业利润最大化。
Where else maximizes industry profits?
还有什么地方可以实现行业利润最大化？
Anybody?
有人吗？
Well, how about all the points in between?
那么，介于两者之间的所有点又如何呢？
Here, Firm 1 produced nothing and Firm 2 produced a monopoly quantity; and here Firm 2 produced nothing and Firm 1 produced a monopoly quantity.
在这里，企业 1 没有生产任何产品，而企业 2 则生产垄断数量；在这里，企业 2 没有生产任何产品，而企业 1 则生产垄断数量。
But you could also just split the monopoly quantity, for example, half half at this point here.
但你也可以将垄断数量分开，例如此时一半。
So if the firms wanted to make more money, the only thing they could do is they could sign an agreement saying, why don't each of us produce not our Cournot quantity, but produce half monopoly profits.
因此，如果企业想赚更多的钱，他们唯一能做的就是签署一份协议，说为什么我们每个人不生产我们的古诺数量，而是生产一半的垄断利润。
I'm sorry, half the monopoly quantity and that would produce this much each.
抱歉，垄断数量的一半，每个产量就这么多。
So Firm 1 would be producing half its monopoly quantity and Firm 2 would be producing half its monopoly quantity.
因此，企业 1 将生产其垄断数量的一半，而企业 2 将生产其垄断数量的一半。
So what's wrong with that agreement?
那么这个协议有什么问题呢？
What are they?
这些是什么？
They're two water companies, so they're Poland Spring and Coca-Cola I guess these days, sign this agreement saying that each one's going to produce half monopoly quantity and what's going to go wrong with that agreement?
他们是两家自来水公司，所以他们是波兰泉水和可口可乐，我想这些天，签署了这份协议，规定每家公司将生产一半的垄断数量，那么该协议会出什么问题吗？
The guy in red.
那个红衣人。
Professor Ben Polak: It's illegal.
本·波拉克教授：这是非法的。
So even without there being an Attorney General, somebody might be awake in the justice department and notice that that's actually illegal.
因此，即使没有司法部长，司法部门也可能有人意识到这实际上是非法的。
It's illegal to sign an agreement--to sign a contract saying you're going to restrict quantities.
签署协议——签署一份合同说要限制数量——是违法的。
It's illegal, so they can't sign that as a contract, but they they can just agree to do it.
这是非法的，所以他们不能签署合同，但他们可以同意这样做。
So Coca-Cola and Poland Spring could just agree to produce half the quantity of water each.
因此，可口可乐和波兰之泉可以同意各自生产一半的水量。
What's going to go--what might go wrong in that agreement?
将会发生什么——该协议可能会出现什么问题？
Let's just suppose that that game's just been played once for now.
我们假设该游戏目前只玩过一次。
Suppose that this is Coca-Cola's quantity and this is Poland Spring's quantity, and suppose you're the manager of Poland Spring, so water is coming out of the ground in Maine for you and you know that this Coca-Cola guy is going to produce this quantity here, so this is qM over 2.
假设这是可口可乐的数量，这是波兰泉的数量，假设你是波兰泉的经理，所以水从缅因州的地下为你流出，你知道这个可口可乐的家伙将在这里生产这个数量，所以这是 qM 大于 2。
So let's pick on our two managers; let's have two people who have spoken before, so the guy in the red shirt's name is?
让我们来挑选一下我们的两位经理吧；我们有两个人之前说过话，那么穿红衬衫的那个人叫什么名字？
Professor Ben Polak: Steve, and I guess in red he should be the Coca-Cola guy, and let's pick on our Jimmy Stewart from last week, whose name is Patrick.
本·波拉克教授：史蒂夫，我想穿红色衣服的他应该是可口可乐的人，让我们选择上周的吉米·斯图尔特，他的名字叫帕特里克。
Can I get a mike in on Patrick?
我可以给帕特里克拿个麦克风吗？
So Steve and Patrick are respectively the managers of Coca-Cola and Poland Spring and Patrick believes that the Coca-Cola manager is going to--may be we should just make this Coke and Pepsi since two identical--they're near enough and identical, right?
所以史蒂夫和帕特里克分别是可口可乐和波兰之泉的经理，帕特里克相信可口可乐经理会——也许我们应该把可口可乐和百事可乐制造成相同的——它们足够接近并且相同，对吗？
So these are Coke and Pepsi, that will confuse me less.
这些是可口可乐和百事可乐，这样我就不会那么困惑了。
So Patrick, our manager of Pepsi believes that Coca-Cola is going to produce this quantity and he's agreed to produce this quantity.
因此，我们的百事可乐经理帕特里克相信可口可乐将生产这个数量，并且他同意生产这个数量。
What is Patrick actually going to do?
帕特里克到底要做什么？
Patrick, what are you going to do?
帕特里克，你要做什么？
Student: So I should cheat and pick the quantity on my best response line that's much farther out so I'll produce more than my quantity.
学生：所以我应该作弊并在我的最佳响应线上选择更远的数量，这样我就会生产比我的数量更多的东西。
Professor Ben Polak: All right, so Patrick (being Jimmy Stewart or not, actually) when he's in the--when he's playing the manager of Pepsi he's going to produce more of this undrinkable liquid and produce this quantity here.
本·波拉克教授：好吧，所以帕特里克（实际上是不是吉米·斯图尔特）当他扮演百事可乐的经理时，他将生产更多这种无法饮用的液体，并在这里生产这个数量。
So what is this?
那么这是什么？
This is Patrick's best response to the other guy producing the monopoly quantity.
这是帕特里克对另一个生产垄断数量的人最好的回应。
So Patrick's response in Pepsi is to overproduce relative to the monopoly quantity, actually overproduce even relative to the Cournot quantity and produce all the way out here.
因此，帕特里克在百事可乐的反应是相对于垄断数量生产过剩，实际上甚至相对于古诺数量生产过剩，并在这里一路生产。
Okay, so Patrick's producing here but what about Mr. Coca-Cola guy?
好吧，帕特里克在这里制作，但是可口可乐先生呢？
Now, Mr. Coca-Cola guy knows Patrick pretty well, they've been in the same industry for a while and Mr. Coca-Cola guy, whose name is?
现在，可口可乐先生对帕特里克很了解，他们在同一行业已经有一段时间了，可口可乐先生，他的名字是？
Professor Ben Polak: Steven.
本·波拉克教授：史蒂文。
Steven presumably knows that Patrick is actually going to produce this quantity--I'm sorry this quantity.
史蒂文大概知道帕特里克实际上会生产这个数量——我很抱歉这个数量。
So Steven, what should you produce?
那么史蒂文，你应该生产什么？
Student: Increase my own production to match my best response line.
学生：增加我自己的产量以匹配我的最佳反应线。
Professor Ben Polak: Good, so Steven, anticipating that Patrick is going to think that Steven's a sucker but Patrick's going to cheat on him and produce too much, Steven's going to produce a best response to that and he's going to produce this quantity here.
本·波拉克教授：很好，所以史蒂文，预计帕特里克会认为史蒂文是个傻瓜，但帕特里克会欺骗他并生产太多，史蒂文将对此做出最佳反应，他将在这里生产这个数量。
So what is this?
那么这是什么？
This is Player 2's best response, so Player 1's best response to Player 2 producing half monopoly output.
这是玩家 2 的最佳响应，因此玩家 1 对玩家 2 产生半垄断输出的最佳响应。
But Patrick knows Steven pretty well; he knows those guys who run Coca-Cola are pretty smart guys, so Patrick knows that the guy who runs Coca-Cola is going to anticipate that the guy who runs Pepsi is going to cheat on the guy who runs Coca-Cola, and hence the guy who runs Coca-Cola is going to play a best response to Patrick's cheat on quantity.
但帕特里克很了解史蒂文。他知道那些经营可口可乐的人非常聪明，所以帕特里克知道经营可口可乐的人会预见到经营百事可乐的人会欺骗经营可口可乐的人，因此经营可口可乐的人将对帕特里克在数量上的欺骗做出最好的回应。
So what quantity is Patrick going to produce?
那么帕特里克要生产多少数量呢？
Student: I'll increase my production then; I'll be pretty close to the Cournot equilibrium.
学生：那我就增加产量吧；我将非常接近古诺均衡。
Professor Ben Polak: All right, so you're going to go to here; so this point here is--I can't even write this.
Ben Polak 教授：好的，所以你要去这里；所以这一点是——我什至无法写这个。
This is the best response of Player 1 to the best response of Player 2, to the best response of Player 1 to Player 2 producing half monopoly output and there are lots of brackets here.
这是玩家 1 对玩家 2 的最佳响应、玩家 1 对玩家 2 产生半垄断输出的最佳响应，这里有很多括号。
Can anyone see where this process is going?
谁能看到这个过程的进展情况吗？
It's going back to the Nash Equilibrium.
这又回到了纳什均衡。
Each of them is trying to play a best response for what they anticipate the other person's going to do.
他们每个人都试图对他们预期对方将要做什么做出最好的反应。
And in this game if they keep on doing that, it's going to drag them back to Nash Equilibrium.
在这场游戏中，如果他们继续这样做，就会把他们拖回纳什均衡。
But I want to be careful here.
但我想在这里小心一点。
This won't be true of all games.
并非所有游戏都如此。
But in this game, playing best response to each other, figuring out that in fact the other guy is going to cheat on me, or the other guy is anticipating that I'm going to cheat on him, or the other guy is going to anticipate that I'm going to anticipate that he's going to cheat on me, etc., etc., will eventually drag us back to the Cournot quantity.
但在这个游戏中，彼此做出最佳反应，弄清楚实际上另一个人会欺骗我，或者另一个人预计我会欺骗他，或者另一个人会预计我会预计他会欺骗我，等等，最终会将我们拖回古诺量。
So it's going to be pretty difficult for us to sustain this joint monopoly output, this collusive agreement.
因此，我们要维持这种联合垄断产出、这种串通协议将是相当困难的。
We can't let the courts enforce it.
我们不能让法院强制执行。
We're Coca-Cola and Pepsi, so we really don't want to have to bring the mafia in, although maybe we do, I don't know.
我们是可口可乐和百事可乐，所以我们真的不想让黑手党介入，尽管也许我们会这样做，我不知道。
So basically, we're stuck with this verbal agreement and we both have an incentive to cheat and produce more whatever it is, sugar water.
所以基本上，我们都坚持这种口头协议，我们都有动机作弊并生产更多的糖水。
Now, in practice, this is not the only problem facing two firms who are trying to produce the monopoly output.
现在，在实践中，这并不是两家试图生产垄断产品的公司面临的唯一问题。
In practice, when firms try and have these agreements, which are not contracts, to try and produce joint monopoly output, what else goes wrong?
在实践中，当企业试图通过这些非合同协议来尝试生产联合垄断产出时，还会出现什么问题呢？
So you can imagine some firms trying to have an agreement.
所以你可以想象一些公司试图达成协议。
We know they can't sign a legal agreement, but let's take that off the table.
我们知道他们无法签署法律协议，但我们还是把这个排除在外吧。
So, for example, in around 1900 in America or a little bit earlier, let's say 1880 in America, it really isn't clear that it was illegal to write agreements to say we'll restrict quantities.
因此，举例来说，在美国大约 1900 年或更早一点，比如说在美国 1880 年，确实不清楚签订限制数量的协议是否违法。
So firms did use to write that kind of agreements, but still something went wrong.
因此，公司确实曾经编写过此类协议，但仍然出现了问题。
What went wrong?
出了什么问题？
So we're getting a little bit further away from the game and more back into the real world.
所以我们离游戏越来越远，更多地回到现实世界。
What kind of things went wrong?
出了什么样的问题？
I want to get somebody who's near a mike.
我想找一个靠近麦克风的人。
Can I get the woman here with the Yale shirt?
我可以把那个穿耶鲁衬衫的女人叫过来吗？
Student: Without a contract there's no means of enforcement.
学生：没有合同就没有执行的手段。
Professor Ben Polak: All right, so it might be that--again, the problem with enforcement--although actually in 1880 America, it's not clear that they couldn't have enforced that contract.
Ben Polak 教授：好吧，所以这可能是——再次是执行方面的问题——尽管实际上在 1880 年的美国，尚不清楚他们是否无法执行该合同。
So one problem is unenforceability but that might--far off ago that might have been a problem.
因此，一个问题是不可执行性，但这可能——很久以前这可能就是一个问题。
What else?
还有什么？
The guy next to her.
她旁边的那个男人。
Student: If they're not at the competitive output they could undercut price and take the entire market.
学生：如果他们的产量不具有竞争力，他们可能会降低价格并占领整个市场。
Professor Ben Polak: Let's be careful.
本·波拉克教授：我们要小心一点。
We'll come back to that next time, but right now we're competing in quantities.
我们下次会再讨论这个问题，但现在我们正在数量上进行竞争。
So we're not fixing prices here, we're not even naming price.
所以我们不会在这里固定价格，我们甚至不会命名价格。
We're just producing Coca-Cola and Pepsi and for want of a better word, spewing it out into the market.
我们只是生产可口可乐和百事可乐，并且需要一个更好的词来形容，那就是把它们扔到市场上。
What else goes wrong here?
这里还有什么问题吗？
Well, one thing that goes wrong is that suppose Coke and Pepsi were able to--either to write a contract or whatever--to sustain joint monopoly output at this high price, this price which is actually--producing positive profits in the industry--it is going to turn out, therefore the price is going to be above costs.
好吧，出错的一件事是，假设可口可乐和百事可乐能够——无论是签订合同还是其他什么——以如此高的价格维持联合垄断产出，这个价格实际上——在行业中产生正利润——结果将会是，因此价格将高于成本。
These firms're making all the profits, what do you thinks going to happen in this industry?
这些公司赚取了所有利润，您认为这个行业会发生什么？
This industry that's got a lot of profit around it, what's going to happen in this industry?
这个利润丰厚的行业，这个行业会发生什么？
Yeah, the guy in the blue shirt here; Ale this guy here.
是的，就是这里穿蓝色衬衫的那个人；啤酒这个家伙在这里。
Professor Ben Polak: Another firm is going to come in and produce a similar product.
本·波拉克教授：另一家公司将介入并生产类似的产品。
So Dr. Pepper or something, is there one?
那么 Pepper 博士之类的，有吗？
Someone else is going to come in and produce cola in this industry and that's exactly what happened in the U.S. at the turn of the last century.
其他人将会进入这个行业生产可乐，这正是上世纪之交在美国发生的情况。
Companies did produce agreements to restrict, for example, the production of paper and the production of rubber, and the production of steel, and the production of iron, and the production of railway lines, actually, even quite complicated things.
公司确实签订了协议来限制，例如纸张的生产、橡胶的生产、钢铁的生产、铁的生产、铁路线的生产，实际上，甚至是相当复杂的事情。
Sure enough what you see very quickly emerging is new entrants entering the market to say, hey these firms are restricting their quantities, we can get in there and make money.
果然，你很快就会看到新进入者进入市场说，嘿，这些公司正在限制他们的数量，我们可以进入那里赚钱。
So new and a competitive fringe of firms is going to enter and drive prices down.
因此，新的、具有竞争力的边缘公司将进入并压低价格。
Now, I'm talking about 1900 America where has that happened in the twentieth century more dramatically?
现在，我谈论的是 1900 年的美国，二十世纪的哪里发生过更戏剧性的事情？
We know the early example in sort of Golden Age America, but where else did we see a competitive fringe enter when there was a collusive agreement to keep prices--to keep quantities down?
我们知道美国黄金时代的早期例子，但是当存在串通协议以保持价格（以减少数量）时，我们还能在哪里看到竞争性边缘进入？
Professor Ben Polak: Good, so airlines is an example; we've seen that.
Ben Polak 教授：很好，航空公司就是一个例子；我们已经看到了。
Where else?
还有哪里？
Oil is probably the classic example.
石油可能是一个典型的例子。
Airlines is a good example.
航空公司就是一个很好的例子。
Okay, so in oil we all know that in the late 60s, early 70s, OPEC was formed precisely to restrict quantity among the major oil producing countries, and very quickly we see companies take--other countries take advantage of this to start producing oil profitably.
好吧，在石油方面，我们都知道，在 60 年代末、70 年代初，欧佩克的成立正是为了限制主要石油生产国之间的数量，很快我们就看到其他国家利用这一点开始生产石油以获取利润。
So who were the competitive fringe against OPEC?
那么谁是欧佩克的竞争边缘呢？
Anybody?
有人吗？
The Brits were for a start, the Brits--England sort of--Scotland I should say.
英国人首先是英国人——我应该说是英格兰——苏格兰。
Britain anyway started producing oil in the North Sea; lots of countries in Latin America started looking and finding oil, and of course, Russian oil started being very, very profitable.
不管怎样，英国开始在北海生产石油；拉丁美洲的许多国家开始寻找石油，当然，俄罗斯石油开始变得非常非常有利可图。
So there are various reasons why it's hard to maintain this collusive agreement.
所以说这个合谋协议很难维持下去是有多种原因的。
One is there's an incentive to cheat and another is that other firms are going to enter.
一是存在作弊动机，二是其他公司将进入。
Before we leave this, let's just pose the question we started with.
在我们结束这个之前，让我们先提出我们开始时提出的问题。
Suppose, in fact, we do end up back at the Cournot quantity.
事实上，假设我们最终回到了古诺量。
So here we are back at the Cournot quantity.
所以我们又回到了古诺量。
How does this quantity compare and how do therefore the prices compare, and how do profits compare with monopoly prices on the one hand, and competitive prices on the other?
这个数量如何比较，因此价格如何比较，以及利润如何一方面与垄断价格相比，另一方面与竞争价格相比？
So we know the quantity that's going to be produced.
所以我们知道将要生产的数量。
We figured that out; here it is.
我们想通了；这里是。
We know the quantities going to be produced.
我们知道要生产的数量。
Each firm is going to produce a - c over 3b and there are two such firms.
每家公司将生产超过 3b 的 a - c，并且有两家这样的公司。
So the total quantity produced in the market--the total quantity will be 2a - c over 3b.
因此，市场上生产的总量——总量将是 2a - c 超过 3b。
How does that compare to the monopoly quantity?
与垄断数量相比如何？
Well, the monopoly quantity was a - c over 2b and the competitive quantity was a - c over b, just to remind you of those, they're on our picture.
好吧，垄断数量是 a - c 超过 2b，竞争数量是 a - c 超过 b，只是为了提醒您这些，它们在我们的图片上。
Here's a - c over 2b and here's a - c over b.
这是 a - c 超过 2b，这是 a - c 超过 b。
So this is the total quantity produced on this equilibrium, in this Cournot Nash Equilibrium.
因此，这是在古诺纳什均衡中该均衡下产生的总量。
How did it compare to the monopoly quantity and to the competitive quantity?
与垄断数量和竞争数量相比如何？
Anybody?
有人吗？
Just staring at the board, which is of these is bigger?
盯着黑板看，哪个更大？
So I claim that this total quantity being produced is less than the competitive quantity, but more in total than the monopoly quantity.
所以我声称这个生产总量小于竞争数量，但总体上大于垄断数量。
I was about to get them the wrong way around.
我差点就让他们搞错了。
Total quantity being produced is less than would be produced under perfect competition, but more than would be produced under monopoly.
生产总量低于完全竞争条件下的产量，但高于垄断条件下的产量。
Consequently, prices are going to go the other way and consequently prices are going to be highest under monopoly, lowest on the competition, and somewhere in between in this Cournot situation.
因此，价格将走向相反的方向，因此，垄断下的价格将最高，竞争下的价格最低，在古诺情况下，价格将介于两者之间。
So from the point of view of the producers, this Cournot Equilibrium is worse than monopoly, but better than perfect competition.
所以从生产者的角度来看，这种古诺均衡比垄断更糟糕，但比完全竞争更好。
And from the point of view of the rest of us, the consumers, this Cournot quantity is worse than perfect competition but better than monopoly.
从我们其他人，即消费者的角度来看，这个古诺量比完全竞争差，但比垄断好。
The only rider on that being, if they're producing Coca-Cola and you have any kind of concern for your teeth, maybe you shouldn't produce so much anyway.
唯一的附加条件是，如果他们生产可口可乐，而你对你的牙齿有任何担忧，也许你无论如何都不应该生产那么多。
So, so far what we've done is we've looked at this sort of classic, I admit not the most exciting game in the world, but classic application of Game Theory to imperfect competition.
所以，到目前为止，我们所做的就是研究这种经典游戏，我承认这不是世界上最激动人心的游戏，而是博弈论在不完美竞争中的经典应用。
Next time I'm actually going to take this a bit further but I'm going to leave this game behind and look at other ways in which we could study imperfect competition using Game Theory.
下次我实际上会更进一步，但我将把这个游戏抛在脑后，看看我们可以使用博弈论研究不完美竞争的其他方法。