耶鲁大学博弈论公开课 - 第13集 顺序游戏-道德风险，奖励和饥饿的狮子

视频全文转录（中英双语）

以下为完整中英双语转录，已加标点。英文在前，中文在后，逐段对照。

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

[段 1]

Okay, so I want to set up a new topic today, and to get us started I thought we’d play a game. So the game is going to be called Cash and a Hat, and we’ll see what this game is like in a minute. so the idea is this, there’s going to be two players I’m going to pick on two of you I hope I can find people who brought some money to class alright, so player one will have a choice player one can put nothing one dollar or three dollars into a hat the hat will then be given to player two and player two can look at what’s in the hat and either she can match what’s in the hat, i.e. add the same amount in, so one if it’s one or three if it’s three, or she can simply take the cash. All right, the payoff of this game will be as follows. Player one, if they put nothing in, they’re not going to get anything If they put one in and it matched then they double their money so they get two back If they put three in and it matched then they double their money so they get six back they’ll net three. However, if they put one in and player two takes it, they’ve just lost their dollar. And if they put three dollars in and player two takes it, they’ve lost three dollars.

[译文 1]

好的，今天我想开始一个新话题。为了让大家进入状态，我想我们先玩个游戏。这个游戏叫做“现金与帽子”，我们马上来看看这个游戏怎么玩。游戏的规则是这样的：会有两个玩家，我会从你们当中挑两个人，希望我能找到带钱来上课的人。玩家一会有一个选择，玩家一可以往帽子里不放钱、放一美元或放三美元。然后帽子会递给玩家二，玩家二可以看看帽子里有多少钱，然后她可以选择匹配帽子里面的钱，也就是放入同样的金额，如果是一美元就放一美元，如果是三美元就放三美元，或者她可以直接把现金拿走。这个游戏的收益如下：玩家一，如果什么都不放进去，他们不会得到任何东西。如果放了一美元且被匹配了，那么他们资金翻倍，得到两美元回来。如果放了三美元且被匹配了，那么他们资金翻倍，得到六美元回来，净赚三美元。但是，如果他们放了一美元而玩家二拿走了钱，他们就损失了一美元。如果他们放了三美元而玩家二拿走了钱，他们就损失了三美元。

[段 2]

Everyone understand that? Pretty simple. from player 2’s point of view if player 2 matches then they get their investment back plus $1.50 if they match 1, so they get $2.50 back in all, and they get their investment back plus $2 if they match 3 so that’s if they get 5 back in all and of course if they simply take the money out of the hat and put it in their pocket then that’s what they get in the game once again, if player 2 matches with one dollar, one dollar on the hat and she matches, then she gets back two fifty for a profit of one fifty. If there’s three dollars and she matches three, she gets back five for a profit of two. And if she simply takes the money out of the hat and puts it in her pocket, then she gets how much money was in the hat. Alright so I here will be the provider of the hat We use the same hat we used before And if necessary I provide sheets of paper we can write IOUs on But I hoping we can play for real cash Later on, it would be nice to get a chair here. But for now, let me just go down here. And I’m going to grab this mic. Who here wants to be player one?

[译文 2]

大家都理解了吗？相当简单。从玩家二的角度来看，如果玩家二选择匹配，那么如果匹配一美元，他们拿回投资后还能额外得到1.50美元，总共得到2.50美元回来；如果匹配三美元，他们拿回投资后还能额外得到2美元，总共得到5美元回来。当然，如果他们直接把钱从帽子里拿出来放进自己的口袋，那就是他们在这个游戏中得到的金额。再说一次，如果玩家二用一美元匹配帽子里的一美元，她拿回2.50美元，利润是1.50美元。如果有三美元她匹配三美元，她拿回5美元，利润是2美元。如果她直接把帽子里的钱拿出来放进自己的口袋，那她得到的就是帽子里原本有的金额。好的，我在这里充当帽子的提供者。我们用之前用过的同一个帽子。如果有必要的话，我会提供纸张让大家写欠条。但我希望我们能玩真的现金。以后能有个椅子坐就好了。但现在，让我走到下面去。我要去拿这个麦克风。谁想当玩家一？

[段 3]

Who brought some money to class today? I’m quite willing to pick on somebody. All right, good, good, good. So player one is, what’s your name again? Justin. Justin. So hold on to that hat for a second. Alright. And who wants to be player two? Alright. So this gentleman here, whose name is? Nate. Nate. Alright. So we have Justin and Nate. Alright. So Justin, you have to decide how much money you’re going to put in the hat. Did you bring some money too, Nate? Better make sure you have, otherwise borrow some from your neighbours. Alright. I’m going to put in a buck. Alright. Alright. So the money’s been put in the hat and delivered to Nate. I’m going to put in the buck too, so that I get… Alright so if we empty out the hat here our beautiful pink hat I should really have the hat passed across the room rather than have me do it but we have in the hat so I going to pay each I going to pay what am I going to pay I going to pay player 1 I going to give back their original dollar and give them in a second And I going to play a 2 Just hold the hat Do that for me Yes. Well, you’ve got your money back. Trying to cheat you here.

[译文 3]

谁今天带钱来上课了？我很愿意挑一个人。好的，好的，好的。玩家一是——你叫什么名字来着？Justin。Justin。等一下，先把那个帽子拿好。好的。谁想当玩家二？好的，这位先生，叫什么名字？Nate。Nate。好的。我们有Justin和Nate了。好的，Justin，你得决定往帽子里放多少钱。Nate，你也带钱来了吗？最好确认一下，不然的话跟邻居借一点。好的，我要放一美元进去。好的。好的。钱已经放进帽子并递给Nate了。我也要放一美元进去，这样我就能……好的，如果我们把帽子倒空，这是我们漂亮的粉色帽子，我应该让帽子在教室里传一下而不是我自己动手，但我们已经把钱放进去了，所以我打算付给每个——我打算付给玩家一，我打算把他们原本的一美元还给他们，再额外给他们一美元。而我要付给玩家二——先拿着帽子——帮我做一下。是的。好了，你拿回你的钱了。我这里是在骗你。

[段 4]

Is that it? All right. So play a… I’ll get you the rest in a second. Hang on a second. For now. So double the money. All right. All right. All right. One reason to take this class is if you play well, you get money. All right. Now let’s just try again. All right. So we had one round of this. Let’s have another round. Who wants to be player one now? All right. So Katie is player one. All right. Katie, do you bring some money? Yeah, sure. All right. And who wants to be player two? Someone further away. Let’s have Stephen, isn’t it? Is that right? Yeah. So Stephen’s going to be player two. Do you bring some cash? I think so. All right. All right. Otherwise, borrow it from your neighbors. I can have IOUs here. So here’s the house. I’ve only got coins. Oh, you’ve got coins? Oh. All right. All right. We’ll put it in a bag. Okay. Okay, great. So pass the hat down. We’ll see if it makes it there. Test the honesty of the class here. It’s working its way down. Here we go. All the way down to Stephen. Check how much is in there. There’s a dollar here. Check how much is in there. There’s a dollar in here. There’s a dollar in there, so you can decide whether to match or not.

[译文 4]

就这样吗？好的。那么玩一局——我等一下把剩下的给你。先等一下。现在先把钱翻倍。好的，好的，好的。上这门课的原因之一就是如果你玩得好，就能赚钱。好的。现在我们再来一次。好的。我们已经玩了一局了。再来一局。谁想当玩家一？好的。Katie是玩家一。好的，Katie，你带钱了吗？是的，当然。好的。谁想当玩家二？找个离远一点的。让我们有Stephen，是不是？是这样吗？是的。Stephen当玩家二。你带现金了吗？我想是的。好的，好的。不然的话，跟邻居借吧。我这里有欠条可以用。这是帽子。我只有硬币。哦，你有硬币？哦。好的，好的。我们把它放袋子里吧。好的。好的，很好。把帽子传下去。看看能不能传到那里。测试一下这个班的诚信度。正在往下传。开始了。一直传到Stephen那里。看看里面有多少钱。这里有一美元。看看里面有多少钱。这里有一美元。这里有一美元，所以你可以决定是匹配还是不匹配。

[段 5]

Okay, I’ll match it. Alright, so Stephen’s going to match as well. Alright, once again we have this time, rather annoyingly, a dollar and some coins in here, which I will empty on the stage to prove it to everybody. Alright, and I will… Alright, there are coins in here. So I’ll match this in a second and give it back to you guys. Alright, so everyone understand the game? Alright, everyone understand how this game works? So we’re going to spend a while discussing this. and we’d go on playing except I’d eventually lose so much money I’m going to run out of lunch money the CAs would object. Alright, so what I want to do is I want to analyse this game, I want to think about what this game’s about, what’s really going on here. Alright, so first this is just a little game involving putting some money in a hat but I want to suggest to you that this is a toy version of a much more important game. This is a toy version of a game involving a lender and a borrower. So you could think of our player ones here. That was Katie on the second round and is it Justin on the first round? Justin on the first round Imagine them working in an investment bank or perhaps in a venture capitalist firm right and what they doing is they giving a loan to somebody some budding entrepreneur who’s come up with a new project.

[译文 5]

好的，我来匹配。好的，所以Stephen也要匹配了。好的，这一次，颇为烦人的是，帽子里有一美元和一些硬币，我会把它们倒在舞台上向大家证明。好的，我会——好的，这里有硬币。所以我等一下会匹配这个，然后把它还给你们。好的，大家都理解这个游戏了吗？大家都理解这个游戏怎么玩了吗？我们会花一些时间来讨论这个游戏。我们会继续玩下去，只是我最终会输掉太多钱，午饭钱都要花光了，助教们会有意见的。好的，我想做的是分析这个游戏，我想思考一下这个游戏是关于什么的，这里真正发生了什么。好的，首先这只是一个涉及往帽子里放钱的小游戏，但我想要向你们建议，这是关于一个更重要的游戏的玩具版本。这是一个涉及贷款人和借款人的游戏的玩具版本。所以你们可以想想我们这里的玩家一。在第二轮是Katie，第一轮是Justin对吧？第一轮是Justin。想象他们在一家投资银行或者在一家风险投资公司工作，对吧，而他们做的是把钱借给某个人，一个崭露头角的企业家，他提出了一个新项目。

[段 6]

So Steven in round two and who was my budding entrepreneur in round one? What was your name? Nate in round one have come up with some budding project, they’ve left Yale perhaps after their junior year, they’ve left early because they’ve got some great idea for something which is going to make them millions, so either it’s a new mousetrap or a new version of Facebook or something, and they go to the, that’s half isn’t it, so something better than a new version of Facebook, and they go to this venture capitalist firm, maybe it’s some firm in New York, or maybe it’s the Yale Investment Trust, whatever, and they explain this great idea to them, and they ask for some money to invest in this firm to buy machinery and to pay early wages and so on. And the lender, the guy who works at the venture capitalist firm, has to decide how much money to invest in this project. After this money has been invested in the project, the person who borrowed it faces choices. They could go forward with their project, work hard, spend the money on the things they’re supposed to spend, or they could just disappear to Mexico All right Go back to Yale for that matter And there actually something in between they could do which is less dramatic than disappearing to Mexico All right All right Go back to Yale for that matter All right And there actually something in between they could do which is less dramatic than disappearing to Mexico They could just not work particularly hard shirk perhaps join in someone else project and just let the money run down without the lender really knowing about it.

[译文 6]

所以第二轮的Steven和第一轮的我的崭露头角的企业家，你叫什么名字？第一轮的Nate，提出了某个崭露头角的项目，他们可能已经从耶鲁退学了，也许是在大三之后退学，因为他们有了某个绝妙的点子，这个点子会让他们赚到几百万，所以要么是个新型捕鼠器，要么是新版Facebook之类的，而他们去找这个——那不是一半吗——所以是比新版Facebook更好的东西，而他们去找这家风险投资公司，也许是在纽约的某家公司，也许是耶鲁投资信托，无论是什么，他们向他们解释这个绝妙的点子，然后他们请求一些钱来投资这个公司，买机器设备和支付早期工资等等。而贷款人，在风险投资公司工作的家伙，必须决定在这个项目上投入多少钱。在这笔钱投入项目之后，借款的人面临选择。他们可以继续推进他们的项目，努力工作，把钱花在应该花的地方，或者他们可以直接消失去墨西哥。好的——回到耶鲁也可以。实际上还有介于两者之间的做法，他们可以做的事情没有去墨西哥那么戏剧化。好的——回到耶鲁也可以。好的，实际上还有介于两者之间的做法，他们可以做的事情没有去墨西哥那么戏剧化。他们可以不太努力工作，偷懒，也许去参与别人的项目，让钱就这样消耗掉而不让贷款人真正知道。

[段 7]

All right? So this is a very real problem that some of you, some of the budding entrepreneurs in the room, are going to face when you leave Yale. And more of you who are going to end up working for investment banks, perhaps unfortunately, are going to face as well. All right? Okay, so we’re going to spend the whole of today analyzing this, but before we even start, let’s notice that there’s something different about this game, other than its sheer triviality, there’s something different about this game than games we’ve played all the way up to the midterm so far. What’s different about this game? What’s different? Yeah, can I get a mic in here? Sorry. Yes, what’s different? The moves aren’t simultaneous. So moves are not simultaneous. This is a sequential move game. Put the rules up here and bring this down. So for the first time we looking at a sequential move game And we going to spend most of the rest of the term looking at sequential move games or at least looking at games that involve sequential elements. Now what’s really, what makes this a sequential move game, let’s be careful about this, what makes it a sequential move game is not simply that player one moved first and player two moved second, although that’s true. what really made this a sequential move game is that player 2 knew what player 1 had done before he got to make his move.

[译文 7]

好的，这是一个你们中的一些人——房间里的一些初出茅庐的企业家——在离开耶鲁后会面临的一个非常现实的问题。而你们中更多最终会进入投资银行工作的人，也许不幸地，也将面临这个问题。好的？我们今天会花一整天来分析这个问题，但在我们开始之前，让我们注意一下这个游戏除了其纯粹的琐碎性之外，与我们到目前为止一直到期中考试所玩的游戏有什么不同。这个游戏有什么不同？有什么不同？嗯，能给我一个麦克风吗？抱歉。是的，有什么不同？行动不是同时的。所以行动不是同时的。这是一个序贯行动游戏。把规则写在这里，把它拿下来。所以这是我们第一次看序贯行动游戏，我们将在本学期剩余的大部分时间里研究序贯行动游戏，或者至少研究涉及序贯元素的游戏。现在真正使它成为序贯行动游戏的是什么，让我们仔细一点，使它成为序贯行动游戏的并不仅仅是玩家一先行动、玩家二后行动，虽然这是真的。真正使它成为序贯行动游戏的是，玩家二在做出他的选择之前就知道玩家一做了什么。

[段 8]

It isn’t the timing per se that matters. It’s going to turn out it’s the fact that player 2 could observe player 1’s choice before having to make his or her choice that matters. And notice, just while we’re on the subject, more than that, player 1 knew this was going to be the case. Alright, so let’s get that down. So in this game, player two knows player one’s choice before she chooses. She being player two. Let’s say before she chooses. choice before she chooses. She being player two. Let’s say before two chooses. And second, player one knows that this will be the case. And the way we dramatize this just now is player one put the money in the hat, the hat was transported across the classroom with people very honestly not stealing the money to player two. Player two could look in the hat, could see how much money was in there before Stephen or Nate had to make that choice. Is that right? All right. So how do we go about analyzing games that have this sequential structure?

[译文 8]

重要的不是时机本身。关键在于玩家二能够在做出选择之前观察到玩家一的选择，仅此而已。请注意，当我们谈到这个话题时，远不止于此，玩家一知道情况会是这样。好吧，让我们把它记下来。所以在 这个游戏中，玩家二在选择之前知道玩家一的选择。她——玩家二——在选择之前知道。让我们说在玩家二选择之前。其次，玩家一知道情况会是这样。我们刚才戏剧化地呈现这一点的方式是，玩家一把钱放进帽子里，帽子被非常诚实地——没有人偷钱——运过教室到玩家二那里。玩家二可以在帽子里看，可以在斯蒂芬或内特必须做出选择之前看到里面有多少钱。对吗？好的。那么我们如何分析具有这种序贯结构的游戏呢？

[段 9]

So it turns out that a useful way to analyze them, and a way I want to get us used to today already, is to draw a tree. so in the first half of the class we drew a lot of matrices now we’re going to draw trees and for those people who haven’t seen trees before it’s not a big deal, it’s an object that looks like a tree that’s why it’s called a tree alright, so let’s have a look so in this particular game here is player one making her choice and in fact she has three possible choices She can put nothing 1 or 3 into the hat Player 2 then chooses, although really player 2 only has choices to make if there’s some money in the hat, and player 2 has two choices in this particular game in either case. either player two is going to add a dollar or three dollars into the hat or they’re going to disappear off to Mexico taking our investors’ lunch money with them and let’s put down the payoffs and let’s put down as payoffs the net gains they make so if nothing goes in no one makes any money so zero zero will be the payoff if one is matched by one then the investor, the lender, doubles her money, so she makes a net profit of one.

[译文 9]

所以事实证明，一种有用的分析方法，也是我今天想让你们习惯的方法，是画一棵树。所以在课堂的前半部分我们画了很多矩阵，现在我们要画树，对于那些以前没见过树的人来说，这不是什么大事，它是一个看起来像树的东西，这就是为什么它被称为树，好的，让我们看看，在这个特定的游戏中，玩家一做出她的选择，实际上她有三种可能的选择。她可以往帽子里放零、一或三。然后玩家二选择，虽然实际上玩家二只有在帽子里有钱的情况下才有选择要做出，而且玩家二在这个特定的游戏中在两种情况下都有两个选择。玩家二要么往帽子里加一美元或三美元，要么他们要去墨西哥消失，带着我们投资者的午餐钱，让我们把收益写下来，让我们把净收益作为收益写下来，所以如果什么都没有放进去，没有人会赚钱，所以零比零将是收益。如果一被匹配为一，那么投资者、放贷者会把她的钱翻倍，所以她净赚一。

[段 10]

If the money is taken out by player two, then she loses one. Right, down here, if two matches her investment of three, she doubles her money again so she makes a net profit of three And if the money is taken out she loses 3 Everyone all right with that Let do player 2 payoffs In the case in which he matches 1, he makes a net profit of 150. In the case in which he just steals the 1, he makes a net profit of 1. And down here, in the case where he matches 3, he makes a net profit of 2. he gets 5 back that he’d invested 3 to start with and here if he just takes the money out he makes a profit of 3 alright so this game is just illustrated on the board for some of you this is the first time you’ve seen a tree but I’m going to claim it isn’t such a complicated object and we could spend a lot of time analysing this in terms of connected graphs and so on but it isn’t really worth it, it’s just a tree alright Okay, so let’s just make sure we understand that the payoffs here represent player 1’s payoff and player 2’s payoff, respectively. All right. So how do we analyze what to do in these games? It a good idea always to write up the tree like it a good idea to write up the matrix But how to analyze what we should do Well before we do that let me just grab the mic and find out from our players what they should do All right All right so where was my first investor All right, so Justin, why did you put $1 in there?

[译文 10]

如果钱被玩家二拿走了，那么她亏一。对，在下面，如果二匹配了她的三投资，她再次把钱翻倍，所以她净赚三。如果钱被拿走了，她亏三。大家这个都明白吗？让我来算玩家二的收益。在他匹配一的情况下，他净赚150。在他偷了一的情况下，他净赚一。在这里，在他匹配三的情况下，他净赚二。他拿回5，而他最初投资了3，这里如果他只是把钱拿走，他赚3。好的，这个游戏就这样在黑板上说明了。对你们中的一些人来说，这是你们第一次看到树，但我会说它并不是一个那么复杂的物体，我们可以花很多时间用连通图等方面来分析它，但这真的不值得，它只是一棵树。好的。好的，让我们确认一下这里的收益分别代表玩家一的收益和玩家二的收益。好的。那么我们如何分析在这些游戏中应该怎么做呢？一个好主意总是把树写出来，就像一个好主意是写矩阵一样。但是如何分析我们应该做什么呢在我们做那之前，让我拿麦克风问问我们的玩家他们应该怎么做。好的，好的，我第一个投资者在哪里？好的，贾斯汀，你为什么往里面放了一美元？

[段 11]

Well, if I put $1 in, he’s an incentive to put $1 in too. If I put in $3, he’s just going to take the money and run. All right, okay, so what’s Justin doing? Justin is looking forward, if you like. He’s putting himself in player two’s shoes. This was who was our investor our receiver at Nate’s Nate Nate shoes and anticipating what Nate’s gonna Do and as Justin said if he puts in three Nate’s gonna have an incentive to take the money and run in fact What would need to donate if three had been in the hat what would you have done? I like Justin, but I would have taken the money all right all right even though. You know Justin You’ve taken the money and disappeared somewhere. We don’t quite know right right is the same true for the other pair So it’s okay. You also put one in is that your explanation as well same reason same reasoning, okay? So everyone figured out what was going on, and once again we think probably, let’s try, Stephen, if there’d been three dollars in the hat, what would you have done? I would have taken it. You’d have taken it, all right? So we’re basically getting what’s predicted here out of the game. All right? And let’s just see that more formally, that idea. So the idea here is that the players who move early on in the game… out of the game.

[译文 11]

嗯，如果我放一美元，他有动机也放一美元进去。如果我放三美元，他就会拿钱跑。好吧，好的，贾斯汀在做什么？贾斯汀在向前看，如果你愿意这样说的话。他设身处地地为玩家二着想。这是我们的投资者，我们的接收者——在内特的内特——的立场，预期内特会怎么做。正如贾斯汀所说，如果他放三，内特就会有动机拿钱跑，事实上如果帽子里有三，需要捐出什么，你会怎么做？我喜欢贾斯汀，但我会拿钱。好的，好的，即使——你知道贾斯汀——你拿钱然后消失到某个地方。我们不太知道。对，对另一对也是这样。所以没问题。你也放了一，是吗？这也是你的解释？同样的原因，同样的推理，好的？所以每个人都弄清楚发生了什么，而再一次我们认为可能，让我们试试，斯蒂芬，如果帽子里有三美元，你会怎么做？我会拿。你会拿，好的？好的，所以我们基本上从游戏中得到了预测的结果。好的？让我们更正式地看看那个想法。所以这里的想法是，在游戏早期行动的玩家们……出局了。

[段 12]

Alright? And let’s just see that more formally, that idea. So the idea here is that the players who move early on in the game should do something we’ve always talked about before. They should put themselves in the shoes of the other players. But here, that takes the form of anticipation. They’re anticipating what players down the tree are going to do. So the key idea here is anticipation. Alright, what they’re going to do is they’re going to look forward down the tree, imagine themselves in the shoes of the later players, look at the incentives facing those later players, imagine that they do the best they can, those later players do the best they can, and then walk backwards through the tree. So the key idea here is to look forward, look forward to the end of the tree, and work back. Look forward and work back. That exactly the process that Katie and Justin describe themselves as doing In this tree let have a go at this So let imagine ourselves in Stephen or Nate shoes having found, as they did in fact, having found one dollar in the hat. They then are making a choice between adding a dollar, which nets them a dollar fifty, or taking the dollar, which nets them one. One fifty is bigger than one, so we think they’re going to go this way.

[译文 12]

好吗？让我们更正式地看看那个想法。所以这里的想法是，在游戏早期行动的玩家应该做我们以前一直谈论的事情。他们应该设身处地为其他玩家着想。但在这里，这采取的是预期的形式。他们在预期树下游的玩家会做什么。所以关键的想法是预期。好的，他们要做什么是他们将沿着树向下看，想象自己置身于后期玩家的位置，看看那些后期玩家面临的激励，想象他们尽可能做得好，那些后期玩家尽可能做得好，然后沿着树往回走。所以关键的想法是向前看，向前看到树的末端，然后往回工作。向前看，往回工作。这正是凯蒂和贾斯汀描述自己所做的过程。在这个树上让我们试一试。所以让我们想象自己处于斯蒂芬或内特的位置，发现——正如他们实际上所做的那样——帽子里有一美元。然后他们正在做出选择，要么加一美元，这给他们净赚1.5，要么拿这一美元，这给他们净赚1。1.5大于1，所以我们认为他们会走这边。

[段 13]

Alright, everyone happy with that? Conversely, if they found themselves with $3.50, then if they add $3, they match, they’re going to get $2. They’re going to net $2. And if they take the money out, they’re going to get away with $3. 3 seems bigger than 2, so we think they’re going to go this way. Again, we’re assuming that these are their real payoffs. okay, so from player 1’s point of view since player 1 knows that player 2 will observe the choice before making her own choice and since player 1 can put him or herself in player 2’s shoes and anticipate this choice player 1 is essentially choosing between what? if she puts in 0, she gets 0 if she puts in 1 she knows 2 will match and she double her money and get 1 and if she puts in three then she knows player two will take the money and run in which case our lender will have lost three dollars So she’s choosing between zero, one, and minus three, and she’s going to choose one. Which is exactly what happened in the game.

[译文 13]

好的，大家都同意这样吗？反过来，如果他们有3.5美元，然后如果他们再加3美元匹配，她就会得到2美元。她净赚2美元。如果她把钱取走，她就能拿走3美元。3比2大，所以我们认为她会走这条路。同样，我们假设这些就是他们实际的收益。好，从参与者1的角度来看，既然参与者1知道参与者2会先观察选择再做出自己的选择，而且既然参与者1能站在参与者2的立场上预测这个选择，那么参与者1本质上是在选择什么？如果她投入0，她得到0；如果她投入1，她知道2会匹配，她的钱会翻倍，得到1；如果她投入3，那么她知道参与者2会拿钱跑掉，在这种情况下我们的贷款人会损失3美元。所以她在零、一和负三之间选择，她会选择一。这正是游戏中实际发生的情况。

[段 14]

Everyone happy with how we did that? so this idea of starting at the last player the player who moves last solving out what they’re going to do and then working our way back through the tree has a name the name for this is backward induction and I apologise for the business school students in the room who’ve had this hammered into them too many times already so I apologise for them in advance alright, backward induction now it turns out there’s precisely one controversial thing about backward induction which is whether you should say backward induction or backwards induction so I’m going to leave the S off and call it backward induction but it’s up to you which you think is correct English is alright ok so since we got this game here let talk about it a bit this idea of the lender and the borrower It not an unimportant situation we simplified it down to a very simple choice here but it’s a very basic choice out there in the real world. All right? And it’s an important choice, after all, what keeps the economy running is the ability of lenders to lend money to businesses that then invest them profitably and are able to make returns. This underlies a whole bunch of stuff going on in the economy. All right? So let’s talk about this.

[译文 14]

大家都同意我们刚才的做法吗？这种从最后一个玩家开始、从最后行动的玩家开始解决问题、然后沿着树往回推的方法有一个名字，这叫做逆向归纳法。我要向教室里那些已经被这个词轰炸过太多次的商学院学生道歉，所以我提前为他们道歉。好，逆向归纳法。现在事实证明关于逆向归纳法只有一件事是有争议的，那就是应该说backward induction还是backwards induction。所以我要把S去掉，叫做backward induction，但你可以自行决定哪个是正确的。好，英语没问题。好，既然我们这里有这个游戏，让我们来讨论一下。贷款人和借款人的这个概念并不是一个不重要的情况。我们把它简化成一个非常简单的选择，但这是一个在现实世界中非常基本的选择。好吗？这是一个重要的选择，毕竟，维持经济运转的是贷款人向企业放贷的能力，这些企业随后进行有利可图的投资并能够获得回报。这构成了经济活动中大量事务的基础。好吗？让我们来谈谈这个。

[段 15]

And the first thing I want to talk about is I want to point out that there’s a problem here. There’s a bad thing here. Much like there was a bad thing in the very first class of the semester. In the very first class of the semester, the bad thing was a prisoner’s dilemma. All right? But here it’s a little different. But let’s focus on it a while. So the bad thing is we ended up here. Not a disaster, right? The lender doubled her money. The borrower was able to go ahead with the project on a small scale and make some money. The bad thing, however, is that we would have liked to end up here. Had we been able to have a large project funded with $3 and had the borrower here. Alright? Had we been able to have a large project funded with three dollars and had the borrower repaid those dollars so matched in effort or whatever it happens to be then we’d have ended up at an outcome that is better not just for the lender it’s obviously better for the lender but it’s also better for the borrower. Everyone see that? So the outcome we’d like to have reached gets the lender 3 where she’s only getting 1 where we ended up and it gets the borrower 2 where he’s only getting 150 where we actually ended up.

[译文 15]

我想谈的第一件事是，我想指出这里有一个问题。这里有一件坏事。就像学期第一堂课里有一个坏事一样。在学期第一堂课里，坏事是一个囚徒困境。好吧？但这里有点不同。但让我们先关注它一会儿。所以坏事是我们最终到了这里。这不是一场灾难，对吧？贷款人让她的钱翻倍了。借款人能够以小规模推进项目并赚一些钱。然而坏事是我们本来希望能够到达这里。如果我们能够有一个用3美元资助的大项目，而且借款人这里。好吧？如果我们能够让一个大项目获得3美元的资助，并且借款人偿还那些美元，在努力或其他方面与之匹配，那么我们就会到达一个不仅对贷款人更好、而且对借款人也更好的结果。大家明白吗？所以我们希望达到的结果让贷款人得到3，而她只得到了1；让借款人得到2，而他实际上只得到了150。

[段 16]

Why is it that we were unable to both of our pairs, both Justin and Nate and Katie and Stephen, why were we unable to get to here? Why were we unable to get to here? May I take this? what prevents us from getting to this good outcome let’s go back to Katie a second see if we can yeah you go ahead I’ll come that right alright so Katie was saying why she invested one I picked on Justin before So here this good outcome It better for you It better for Stephen who your borrower Why aren we getting to this 3 outcome Because if I play three, him matching my money is dominated. Strictly dominated. alright so the problem here the problem here is Katie would like to invest three if she knew in fact Stephen was going to match but she knows Stephen’s not going to match right Stephen in fact is going to run off with the cash alright it’s going to end up being spent at Starbucks or something alright and from Stephen’s point of view he would actually like to be able to borrow the three dollars he would like to be able to end up at this 3-2 outcome as well the problem is he knows he knows that Katie knows and Katie knows that he knows that in fact he’s going to run off with the cash is that right? is that right? so we’re in a bit of a problem here, we’d like to get this good outcome but incentives are preventing us from getting there what do we call this kind of situation? what do we call this kind of problem? anybody no takers alright this is called moral hazard This is called moral hazard.

[译文 16]

为什么我们两对，Justin和Nate以及Katie和Stephen，都无法到达这里？为什么我们无法到达这里？我可以拿这个吗？是什么阻止我们得到这个好的结果？让我们回到Katie一会儿，看看我们能不能……对，你继续说……我会说到那儿的。好，所以Katie说的是为什么她投了1。我之前选了Justin。所以这里这个好结果对你更好。对Stephen更好，你的借款人。为什么我们不能到达这个3的结果？因为如果我投3，他匹配我的钱就会被严格占优。这被严格占优了。好，所以这里的问题，问题是Katie想要投3如果她知道Stephen会匹配的话，但她知道Stephen不会匹配。没错，Stephen实际上会拿着现金跑掉。好，这最终会被花在星巴克什么的。而从Stephen的角度来看，他其实想要能够借到那3美元。他想要能够到达这个3-2的结果。问题是，他知道他知道Katie知道，而Katie知道他知道她知道他知道，实际上他会拿着现金跑掉。是这样吗？是这样吗？所以我们这里有点问题，我们想要得到这个好的结果，但激励机制阻止我们到达那里。我们把这种情况叫什么？我们把这个问题叫什么？有人知道吗？好吧，这叫做道德风险。这叫做道德风险。

[段 17]

How many of you have heard the term moral hazard before? All right, a number of people have heard it. So here we are, moral hazard, here is the problem that the agent, in this case the borrower, will have incentives to do things that are not in the interests of the principal. If we’re not careful, for example by giving too big a loan, the incentives of the borrower will be such that they will actually not be aligned with the incentives of the lender, and that will prove to be bad for the lender. but notice the existence of this moral hazard problem isn’t only bad for the lender it ends up being bad for the borrower as well let me give you another example in insurance there’s a classic the classic moral hazard problem if an insurance company insures me against having my car stolen there’s a moral hazard problem in that if the car is fully insured I might now have the incentive not to bother to lock my car or to leave it anywhere on the street in New Haven Because I’m not bearing the cost. So the insurance company needs to worry about that in writing an insurance contract for me, and in practice what the insurance company does is it forces me to take a deductible. It doesn’t allow me full insurance. It makes sure that some of the cost of having a car stolen is going to fall on me.

[译文 17]

你们有多少人以前听说过道德风险这个词？好的，有相当多人听说过。所以这就是道德风险，这里是代理人——在这种情况下是借款人——会有做不符合委托人利益的事情的激励的问题。如果我们不小心，例如贷款额过大，借款人的激励就会与贷款人的激励不一致，这将证明对贷款人是不利的。但请注意，这种道德风险问题的存在不仅仅对贷款人不利，它最终对借款人也同样不利。让我给你们另一个例子。在保险中有一个经典的例子，经典的道德风险问题：如果一家保险公司为我投保汽车被盗，如果汽车是全额投保的，我现在可能就没有激励去费心锁车或者把它停在纽黑文的任何街道上。因为我不是在承担成本。所以保险公司在为我撰写保险合同时需要担心这一点，在实践中，保险公司做的是迫使我承担免赔额。它不允许我全额投保。它确保汽车被盗的部分成本会落在我身上。

[段 18]

That’s bad for me, by the way, because it means I can’t get full insurance. All right? And notice that what happened here is rather similar. In this case, both the lender and the borrower would rather have a big project, a big loan, and have the agent pay back that loan. They’d prefer this 3-2 outcome. But they can’t get there, and therefore, rather than having a full-scale project, case you’re Justin only offered the borrowers a small-scale project. Alright? So the idea here in this example was, in this example, what happened was we kept the size of the project or the size of the loan, you can think of this as the project if they’re borrowing something, small to reduce the temptation to cheat. To reduce that temptation not to repay the loan. So these problems are all over society, but they’re particularly prevalent in situations involving lenders and borrowers. So a good question is, how might we solve this problem? A lot of you are about to go out and try and borrow money to start your projects, to run your new version of Facebook, whatever. And a lot more of you, as we said before, are going to end up loaning money, perhaps someone else’s money probably at least for a while and we want to know how you might solve this moral hazard problem we’ve seen one way to solve it one way is to keep the size of the project small what else could we do let me come down and try and have a bit of a discussion What else could we do Stephen what else could we do You with the borrower what else can we do Impose laws.

[译文 18]

这对我来说是不好的，顺便说一句，因为这意味着我无法获得全额保险。好吗？请注意，这里发生的事情相当类似。在这种情况下，贷款人和借款人都宁愿有一个大项目、一笔大贷款，并让代理人偿还那笔贷款。他们宁愿这个3-2的结果。但他们无法到达那里，因此，与其有一个全面展开的项目，不如……你只向借款人提供一个小规模的项目。好吧？所以这个例子的想法是，在这个例子中，我们做的是保持项目规模或贷款规模——你可以把它想象成项目如果他们在借什么东西——很小，以减少欺骗的诱惑。减少不偿还贷款的诱惑。所以这些问题遍布整个社会，但在涉及贷款人和借款人的情况中尤为普遍。所以一个好问题是，我们怎样才能解决这个问题？你们中很多人即将出去尝试借钱来启动你们的项目，运行你们新版的Facebook什么的。而且你们中更多的人，就像我们之前说的，最终会去贷款，可能是别人的钱，至少在一段时间内。我们想知道你们如何解决这个道德风险问题。我们已经看到了一种解决方法，一种方法是保持项目规模小。我们还能做什么？让我下来试着进行一点讨论。我们还能做什么？Stephen，我们还能做什么？你是借款人，我们还能做什么？制定法律。

[段 19]

We can impose laws, okay. So we can impose laws, much like we talked about in President’s Lemma, we could regulate this market. There’s going to be a little bit of a problem we’re going to run into in regulating the law, in using the law here. What’s the problem we’re to run into here? Well, we do have laws that regulate borrowers and lenders. What’s the law that regulates borrowers and lenders? Bankruptcy law, right? So we have law that regulates to some extent what lenders and borrowers can do. One of the things we do in that law is we limit the degree to which we’re allowed to punish the borrowers. So bankruptcy law pretty much says we’re going to put some limit on how much Katie can inflict pain on on Stephen for running off with the lunch money. Stephen can simply say I can’t repay, I’m bankrupt and you know he’s more or less allowed to have a fresh start. So the law would be good here but there’s limits to what we can do. We could go back to the Dickensian world of throwing Stephen in jail for not repaying the loan but it tough There are downsides to that it turns out So what else could we do Yeah I going to have to dive in there a little bit so shout into the mic Venture capitalists can impose restrictions on what the person can do with the money All right, all right, so you could try and say there’s only certain things you can do with the money, and for example, to make that credible, what you might have to do is to say, show me what you’re going to do with the money, show me the receipts.

[译文 19]

我们可以制定法律。好吧，我们可以制定法律，就像我们在校长定理中讨论的那样，我们可以对这个市场进行监管。但在使用法律进行监管时，我们会遇到一些问题。我们面临什么问题呢？我们确实有规范借款人和贷款人的法律。规范借款人和贷款人的法律是什么？破产法，对吧？所以我们确实有法律在一定程度上规范借款人和贷款人的行为。我们在破产法中做的一件事是限制对借款人的惩罚程度。破产法基本上说的是我们要对Katie能对拿着午餐钱跑掉的Stephen施加的痛苦程度设定一些限制。Stephen可以简单地说他还不起，他破产了，而且他多多少少被允许有一个新的开始。所以法律在这方面是好的，但我们能做的事情有限。我们可以回到狄更斯时代的做法，把Stephen关进监狱因为他没有偿还贷款，但这很残酷。事实证明这样做有缺点。那么我们还能做什么？嗯，我需要再深入一点，大声对着麦克风说：风险资本家可以对借款人如何使用这笔钱施加限制。好吧，好吧，所以你可以试着说，这笔钱只能用于某些特定的事情，例如，要使这可信，你可能不得不说，把你要怎么花这笔钱给我看，把收据给我看。

[段 20]

All right, all you could say is, I will only give you the money if you show me exactly how you’re going to spend this. That’s a good solution. Notice that you could regard that as changing the order of play. It’s a little bit like saying, let’s have the borrower have to move first. Let’s have the borrower have to commit what their actions are going to be, how they’re going to spend the money, and show the contracts before the lender lends them the money. And that’s a good solution. But again, there are limitations to this solution. What are the limitations to that solution in the real world? Let’s go back to all of you are thinking about making millions with your new Facebook. What are the limitations to having some contracts with the bank, you know, with Chase, saying exactly how you’re going to, not only saying exactly how you going to spend the money but actually detailing it already with contracts ahead of time What are the problems for that Someone else Someone thinking of going into business here Let me pick on somebody a second So what your name sir Kelly. Kelly. So imagine you have some project. You’re going to borrow some money from Chase or Mr. Swenson to set up this fund. Why might you worry about having everything written out and contractually ahead of time?

[译文 20]

好吧，你可以说，除非你告诉我你打算怎么花这笔钱，否则我不会把钱给你。这是一个很好的解决方案。注意，你可以把这看作改变了行动顺序。这有点像说，让借款人先行动。让借款人必须承诺他们要做什么，怎么花这笔钱，在贷款人借给他们钱之前出示合同。这是一个很好的解决方案。但同样，这个解决方案也有局限性。在现实世界中，这个解决方案的局限性是什么？让我们回到你们都在想着用新的Facebook赚几百万的时候。与银行，比如Chase，签订合同，精确说明你打算怎么花这笔钱，不仅要精确说明你怎么花这笔钱，还要提前在合同中详细说明，这样做有什么问题？其他人，有谁想创业的？让我点一个人。那位先生，你叫什么名字？Kelly。Kelly。假设你有一个项目。你要从Chase或Swenson先生那里借一些钱来设立这个基金。为什么你会担心把一切都提前写进合同里呢？

[段 21]

I mean, then it restricts your freedom on what your ideas are, I guess. Right. So one problem is a sheer lack of flexibility. If in fact the entrepreneur is not going to be flexible in how they actually run the project, there’s no point in being an entrepreneur in the first place. There’s a limit to how much control you want to give to the lender. The lender doesn’t really want to run the project for you. There’s also simply a problem of timing. It’s simply not going to be possible to specify all the expenditures of a project up front. You’re going to need some money to do some things ahead of time. alright, so it’s a good idea, changing the order of play is a good idea but there’s going to be limitations to this, what else could you do as the lender what else could you do thinking of loaning some money in here loaning some money to one of your classmates for some project, let’s try again something like loan money over time in stages and observe progress I’m thinking of loaning some money in here. Loaning some money to one of your classmates for some project. Let’s try again. Something like loan money over time in stages and observe progress. Good. So one possibility is to break the loan up and let it come in small installments.

[译文 21]

我是说，这样会限制你想法的自由，对吧。所以一个问题就是缺乏灵活性。如果企业家实际上不能灵活地经营项目，那一开始就根本没必要当企业家。你想要给贷款人的控制权是有限度的。贷款人其实并不想替你经营项目。还有一个就是时机问题。不可能提前规定好一个项目的所有开支。你会需要一些钱提前做些事情。好吧，所以改变行动顺序是个好主意，但它也有局限性。作为贷款人你还能做什么？想着借钱给你的某个同学做项目，试试分期付款并观察进展。我想到了。借钱给你的某个同学做项目。再试一次。像分期付款那样借钱，分阶段给钱并观察进展。好。一个可能的做法是把贷款拆开，分成小额分期付款。

[段 22]

If you do well on the first installment, I’ll give you a bigger installment next time. And notice that that’s a little bit like something we talked about the very first week. It’s a little bit like taking this one-shot game and turning it into a repeated game, right? It’s turning a one-shot interaction into a repeated interaction. And we’ll come back and talk about repeated interactions later on in the course. Again, notice that there might be some limitations to this. I mean, I think it’s a good idea and in general you should be trying to do this, but it could just be that to set up, for Nate to set up his new Facebook and for Stephen to set up his new mousetrap factory, they just need a chunk of money at the beginning. There may be some limit to how little money you can give them at the beginning since they have to hire workers and set up the factory and make some big splash in advertising and so on and so forth. Alright, so again it’s a good idea, but there may be limitations here. What else could you do Let have a look at the numbers on the board Right now the numbers on the board say that if Stephen mousetrap project were you the Facebooker If Steven mousetrap project goes well and it ends up being a big project with lots of money available there are five units of money available in profit right, three plus two.

[译文 22]

如果你第一期做得好，下次我会给你更大的一期。注意，这有点像我们第一周讨论的东西。这有点像把这个一次性博弈变成一个重复博弈，对吧？它把一次性的互动变成了重复的互动。我们会在课程后面回来讨论重复互动。同样，注意这可能有局限性。我的意思是，我认为这是个是个好主意，总体上你应该尽量这样做，但可能是Nate要创办他的新Facebook，Stephen要创办他的新捕鼠器工厂，他们一开始就需要一大笔钱。你一开始能给他们的钱可能有个下限，因为他们需要雇工人、建工厂、做大规模广告等等。好吧，所以这又是个好主意，但可能有局限性。你还能做什么？让我们看看黑板上的数字。现在黑板上的数字说，如果Stephen的捕鼠器项目——你们这些Facebook创业者——如果Stephen的捕鼠器项目进展顺利，最终成为一个有大把钱可赚的大项目，有五个单位的利润，对吧，三加二。

[段 23]

The way we’ve designed things so far our lender, I gave you these payoffs in the game, the lender is going to double her money, she’s going to get six-packs from it to net three, and Stephen’s going to get two. So the division of that five is three and two. But we don’t have to divide the money like that. If you’re a lender, you may want to think about how you divide up the spoils of a successful project. So how else could you divide up those five dollars, that three plus two, in a way that might be better for everybody?

[译文 23]

到目前为止我们设计的方案，我们的贷款人，我在博弈中给你们展示的这些收益，贷款人会把她的钱翻倍，她会从中得到六包东西，净得三，而Stephen会得到二。所以这五个单位的分配是三和二。但我们不一定要这样分配这笔钱。如果你是贷款人，你可能会想思考如何分配一个成功项目的收益。那么你还能怎么分配这五块钱，也就是三加二，才能对大家都更好呢？

[段 24]

Nate? give the investor $3.01 if they do that other choice and then take a little bit of a hit but that way you’ll still have something that’s pretty optimal to the other choice that we came to before I’m guessing people didn’t hear that but that was right so what you could do here is you could redesign the payoffs of this project in the event that it successful what you could do is take these 5 units of profit and instead of having 3 which is written in a different color we could give the borrower the entrepreneur 3 leaving 1 to the lender All right, so we could change the payoffs of this contract to be 1.9, 3.1, in the event of a big project. why does that help? because now our borrower Nate or Stephen were they to end up with a hat with three dollars in it they now will find it in their interest to match the three dollars and get 3.1 rather than 3 alright so what’s this an example of? this idea of changing the contract to give the borrower incentives to repay, incentives not to shirk, incentives not to disappear with the cash, is an example of what’s called incentive design. All right? So the idea here is in all of businesses incentives are not given by God they designed by the people who write the contract And if you’re either the borrower or the lender, you should be thinking about writing a contract that’s going to achieve the end that you want.

[译文 24]

Nate？如果他们做那个其他选择就给投资者3.01美元，然后你会受到一点损失，但那样你仍然会有相当不错的结果，接近我们之前得出的另一个选择。我想人们没听清楚，但这是对的。那么你能做的是，在项目成功的情况下，你可以重新设计这个项目的收益。你能做的是拿这五个单位的利润，不按另一种颜色写的三来分配，而是给借款人企业家3，贷款人拿1。好吧，所以我们可以把这个合同的收益改成1.9、3.1，在一个大型项目的情况下。这为什么有帮助？因为现在我们的借款人Nate或Stephen，如果他们最终帽子里有三美元，他们现在会发现匹配这三美元并得到3.1而不是3是符合他们利益的。好吧，这是什么的例子？改变合同以给借款人还款的激励、不偷懒的激励、不拿着现金跑路的激励，这个想法就是所谓的激励设计的例子。好吧？这里的想法是，在所有商业活动中，激励不是上帝给的，而是写合同的人设计的。如果你既是借款人又是贷款人，你应该考虑写一个能实现你目标的合同。

[段 25]

Now notice in this particular example, exactly as Nate said, the lender’s going to take a bit of a hit here, they’re not going to get a 100% return, but they’re ending up doing better than they would have done by giving a small loan. They’ve ended up getting 1.9 rather than 1. They’ve ended up getting 1.9 rather than 1. So in this particular example, it won’t always be the case, but in this example, they’re taking a smaller share of a larger pi. and sometimes a smaller share of a larger pi is bigger than a larger share of a smaller pi not always but sometimes right the reason the pi is larger is we’re able now in an intensive compatible way we’re able to go ahead and have a large project so in this example the smaller share of the larger pi actually ended up being bigger than the larger share of the larger pi is we’re able now, in an intensively compatible way, we’re able to go ahead and have a large project. So in this example, the smaller share of the larger pi actually ended up being bigger than the larger share of the smaller pi. So a smaller share of a larger pi can be bigger than a large share of a small pi. not always of course alright this is just an example alright now let’s just be a little bit careful here alright so in this particular example even though this 1.9 this return that our lender is able to make by accepting a smaller share of a larger pie even though it’s a bigger absolute return it’s smaller in another sense And what sense is it smaller?

[译文 25]

现在注意，在这个特定的例子中，正如Nate所说，贷方在这里会有一点损失，他们不会获得100%的回报，但他们最终会比发放小额贷款做得更好。他们最终得到的是1.9而不是1。他们最终得到的是1.9而不是1。所以在的这个特定例子中，情况并不总是如此，但在本例中，他们拿的是较大馅饼中较小的份额。有时候较大馅饼中较小的份额比小型馅饼中较大的份额更大，当然并不总是如此，但有时确实如此。之所以馅饼更大，是因为我们现在能够以一种激励相容的方式，能够进行一个大项目。所以在在这个例子中，较大馅饼中较小的份额实际上最终比小型馅饼中较大的份额更大。所以较大馅饼中较小的份额可能比小型馅饼中较大的份额更大。当然并不总是如此，好了，这只是一个例子。好，现在让我们在这里稍微谨慎一点。所以在在这个特定例子中，即使这个1.9——贷方通过接受较大馅饼中较小的份额所能获得的这个回报——即使这是一个更大的绝对回报，它在另一个意义上却更小。什么意义上它更小？

[段 26]

Let’s be careful here. So, what sense is it to say, look, it’s 1.9. 1.9 is bigger than 1. That’s got to be a good thing. But since some of you actually are going to go out into investment banks you might be posed this question Let me just make sure we don make a blunder that going to spoil your interview So what might you be worried about as an investment banker about this deal about this contract Somebody else? Anybody else? I’ll come down again, it’s all right. What might you be worried about? Be honest, who here has been interviewing with either investment banks or venture capital firms or private equity firms. Raise your hands. Oh, come on, it’s going to be more than that. All right, all right. There was a hand, where was the hand at the back? There was a hand way back here. No? Yeah? So what might be wrong with this project from your point of view? Can I get the mic on that side? This gentleman here. What might be wrong with the project from your point of view? If you could actually just find three small projects, then you could still get 100% returns just by dividing it up. Good, good, you’re going to make lots of money from Morgan Stanley or whatever it is. Good, good, your name is?

[译文 26]

好，让我们在这里谨慎一点。所以，说这是什么意义上的——看，这是1.9。1.9比1大。这一定是一件好事。但是既然你们中有些人实际上将进入投资银行，你们可能会被问到这个问题。让我确保我们不会犯一个会毁掉你们面试的错误。那么作为投资银行家，你可能对这个交易、对这份合同担心什么？其他人？有谁？好的，我会再下来，没关系。你可能担心什么？说实话，这里有多少人在面试投资银行或风险投资公司或私募股权公司。请举手。哦，来吧，不会只有那么点。有只手，在后面那儿。有只手在很后面。没有吗？是的？那么从你的角度来看，这个项目可能有什么问题？我能让那边的话筒打开吗？这位先生。从你的角度来看，这个项目可能有什么问题？如果你真的能找到三个小项目，那么通过分割，你仍然可以获得100%的回报。好的，挺好的，你将从摩根士丹利或其他什么地方赚很多钱。好的，挺好的，你叫什么名字？

[段 27]

Brian. Brian, right, so he’s a good advert, a good ad to hire Brian at Morgan Stanley, alright? Alright, so what Brian said was, it true that you making a bigger absolute return here this is a bigger absolute return but this return up here is a 100 return on your capital The rate of return on capital is higher making a 100 return on an investment of 1 than making a 1.9 return on an investment of 3. The rate of return is better in the smaller case. So which is the right answer? Should we worry about the rate of return, the 100% rate of return, or should we worry about the absolute return? If you’re in the business of investment banking, who thinks you should worry about the absolute return? Who thinks you should worry about the rate of return? Who thinks it depends? What does it depend on? What does it depend on? Keep me from falling off this thing. What does it depend on? Somebody said it depends. What does it depend on? Depends is only a good compromise vote if you know what it depends on. Yeah, the gentleman here. Since an investment banking firm only has a limited amount of money to invest, you want to see if you can get a higher rate of return investing elsewhere. All right. So there’s two…

[译文 27]

Brian。Brian，对，所以他是摩根士丹利招聘Brian的一个好广告，好吧？好的，所以Brian说的是，虽然你在这里获得了一个更大的绝对回报，但这里的回报是你资本的100%回报。在资本上的回报率更高，在1的投资上获得100%的回报比在3的投资上获得1.9的回报更好。在较小的情况下回报率更好。那么哪个是正确的答案？我们应该担心回报率、100%的回报率，还是应该担心绝对回报？如果你在投资银行业务中，谁认为你应该担心绝对回报？谁认为你应该担心回报率？谁认为这取决于？它取决于什么？它取决于什么？别让我从这东西上摔下来。它取决于什么？有人说取决于。你得知道它取决于什么才算是一个好的妥协投票。是的，那位先生。既然一家投资银行公司只有有限的投资资金，你想看看在别处投资是否能获得更高的回报率。好的，所以这里有两个…

[段 28]

You’re on the right line. There two things to worry about One is what is your supply of funds to invest And the other is what the other supply you worried about as an investment bank or a venture capitalist firm or a private equity investor What the other supply coming your way Yeah the number of projects coming across your door like the demand for your cash, the supply of projects. Alright? Alright, so what we have to worry about here is what is the true opportunity cost of that money? If there are are very few projects out there, all right, then you basically just want to go down the list of projects picking off absolute return. However, to the other extreme, if there’s an infinite supply of projects all coming in, all of which will offer 100% return, then as our banker at the back told us, you should just go for three small projects rather than one large one. Right? But the question is, which is better, three large, it isn’t as simple as saying, yes, we should always go for three small projects, there may not be There are only three small projects out there that offer 100% return. Alright, so what’s going to matter here is what’s the true opportunity cost of the capital, and that’s going to depend on what projects are available to you.

[译文 28]

你在正确的方向上。有两件事需要担心。一是你的投资资金供应，二是你作为投资银行或风险投资公司或私募股权投资者担心的另一个供应。什么是另一个向你走来的供应？是的，来到你面前的项目数量。比如对你现金的需求，项目的供应。好的？好的，所以我们必须担心的是那笔钱的真正机会成本。如果外面很少有项目，那么基本上你只是想按项目列表往下走，选择绝对回报。然而，在另一个极端，如果有无限供应的项目进来，所有这些都将提供100%的回报，那么正如我们后面那位银行家告诉我们的，你就应该选择三个小项目而不是一个大项目。对吧？但问题是，哪个更好，三个大的，之说我们应该总是选择三个小项目并不是那么简单，可能只有三个提供100%回报的小项目。好的，所以这里重要的是资本的真正机会成本是什么，而这将取决于你有哪些项目可供选择。

[段 29]

Alright, this was just an example of incentive design. Just one example of incentive design. Let’s talk about other examples of incentive design. Incentive design has been a lot on the news lately. Who else tends to have incentive contracts other than borrowers? Who else out there tends to have incentive contracts? It’s a big topic in the news these days. So who has incentives written into their contracts? They’re way over here. Let me run over at the risk of blurring the camera. All right? So who else has incentives in their contracts? Managers. Managers. All right? So CEOs have huge incentive clauses in their contracts. All right? Sometimes in the form of options. All right? Why do they have those incentive clauses in their contract? Well, there’s two interpretations of this. One interpretation is it’s just a bad thing and they’re just trying to screw the world. But there’s a more moderate view of this. the more moderate view of this is that those incentive clauses in their contracts are attempts to align the interest of the managers with the interest of the shareholders. Just as this contract is attempting to align the interest of the lender and the interest of the borrower Alright So by managers I took you to mean CEO but what other kind of managers recently in the press very recently this weekend have been talking about incentive contracts Some of you are way over there, I know you’re caught on the wrong side as usual.

[译文 29]

好的，这只是一个激励设计的例子。只是激励设计的一个例子。让我们谈谈激励设计的其他例子。激励设计最近一直是新闻热点。除了借款人之外，还有谁倾向于有激励合同？还有谁倾向于有激励合同？这几天新闻里是个大话题。那么谁在他们的合同中有激励条款？他们在那边很远的地方。让我冒镜头模糊的风险跑过去。好的？所以谁还在他们的合同中有激励？经理人。经理人。好的？所以CEO的合同中有大量的激励条款。有时是以期权的形式。他们为什么要在合同中加入这些激励条款？嗯，对此有两种解释。一种解释是这只是坏事，他们只是在试图坑害世界。但有一种更温和的观点。更温和的观点是，他们合同中的这些激励条款是为了将经理人的利益与股东的利益对齐。正如这份合同试图将贷方和借款人的利益对齐一样。好的，所以当我说到经理人时，我让你们指的是CEO，但还有什么样的经理人在最近的新闻中，最近这个周末一直在谈论激励合同？你们有些人很远，我知道你们照例站在错误的一边。

[段 30]

Yeah, can I squeeze through? I’ll try and squeeze through. Can I squeeze through? Sorry. Alright, sorry. Here we go. Where was it? Where was my answer to that question? Here we go. Managers of baseball teams. All right, so managers of sports teams also have incentive contracts these days, right? Incentives to achieve certain levels, all right? Here it’s not quite clear to me exactly what’s going on, right? We call those incentive contracts, but you might want to worry a little bit. I mean, do we really think that the manager has an incentive to lose otherwise, right? So part of what’s going on with incentive contracts isn’t actually incentive contracts. Part of it is about sharing the risk, right? particularly the kind of contracts that have been written about over the weekend with Joe Torre’s contract for the Yankees, which he turned down, is partly perhaps to give him incentive to try and win, but perhaps is more to do with sharing the risk among the general manager and the manager of the team if they don’t make it to the playoffs But all right they still incentive contracts Now we see incentive contracts elsewhere and we seen them since the Middle Ages Right so in the Middle Ages incentive contracts took a particular form and the form was called two things Peace rates. Let’s put it up here.

[译文 30]

是的，我能挤过去吗？我试试能挤过去吗？抱歉。好的，抱歉。我们开始吧。我那个问题的答案在哪里？开始了。棒球队经理。所以运动队的经理最近也有激励合同，对吧？达到某些水平的激励。好吧，这里我不太清楚到底发生了什么。我们称那些为激励合同，但你可能想要稍微担心一下。我的意思是，我们真的认为经理人有不赢球的动机吗？所以激励合同的一部分实际上不是激励合同。部分是关于分担风险的，对吧？特别是周末报道的那些关于Joe Torre与洋基队的合同，他拒绝了，部分可能是为了给他尝试赢球的激励，但也可能更多地是与总经理和球队经理分担风险，如果他们没有进入季后赛。但好吧，他们仍然是激励合同。现在我们在其他地方也看到了激励合同，我们从中世纪以来就看到了。对，所以在中世纪，激励合同采取了一种特定的形式，这种形式被称为两个东西。Peace rates。让我们把它放上来。

[段 31]

Peace rates. And in agriculture, it took the form of sharecropping. What are peace rates? Somebody? What are peace rates? What are peace rates? Anyone know anyone who’s on peace rates? What is sharecropping? Somebody must be from a farming state. Yeah, there’s somebody out here. The guy in orange. Sharecropping is where the landowner takes a portion of the farmer’s crop at the end of the farming season. Alright, so sharecropping is a contract whereby part of the output of the farm goes to the landowner and part is kept by the farmer. Going back to the Middle Ages, part of the output would stay with the peasants and part of it would go to the lord of the manor Peace rates are a similar idea Rather than paying wages to workers just bundles of cash the amount which they paid depends on output So piece rates would say if you produce 17 yards of cloth then you’ll get paid the revenue that’s derived from three of them. Both of these forms of contracting are there partly to create incentives. They create incentives because they create the incentive for the farmer to increase yields and they create incentives on the part of the worker to increase output. All right? So piece rates are a big part of the story. All right. Incentive design is a pretty big topic and we don’t really have time to go into it much in this course, but it’s worth mentioning that, in fact, the Nobel Prize that was won last week by those three economists we talked about was partly about incentive design.

[译文 31]

计件工资率。在农业中，它采取了分成制佃农的形式。什么是计件工资率？有人知道吗？什么是计件工资率？什么是计件工资率？有谁知道有人是拿计件工资的吗？什么是分成制佃农？一定有人来自农业州。是的，这里有人。穿橙色衣服的那个人。分成制佃农是指在地里的耕种季节结束时，土地所有者拿走农民收成的一部分。好的，所以分成制佃农是一种契约，农场的部分产出归土地所有者，部分由农民保留。回顾中世纪，部分产出留给农民，部分归庄园主。计件工资率是类似的理念——不是向工人支付固定工资，而是一捆捆现金，他们的报酬取决于产出。因此，计件工资率是这样的：如果你生产了17码布料，那么你将获得其中三码所产生的收入。这两种合同形式部分是为了创造激励。它们创造激励，因为它们为农民提高产量创造了激励，也为工人增加产出创造了激励。懂了吗？所以计件工资率是故事的重要组成部分。好的。激励设计是一个相当大的话题，我们在这门课中真的没有太多时间来深入探讨，但值得一提的是，事实上，上周我们讨论的那三位经济学家获得的诺贝尔奖部分就是关于激励设计的。

[段 32]

All right? it’s regarded as an important enough topic for the design of incentives across the science as a whole to have been worthy of winning the Nobel Prize. My guess is there’s another Nobel Prize that’s going to come out in this same area in the next five or ten years. Just to make it clear, you can have problems. You can write incentives badly. It’s a classic story that you’ve all heard of, I’m sure, that in office Just to make it clear, you can have problems. You can write incentives badly. It’s a classic story that you’ve all heard of, I’m sure, that often in the provision of public goods, let’s say bridges or highways or tunnels, the incentives for the construction companies tend to be rather badly written. They’re meant to have incentive clauses, but they never seem to quite get them right. It’s easy to get these incentives wrong. And just to prove this doesn’t just happen to management, let me just tell a story against myself. so a year ago, a year and a bit ago I was picking fruit with my then three year old daughter and I wanted to make sure that we got some fruit home to eat for dinner and she didn’t just eat all the fruit as we picked it, these were raspberries so I decided to have a rule that sounds efficient, I said any item of fruit that gets picked that’s in good condition, we’ll take it home for dinner, but if it’s squashed then we’ll eat it then and there while we’re picking the fruit, alright, so my three year old I proceeded to go along the bushes of raspberries, picking the raspberry, turning around to me and saying, squashed, and putting it in her mouth.

[译文 32]

好的，这个话题被认为足够重要，以至于整个科学领域的激励机制设计都值得获得诺贝尔奖。我的猜测是，在未来五到十年内，这个领域还会产生另一个诺贝尔奖。需要明确的是，你可能会遇到问题。你可能会把激励机制写得很糟糕。这是一个你们肯定都听过的经典故事，在提供公共产品时，比如桥梁、公路或隧道，建设公司的激励机制往往写得很糟糕。他们本来应该有激励条款，但似乎从来没有真正写对。这些激励机制很容易写错。为了证明这不仅仅是管理层的问题，让我讲一个我自己的故事。大约一年前，大概一年多以前，我和我当时三岁的女儿在采摘水果，我想确保我们能带一些水果回家做晚餐，而不是让她在采摘的时候就把水果都吃光。当时采的是覆盆子，所以我决定制定一个听起来很高效的规则：任何被采摘的、状态良好的水果，我们带回家做晚餐；但如果被压坏了，我们就在采摘的地方当场吃掉。好吧，我那三岁的女儿沿着覆盆子灌木丛走，摘下覆盆子，转过身来对我说，压坏了，然后就把水果放进嘴里吃了。

[段 33]

Alright? Squashed, squashed, squashed. Which shows that a three year old knows more than a professor about moral hazard Alright So one thing we can do is worry about incentive design in the design of the contract There another thing we can do here What the other thing we can do here We’re missing out on something very basic. What is it that our borrower, Stephen and Nate, can do? Or put it more generally, for all of you, if you go out and start a company and you borrow some money to start your company when you leave Yale, what are you going to have to do? what’s the borrower what’s the lender what’s the bank going to insist what’s they going to insist on anybody they’re going to insist on collateral they’re going to insist on collateral what is collateral I’m somewhat charmed to see how few of you are going to end up borrowing money but for those of you who haven’t got trust funds you’re going to end up borrowing money so what is collateral? yes, what’s collateral? you let the bank hold on to something right, you let the bank hold on to something in the event that you default on the loan alright you going to let the bank hold on to something in the event that you default on the loan Now for most people here what are they going to post as collateral Let assume that we back to our original contract here we can do this we back to our original case What are most of you going to end up using as collateral if you borrow money?

[译文 33]

好吧？被压垮了，被压垮了，被压垮了。这说明一个三岁的孩子比教授更了解道德风险。好的，我们可以做的一件事是在合同设计中考虑激励设计。我们在这里还可以做另一件事。我们在这里可以做的另一件事是什么？我们遗漏了一些非常基本的东西。我们的借款人Stephen和Nate能做什么？或者更一般地说，对于你们所有人，如果你们毕业后出去创业，借钱创业，你们需要做什么？借款人是什么？贷款人是什么？银行会坚持什么？他们会坚持要求任何人提供什么？他们会坚持要求抵押品。他们会坚持要求抵押品，什么是抵押品？我有点惊讶地看到你们中有很少的人最终会借钱，但对于那些没有信托基金的人来说，你们最终会借钱，所以什么是抵押品？是的，什么是抵押品？你让银行持有某种东西，对吧？如果贷款违约，你让银行持有某种东西。如果贷款违约，你会让银行持有某种东西。现在对于这里的大多数人来说，他们会提供什么作为抵押品？假设我们回到原来的合同，我们可以这样做，我们回到原来的案例。如果你借钱，你们大多数人最终会用什么作为抵押品？

[段 34]

Yeah, everyone’s taking a house. I’m guessing that for most of you, I’m not going to look around the room because I don’t know how many trust fund babies I’ve got in the room, but for most of you it’s going to be what? It’s going to be your parents’ house. All right? So why is it that your parents’ house being posted as collateral is going to prevent you from disappearing to Mexico with the loan? Well, let’s have a look at how that changes the payoffs. Now, if you take the money and run, you disappear to Mexico, but you end up with $1 minus a house here, and $3 minus a house there. Of course we’re relying here on you liking your parents enough not to mind about the fact that we’re sleeping in the rain but as long as that’s the case, as long as that’s the case, with all, I think with high probability you’re now going to decide to return the loan, at least if you can. Is that right? Now notice that the way in which this collateral works there a subtlety to how this collateral works You might think that the way in which collateral works is that now the lender feels safer because even if you end up defaulting on the loan, at least they get this house. All right? And that’s true.

[译文 34]

是啊，每个人都拿到了一栋房子。我猜在座的各位大多数人，我不会环顾房间，因为我不知道这屋子里有多少富二代，但对你们大多数人来说会是什么？是你们父母的房子，对吧？那为什么你们父母的房子被作为抵押品就能阻止你拿着贷款跑路去墨西哥呢？好，让我们来看看这会如何改变收益情况。现在，如果你拿了钱跑路，你跑到墨西哥，但你的结果是一栋房子减一美元，这里一栋房子减三美元。当然我们这里假设你足够喜欢你父母，以至于不在乎我们露宿街头这个事实，但只要情况是这样，只要情况是这样——我认为在大概率下，你现在会决定归还贷款，至少如果你能还的话。对吧？现在注意这个抵押品运作的方式，其中有一个微妙之处。你可能会认为抵押品的运作方式是：现在贷款人感觉更安全了，因为即使你最终违约，他们至少能得到这栋房子。对吧？而这确实是真的。

[段 35]

There’s some truth in that. But that’s really not the key here. Right? Frankly, most bank lenders don’t want your parents’ house. Right? I mean, your parents might have very nice houses, but this isn’t a good housing market right now, and they don’t particularly want to see your parents on the street. The way in which this works is not so much that it gives an extra positive return to the lender, the way in which it works is it gives an extra negative return to the borrower. So let’s just do this backward induction again with the house in place. So with this house in place, as before, you’ll return the loan up here, but now, provided you like your parents enough, you would also return the loan here, because you’d prefer $2 to $3 minus your parents’ house, in which case you’ll get a loan of $3. Alright? So the way in which the collateral worked was by hurting you enough, or in this case hurting your parents enough, in the event of default, All right. So the way in which the collateral worked was by hurting you enough, or in this case hurting your parents enough, in the event of default, in such a way as to change your behavior. But notice, it helps you. So here’s a subtlety coming in here. By issuing collateral, we actually lowered the payoff of the borrower at certain endpoints of the tree.

[译文 35]

这确实有些道理。但这确实不是关键所在。对吧？坦率地说，大多数银行放贷人并不想要你父母的房子。对吧？我的意思是，你父母的房子可能很漂亮，但现在房地产市场不太好，而且他们也不太想看到你父母流落街头。抵押品的作用方式并不是给贷款人带来额外的正向回报，而是给借款人带来额外的负向回报。所以让我们在房子存在的情况下再进行一次逆向归纳。所以在房子存在的情况下，和之前一样，你会在这里偿还贷款，但现在，只要你足够在乎你父母，你也会在这里偿还贷款，因为你宁愿选择$2而不是$3减去你父母的房子，在这种情况下你会获得$3的贷款。好吧？所以抵押品的作用方式是通过在违约的情况下对你造成足够的伤害，或者在这种情况下对你父母造成足够的伤害，好的。所以抵押品的作用方式是通过在违约的情况下对你造成足够的伤害，或者在这种情况下对你父母造成足够的伤害，从而改变你的行为。但请注意，它其实在帮助你。所以这里有一个微妙之处。通过发放抵押品，我们实际上在树的某些末端降低了借款人的收益。

[段 36]

We lowered the payoff of the borrower at certain endpoints of the tree. But as a consequence, we were able to end up at an outcome that was better for the borrower. Sometimes having lower payoffs can actually make you better off. And the reason it makes you better off is it changes the behavior of other players in the game in such a way as it may benefit you. In this example, by… by inducing the lender to give you a bigger loan. All right, so the way the collateral works is it lowers, it lowers your payoffs if you do not repay, but it leads to you being better off. And the reason it makes you better off is it changes. It changes the choices of others, changes the choices of others in a way, in a way that helps you. All right, we’re going to see lots of examples of that in the next couple of days. All right. Now collateral is an example, we talk about and say. design, collateral is also an example or something larger. The larger thing is the idea of commitment. Collateral is a commitment strategy. It’s a commitment strategy. It commits you to repaying the loan. All right. I want to give another example of a commitment strategy. of a commitment strategy. I think this idea of commitment is an important one, and we have just about time to do it.

[译文 36]

我们把借款人在树的某些终点的收益降低了。但这样一来，我们最终得到的结局对借款人更有利。有时候更低的收益实际上会让你更好。其原因是它改变了游戏中其他玩家的行为，使其可能对你有利。在这个例子中，通过……通过促使贷款人给你更大的贷款。好吧，抵押品的作用是降低……如果不清偿，它会降低你的收益，但这会让你更好。其原因是它改变了……它改变了其他人的选择，以一种帮助你的方式改变他们的选择。好吧，接下来几天我们会看到很多这样的例子。好吧。现在抵押品是一个例子，我们讨论并说，设计，抵押品也是一个更大的例子。大一点的概念是承诺。抵押品是一种承诺策略。它是一种承诺策略。它迫使你偿还贷款。好吧。我想再举一个承诺策略的例子。一个承诺策略的例子。我认为承诺这个概念很重要，而且我们刚好有时间做这件事。

[段 37]

So I wanted to go completely away from the context of our lender-borrower game a second and look somewhere else entirely. All right, so we get rid of this for now. I want to take us back to 1066. What happened in 1066? What happened in 1066? What happened in 1066? 1066? I know this is in America and no one gets an education anymore, but what happened in 1066? The Norman conquest took place in 1066, right? So the Norman army invades from Normandy, led by William the Conqueror, and lands on the Sussex Speaches at Hastings. All right? And what I want to imagine is a game involving the Norman army, or William the Conqueror in particular, and the Saxon army. All right, so here’s the little game. So we’re now in the area of medieval military. of medieval military strategy. All right? And here is the game. We’ll start with the Saxons here. The Normans have already invaded. So I guess the Normans have already moved. But here’s the Saxon army making a decision. They’re deciding between fighting and the important medieval military tactic known as running away. And of course the Normans are going to know whether the Saxons are actually going to charge down the beach and attack them, and they are going to have to decide whether to fight or run away. All right?

[译文 37]

所以我想完全脱离我们借贷双方博弈的背景，暂且把目光投向别处。好的，我们先把把它放一边。我想带大家回到1066年。1066年发生了什么？1066年发生了什么？1066年？我知道这是在美国，没人再受什么教育了，但1066年发生了什么？诺曼征服发生在1066年，对吧？于是诺曼军队在William the Conqueror的带领下从诺曼底入侵，在黑斯廷斯的Sussex海滩登陆。好吧？我想让大家想象一个涉及诺曼军队，或者说William the Conqueror本人，和撒克逊军队的博弈。好，这里有一个小游戏。我们现在处于中世纪军事的范畴，中世纪军事战略的范畴。好，来看这个博弈。我们先从撒克逊人开始。诺曼人已经入侵了。我想诺曼人已经移动了。但是撒克逊军队正在做决策。他们在战斗和被称为逃跑的重要的中世纪军事战术之间做出选择。当然，诺曼人将知道撒克逊人是否会冲下海滩进攻他们，他们也将不得不决定是战斗还是逃跑。好吧？

[段 38]

And let’s put the payoffs in. Now leave some space below here. Leave some space down here on your notes. All right? Let’s put the payoffs in. So I’m going to put the Norman payoffs first and the Saxon payoffs second. Okay? Norman payoffs first, Saxon payoffs. Saxon payoff second. So the payoffs are going to be like this. If both sides fight, a lot of people end up dead and we’ll call that 0-0. If the Saxons fight and the Normans run away, the Saxons get two and the Normans get one, because at least they’re alive. If the Saxons run away and the Normans fight, then the Normans get two and the Saxons get one, just flip things around. And if both lots run away, then ultimately it’s good for the Saxons. All right, so this is the game. All right, let’s be careful. I’ve put the Saxon payoff. second. The Saxon payoff second. If we analyze this game by backward induction, we can see that the Normans are in trouble. Why are the Normans in trouble? Because if they are attacked by the Saxons, then fighting yields zero and running away yields 1, so they’re going to run away. And conversely, if the Saxons run away, then in fact the Normans will stay and fight, because it’s easy to stay in fight against people are running away.

[译文 38]

接下来我们把收益放进去。请在下面留点空间。在你的笔记下面留点空间。好吧？把收益放进去。我先写诺曼人的收益，然后再写撒克逊人的收益。好的，诺曼人收益在前，撒克逊人收益在后。收益如下：如果双方都战斗，很多人会死亡，我们记为0-0。如果撒克逊人战斗而诺曼人逃跑，撒克逊人得到2，诺曼人得到1，因为他们至少还活着。如果撒克逊人逃跑而诺曼人战斗，那么诺曼人得到2，撒克逊人得到1，正好反过来。如果双方都逃跑，那最终对撒克逊人有利。好，这就是这个博弈。好，注意一下。我把撒克逊人的收益放在了后面。撒克逊人的收益在后面。如果我们用逆向归纳来分析这个博弈，我们可以看到诺曼人处于困境。为什么诺曼人会有麻烦？因为如果撒克逊人进攻他们，战斗得到的收益是0，而逃跑得到的收益是1，所以他们会选择逃跑。相反，如果撒克逊人逃跑，那么诺曼人实际上会留下来战斗，因为对付正在逃跑的人留下来战斗很容易。

[段 39]

Even I can do that. All right? So they’re going to go for two rather than one. But now the Saxons face this choice. They know that if they attack the Normans, the Normans will run away and the Saxons will get two. But if the Saxons run away, then the Normans will stay and fight, and the Saxons will only get one. So the Saxons are going to end up fighting. All right. Everyone see how we did the back on induction? So this is not a good situation if you happen to be the Norman commander, if you’re the guy who led these troops across the channel. All right? So what did William the Conqueror do? He burnt his ships, right? So let’s now make this game a bit more like the real historical situation. Here’s a move that William the Conqueror, the King of the Normans, can do. He can either not burn his chips or he can burn them. If he burns them, then the game is rather different. Once again, the Saxons can decide whether to fight or run away, but now the Normans really don’t have any choice. They have to stay and fight because swimming back to France wearing armour is difficult. All right. So the person, payoffs become 0-0 and 2-1 as before. All right. So we know now that the Normans are going to stay and fight.

[译文 39]

连我都能做到。好吧？所以他们会争取2而不是1。但现在撒克逊人面临这个选择。他们知道如果他们进攻诺曼人，诺曼人会逃跑，撒克逊人得到2。但如果撒克逊人逃跑，那么诺曼人会留下来战斗，撒克逊人只能得到1。因此撒克逊人最终会选择战斗。好。大家看到我们是怎么做逆向归纳的了吧？如果你是诺曼指挥官，如果你恰好是率领部队渡过海峡的那个人，这可不是什么好情况。好吧？那么William the Conqueror做了什么？他烧了自己的船，对吧？让我们把这个博弈变得更接近真实的历史情境。William the Conqueror，诺曼人的国王，可以做这样一个举动。他可以烧船，也可以不烧。如果他烧了船，博弈就会大不一样。再一次，撒克逊人可以选择战斗或逃跑，但现在诺曼人真的没有选择了。他们必须留下来战斗，因为穿着盔甲游回法国是很难的。好吧？所以收益变成0-0和2-1，和之前一样。好吧？所以我们现在知道诺曼人会留下来战斗。

[段 40]

That’s all that’s available to them. I put it that they didn’t even have the option of running away. If you want, you could put running away yields them, you know, minus infinity or whatever it is to get drowned. All right? So now, if the Saxons, if the Normans have burnt the boats, the Saxons know that if they fight, the Saxons will get zero. If they’re not. run away, they’ll get minus one. So now they’ll run away. And then from William the Conqueror’s point of view, what’s he choosing between? He knows that if he doesn’t burn his boats, the Saxons will fight and his troops will run away. But if he does burn his boats, the Saxons will run away and his troops will fight, so he wants to burn his boats. All right, everyone okay with example? All right. Now this is probably probably, the classic example of a commitment strategy. William the Conqueror in this example, or Cortez, and perhaps the more famous example, burn the boats to get rid of some strategies, to get rid of some choices altogether, and you might think, how can getting rid of choices make me better off? And the reason in a game, particularly in a sequential game, but in the game generally, the reason getting rid of choices can make me better off. is it changes the behavior of people on the other side of the game in such a way as benefits me.

[译文 40]

这就是他们所能做的一切。我说他们甚至没有逃跑的选择。如果你愿意，你可以把逃跑的收益设为负无穷或什么的，让他们被淹死。好吧？如果诺曼人已经烧了船，撒克逊人知道如果他们战斗，撒克逊人会得到0。如果他们不逃跑，他们将得到负1。于是他们会逃跑。然后从William the Conqueror的角度来看，他在选择什么？他知道如果不烧船，撒克逊人会战斗，他的部队会逃跑。但如果他烧了船，撒克逊人会逃跑，他的部队会战斗，所以他想烧船。好，大家对这个例子还有问题吗？好吧。这大概是一个经典的承诺策略的例子。在这个例子中，William the Conqueror，或者Cortez，还有更著名的例子——烧船来消除某些策略，消除某些选择——你可能会想，删除选择怎么能让我过得更好？在博弈中，特别是在序贯博弈中，但一般而言，删除选择能让我更好的原因在于它改变了游戏另一方的行为，使其有利于我。

[段 41]

In this particular example, it makes the other side less likely to fight. All right. So once again, this is a commitment. It’s a commitment. And the way it works is, this example of a commitment is actually to have fewer options. have fewer options, and it changes the behavior of others. If it didn’t change the behavior of others, it wouldn’t be worth doing. All right. So let’s just talk about this a little bit more. There’s another famous example of a military commitment strategy that occurs in the military commitment strategy. movie Dr. Strangelove. How many of you’ve seen the movie Dr. Strange Love? How many have not seen the movie Dr. Strange Love? All right. Good homework exercise for the weekend. Rent the movie Dr. Stranglove. Great. It’s very good movie. All right. So in Dr. Stranglove, there’s a famous commitment strategy. There’s a famous commitment strategy in Dr. Stranglove. What is the famous commitment strategy in Dr. Stranglove? Somebody. Let me get a mic down here. There’s one on the way. There’s a guy in White. There you go. There you go. There you go. Great. Mike, Ali, can we get a mic down here? There’s one on the way. There’s a guy in white. There you go. There you go. There you go. Great. They lose radio contact with the base, which means that they’re going to end up dropping the bomb.

[译文 41]

在这个例子中，它使对方更不可能战斗。好吧。所以再一次，这是一个承诺。这是一个承诺。它的运作方式实际上是拥有更少的选择。拥有更少的选择，并改变他人的行为。如果它没有改变他人的行为，那就不值得做。好吧。让我们再稍微谈谈这一点。还有另一个著名的军事承诺策略的例子，出现在军事承诺策略电影Dr. Strangelove中。你们有多少人看过电影Dr. Strangelove？有多少人没看过电影Dr. Strangelove？好吧。周末的好作业。去租电影Dr. Strangelove。很好。这是一部非常好的电影。好吧。所以在Dr. Strangelove中有一个著名的承诺策略。在Dr. Strangelove中有一个著名的承诺策略。Dr. Strangelove中著名的承诺策略是什么？有人吗？让我把麦克风递过去。马上有人过去。有一位穿白衣服的人。来吧。来吧。来吧。好。Mike，Ali，我们能把麦克风递过去吗？马上有人过去。有一位穿白衣服的人。来吧。来吧。来吧。好。他们失去了与基地的无线电联络，这意味着他们最终会投下炸弹。

[段 42]

All right, that’s true. I was thinking more deliberate. What’s the more deliberate? The guy in red. Ah, wow. There’s somebody in red here. Here we go. The Soviets construct a doomsday device, so if they’re attacked, they automatically launch all of their nuclear weapons. Good. Good. So the worry that the Soviets have is they think the Americans might attack them, and they worry that the Americans might attack them thinking that they won’t retaliate, because they won’t really have any incentive to retaliate once their cities are destroyed. So they construct a device they call the Doomsday device that will automatically launch nuclear missiles back on the Americans if the Russians are attacked. All right, it’s a commitment. It’s a commitment device to make it credible that they will actually respond, were they to be attacked? by the crazy Americans. All right? So there’s a mistake, however, that the Russians make. What is the mistake that the Russians make? What’s the mistake the Russians make? There’s the guy in the Yale sweatshirt here. They don’t tell anyone about the machine. Right. They don’t tell the Americans that they’ve built the doomsday device. All right. So this is really an important idea hidden in what’s really a great movie. Commitment strategies are a good idea. strategies are a good idea, they can make things credible, but the only reason that having fewer strategies is good for you is because it changes the behavior on the other side.

[译文 42]

好吧，确实如此。我在想更刻意的做法。更刻意的是什么？穿红衣服的人。啊，哇。这里有个人穿红色。我们来看看。苏联人建造了一个Doomsday device，这样如果他们受到攻击，他们会自动发射全部核武器。好。好的。所以苏联人的担忧是他们认为美国人可能会攻击他们，他们担心美国人可能会认为他们不会报复，因为他们一旦城市被毁就真的没有任何动机去报复。于是他们建造了一个叫做Doomsday device的设备，如果俄罗斯人受到攻击，它会自动向美国人发射核导弹。好吧，这是一个承诺。这是一个承诺装置，使人们相信他们真的会在受到疯狂美国人攻击时进行报复。好吧？然而，俄国人犯了一个错误。俄国人的错误是什么？俄国人的错误是什么？这里有一位穿Yale运动衫的人。他们没有告诉任何人关于这台机器的事。对。他们没有告诉美国人他们已经建造了Doomsday device。好吧。这真的是藏在一部真正伟大电影里的一个重要想法。承诺策略是个好主意。承诺策略是个好主意，它们可以让事情变得可信，但拥有更少策略对你有利的唯一原因在于它改变了另一方的行为。

[段 43]

In this case, it changes the behavior of the Saxons. It doesn’t work if the other side doesn’t know about it. It’s crucial that the other side knows. So the other players must must know just to hammer this home notice that the expression in the English language is burning your boats it’s not going over to your boats and quietly drilling a little hole in them right it’s burning your boats you want the other side to see this big bonfire on the beach and to know that the boats are no longer available right? just as in Dr. Strangelove, it’s crucial, and it’s a terrible mistake for the Russians not to tell the Americans that they’ve built this machine. All right. So knowledge here is crucial, knowledge of the other side. Now I should just complete the history of this. This didn’t work in the case of the Battle of Hastings. The Saxons attacked anyway, and it just turned, you know, there was a big bloodbath, and the Normans really only won this battle because somebody got a lucky shot and hit King Harold and the eye. So actually, this is a good story, but didn’t they? As a military tactic, not actually a true story. I’m adding that in, because otherwise I’m going to get hundreds of letters from people who watch the video. Alright, now we’ve had a bunch of lessons today, but I’m not done.

[译文 43]

在这个案例中，它改变了撒克逊人的行为。如果对方不知道这件事，那就不会起作用。对方必须知道这一点至关重要。所以其他玩家必须知道——我只想强调这一点——请注意英语中的表达是"烧掉你的船"，而不是偷偷溜到你的船上去在船上钻个小洞，对吧？是烧掉你的船，你希望对方看到海滩上那堆大火，知道船已经不再可用了，对吧？就像《奇爱博士》里一样，至关重要的是，俄国人没有告诉美国人他们建造了这台机器，这是一个可怕的错误。好的。所以知识在这里至关重要，对对方的了解。现在我应该把这段历史讲完。在黑斯廷斯战役中，这招没有奏效。撒克逊人还是发动了进攻，结果你知道，发生了大屠杀，诺曼人之所以赢得这场战役只是因为有人运气好，射中了哈罗德国王的眼睛。所以实际上，这是一个好故事，但实际上并非如此。作为军事策略，这不是真实的故事。我加上这句话，否则我会收到数百封看过视频的人写来的信。好吧，今天我们已经讲了很多课，但我还没讲完。

[段 44]

I want to play one more game. Before I do, though, I want to make sure we understand it. We’re going to play another game, so everybody’s say put. I want to make sure that there’s a bunch of lessons on the board, and I want you to understand what’s important and what’s more important. Everything’s important, but some things are more important. So the idea of commitment is an important idea. idea and the idea of incentive design is an important idea, but there’s one idea here that is more important than anything else. And that idea is backward induction. I’ll put a little sun around it, okay? How important is backward induction? Backward induction? Backward induction is the most important thing I’m going to teach you in the second half of the semester. the semester. It’s probably the most important thing I’m going to teach you in the whole semester, and it may be the most important thing you’re going to learn at Yale. All right? It’s the answer to all questions. If I’m asked you a question, and as happens from time to time, you’ve been sleeping in class, and you wake up, startled, because I’ve now asked you a question, and that camera is on you, right, and you don’t know what the question is, then the answer is backward induction. Alright? I’m stressing this because six weeks from now, whatever it is, six weeks from now, whatever it is, in December, there’s going to be a final exam, and I guarantee now that there will be a question on the final exam that involves backward induction, and I guarantee that at least one person in the room will forget to solve it by backward induction.

[译文 44]

我想再玩一个游戏。不过在此之前，我想确保我们理解这个游戏。我们要再玩一个游戏，所以大家都在说"put"。我想确保黑板上有一堆经验教训，我希望你们理解什么是重要的，什么是更重要的。一切都重要，但有些事情更重要。所以承诺的理念是一个重要的理念。激励机制设计的理念是一个重要的理念，但这里有一个理念比任何其他事情都更重要。这个理念就是后向归纳。我会在它周围画个小太阳，好吗？后向归纳有多重要？后向归纳？后向归纳是我这学期下半场要教给你们的最重要的东西。整个学期我要教给你们的最重要的东西可能就是它，它可能是你们在耶鲁学到的最重要的东西。好的？它是所有问题的答案。如果我问你一个问题，而你像不时发生的那样，一直在课上睡觉，突然惊醒过来，因为我现在问你问题，摄像机正对着你，对吧，你不知道问题是什么，那么答案就是后向归纳。好的？我强调这一点是因为六周后，不管是什么，六周后，十二月，会有期末考试，我现在向你们保证，期末考试一定会有一道涉及后向归纳的题目，而且我保证房间里至少会有一个人忘记用后向归纳来解答。

[段 45]

All right, so are you going to use backward induction on the final exam? Yes, you’re all going to remember it? Okay, okay, good. Now we’ll play one more game, just for fun. All right. Oh, before we play one more game, I’ll do one other thing. Sorry, one other thing before we play one more game. I apologize. I apologize. The one thing I want to do here is I put up a tree here, but I forgot to tell you anything about the tree. one more game, I apologize. The one thing I want to do here is I put up a tree here, but I forgot to tell you anything about the tree. This was a tree, and I would be remiss if I didn’t tell you a few things about trees. So there’s a certain amount of jargon that goes along with trees, and I want you to go read the textbook and know what that jargon is. So these spots, these dots in the tree, these things are called nodes. All right, they’re called nodes. And in fact, the end points of the tree, where the payoffs are, these are also called nodes, but they’re called end nodes. All right, and these branches in the tree, the branches, here they are, the branches are called edges. All right, so a tree consists of nodes, edges, and these missing dots. missing dots are the end nodes.

[译文 45]

好的，你们期末考试会用后向归纳吗？是的，你们都会记得吗？好的，好的，很好。现在我们再玩一个游戏，只是为了好玩。好的。哦，在我们再玩一个游戏之前，我会做另一件事。对不起，在我们再玩一个游戏之前还有一件事。对不起，对不起。我想在这里做的一件事是我放了一棵树在这里，但我忘记告诉你们任何关于这棵树的事情了。再玩一个游戏，我道歉。我想在这里做的一件事是我放了一棵树在这里，但我忘记告诉你们任何关于这棵树的事情。这是一棵树，如果我不告诉你们一些关于树的事情，那就是我的失职。所以树有一些特定的术语，我想让你们去读教科书，知道那些术语是什么。所以这些点，树上的这些点，这些东西叫做节点。好的，它们叫做节点。事实上，树的端点，也就是显示收益的地方，这些也叫作节点，但它们叫做终端节点。好的，树上的这些分支，这些分支在这里，它们叫做边。好的，所以一棵树由节点、边和这些缺失的点组成。缺失的点是终端节点。

[段 46]

The end nodes are associated with payoffs. Do we need to write that? That’s obvious, right? They’re said it with payoffs. And every other node belongs to somebody whose turn it is to make a decision at that node. All right? So these other nodes, the ones that on end nodes, are called decision nodes. And it’s perfectly possible, for example, in our Norman Conquest game, for somebody to have several nodes. somebody could move once, and then later on the game. There may also be noted that it never reached in a game. One last piece of jargon, a root through a tree from the beginning to an end, is called a path. A path. A way of getting through the tree from the beginning to the end. So we’ll have a pop quiz on that jargon later, and now let’s play the last game I want to play. We’ve got ten minutes, right? Okay, everyone understand the jargon. I want to play a game now, all right? So the game we’re going to play is a game we’re going to call The Hungry Lion game. All right? It’s the Hungry Lion game. And what I’m going to do is I’m going to pick on a row of the class. Actually, I’m going to pick on this row of the class. All right. And this row of the class, everyone can see this row.

[译文 46]

终端节点与收益相关联。我们需要写下来吗？那很明显，对吧？它们带有收益。每个其他节点都属于某个人，这个人的回合是在那个节点做决定。好的？所以这些其他节点，不是终端节点的叫做决策节点。而且完全有可能，例如在我们的诺曼征服游戏中，某个人可能有多个节点。某个人可以先走一步，然后游戏继续。后来可能还有一些节点永远不会被达到。还有最后一个术语，从头到尾穿过一棵树的一条路径叫做路径。路径。从头到尾穿过树的一种方式。所以我们之后会对这些术语进行突击测验，现在让我们玩我想玩的最后一个游戏。我们还有十分钟，对吧？好的，每个人都理解这些术语了吧？我现在想玩一个游戏，好的？我们将要玩的游戏叫做"饥饿的狮子"游戏。好的？是"饥饿的狮子"游戏。我要做的是我会选教室里一排人。实际上，我会选教室里的这一排。好的。这一排的同学，大家都能看到这一排。

[段 47]

From up there, you can lean over the balcony. This row of the class, we’re going to imagine that everybody in this row is a lion. All right? They all look like a lion. Not much, but no minute. Pretend they’re lions, right? Suspension of disbelief. All right. They’re all lions and they’re all hungry. Except for one person, who’s this guy at the end, whose name is Alex. So Alex is a sheep. Alex has the misfortune of wandering into this pack of pride of pride of lions and is liable to get eaten because they’re hungry. However, one thing stands between Alex, Alex the sheep and being eaten. The one thing that stands between him and being eaten is that in lion society, the only lion who is allowed to eat the sheep is the head lion. The big lion whose name is Ryan. Ryan is the head lion here. Only Ryan can eat Alex the sheep. No other lion can eat Alex the sheep. All right. Now there’s a catch if Ryan eats Alex, if Ryan the lion eats Alex the sheep. The catch is that if Ryan the lion eats Alex the sheep, then Ryan the lion will fall into a post-perennial stupor, fall asleep, at which point the second largest lion whose name is Chris, Chris, can eat Ryan. And notice, Chris can never eat the sheep.

[译文 47]

从上面那里，你可以探过阳台看。这一排的同学，我们想象这排的每个人都是一头狮子。好的？他们看起来都像狮子。不太像，但假装他们是狮子，对吧？ suspend disbelief。好的。他们都是狮子，而且都很饿。除了一个人，就是坐在最边上的这家伙，他的名字叫Alex。所以Alex是一只羊。Alex不幸误入了这群狮子，可能会被吃掉，因为他们很饿。然而，有一件事挡在Alex这只羊和被吃掉之间。挡在他和被吃掉之间的一件事是，在狮子的社会里，唯一被允许吃掉这只羊的狮子是头领狮子。那只大狮子，他的名字叫Ryan。Ryan是这里的头领狮子。只有Ryan可以吃掉Alex这只羊。其他的狮子都不能吃掉Alex这只羊。好的。现在有一个条件，如果Ryan吃掉Alex，如果Ryan这只狮子吃掉Alex这只羊的话。条件就是，如果Ryan这只狮子吃掉Alex这只羊，那么Ryan这只狮子就会陷入一种持久的昏睡状态，睡着了，届时第二大的狮子，他的名字叫Chris，Chris可以吃掉Ryan。请注意，Chris永远不能吃掉那只羊。

[段 48]

He can only ever eat the lion, the big lion, and only then if the lion is eating the sheep and falls asleep. This is very strict, right? Lion society is very hierarchical like England. All right? Right? If, however, Ryan the lion eats Alex the sheep and is then eaten, forced the sheep and is then eaten by Chris the Lion, then, and only then, he will fall into a stupor at which point he can be eaten by… Isabella. Isabella. Who’s the third largest line and so on. Ever understand the game? No questions, no talking among yourselves. write down what you would do if you were our key decision maker who is Ryan the Lion. Well, before we write it down, can I get Alex to stand up a second? Stand up? All right, the camera on him, right? This is the menu. All right, thank you. All right, all right, all right. Okay, so you have to write down in your notepad whether you, Ryan the Lion, in Ryan’s shoes or paws or whatever, whether you would eat Alex the Sheep. Everyone written something down? All right, now let’s ask Ryan the Lion what he’s going to do. So Ryan, are you going to eat Alex? the sheep? No. He says, no, he’s not going to eat. Why not? Well, because then I’d be… Shout out, shout out.

[译文 48]

他只能吃掉狮子，那只大狮子，而且只有在那只狮子吃掉羊然后睡着的情况下才能吃掉。这非常严格，对吧？狮子社会像英格兰一样等级森严。好的？如果是这样，然而，Ryan这只狮子吃掉Alex这只羊，然后被Chris这只狮子吃掉，然后，而且只有在那时，他才会陷入昏睡状态，届时他可以被……Isabella吃掉。Isabella。第三大的狮子，以此类推。大家都理解这个游戏了吗？没问题，你们之间不要交流。写下如果你是我们关键决策者Ryan这只狮子，你会怎么做。嗯，在我们写下来之前，我能请Alex站起来一下吗？站起来？好的，摄像机对着他，对吧？这是菜单。好的，谢谢。好的，好的，好的。好的，所以你必须在笔记本上写下你，作为Ryan这只狮子，站在Ryan的立场或爪子或其他什么，你会吃掉Alex这只羊吗？每个人都写了点什么吗？好的，现在让我们问问Ryan这只狮子他要做什么。Ryan，你会吃掉Alex这只羊吗？不。他说，不，他不会吃。为什么不？因为那样的话我会……大声说出来，大声说出来。

[段 49]

Then I’d be eaten as well. Then he’d be eaten. Well, let’s see if he would have been eaten. So had he eaten Alex the sheep, then he would have fallen asleep, and then he’d have been in danger of being eaten by Chris. Chris, would you have eaten Ryan? No. Ah, so he wouldn’t have eaten him, in fact. In fact, it looks like Ryan would have got a free lunch, right? There are no free lunches of economics, something’s wrong. All right, all right. And why is Chris worried about it? Chris is worried about it because Chris is worried about Isabella eating him. And what am I doing wrong? What’s wrong with this analysis? By the way, before we say what’s wrong, how many of you in Ryan’s shoes would have eaten the sheep? And how many of you would not have eaten the sheep? Okay, what am I doing wrong? I’m in totally the wrong part of the room. I shouldn’t be here at all, right? I shouldn’t be at all in this part of the classroom. I can’t get round. Wait a second. Excuse me? All right. I should be, which row was my lions? Where’s my lion row? I’m here. I should be way over here with the baby lion whose name is… Ege. So Ege is a little baby lion, very cute. But Ege, if he gets a chance to eat, it’s going to eat.

[译文 49]

那我也会被吃掉。那他就会被吃掉。好的，让我们看看他是否会被吃掉。所以如果他吃了Alex这只羊，他就会睡着，然后他就有被Chris吃掉的危险。Chris，你会吃掉Ryan吗？不会。啊，所以实际上他不会吃掉他。实际上，看起来Ryan会得到一顿免费的午餐，对吧？经济学中没有免费的午餐，肯定哪里出问题了。好了好了。那为什么Chris担心这件事？Chris担心这件事是因为Chris担心Isabella吃掉他。那我哪里做错了？这个分析有什么问题？顺便说一句，在我们说哪里做错之前，如果你是Ryan，你会吃掉那只羊吗？你们中有多少人会吃掉那只羊？有多少人不会吃掉那只羊？好的，我哪里做错了？我完全站错位置了。我根本不该在这里，对吧？我完全不该在教室的这个位置。我过不去。等一下。不好意思？好吧。我应该在，狮子那一排是哪一排？我的狮子排在哪里？我在这里。我应该在那边的位置，和那只叫……Ege的小狮子在一起。所以Ege是一只小狮子，非常可爱。但如果Ege有机会吃东西，它就会吃掉。

[段 50]

Why is he going to eat? Why is he going to eat? Because there’s no one to eat him. All right. So if Ege gets to eat. a chance to eat the second babyest lion whose name is John. John, then Ege will eat. All right? So if John gets a chance to eat Ben. Ben, is John going to eat Ben? John, are you going to eat Ben? No. No, John’s not going to eat Ben because John knows he’ll get eaten by Egey. So Ben, if you get a chance to eat… Vida. Vida, are you going to eat Vida? Are you going to eat Voder? Wait a second. Wait a second. So we just argue that if you eat, then the second largest lion whose name was… John. John is not going to eat you. Yes, okay. So we know the littlest lion is going to eat. So the second littlest lion is not going to eat. So the third little lion can eat safely. So the fourth little lion should not eat. Right? So the fifth little lion should eat. We’ve got eat, not eat, eat, eat, eat, not eat, eat, eat, not eat, eat, eat, not eat, eat, not eat, eat, not eat, eat, not eat, eat. Is that right? Is that right? So in fact, he should have eaten him. But the more important point is, how should we have analysed this game?

[译文 50]

他为什么要吃？他为什么要吃？因为没有人能吃掉他。好吧，所以如果Ege有机会吃第二小的狮子，它的名字是John。那么Ege就会吃。好吧？所以如果John有机会吃Ben。Ben，John会吃Ben吗？John，你会吃Ben吗？不。不，John不会吃Ben，因为John知道自己会被Egey吃掉。所以Ben，如果你有机会吃……Vida。Vida，你会吃Vida吗？你会吃Voder吗？等一下。等一下。所以我们论证的是，如果你吃了，那么第二大的狮子……John。John不会吃你。是的，好的。所以我们知道最小的狮子会吃。所以第二小的狮子不会吃。所以第三小的狮子可以安全地吃。所以第四小的狮子不应该吃。对吧？所以第五小的狮子应该吃。我们有吃、不吃、吃、吃、吃、不吃、吃、吃、不吃、吃、吃、不吃、吃、不吃、吃、不吃、吃、不吃、吃。对吗？对吗？所以实际上，他应该吃掉他的。但更重要的一点是，我们应该如何分析这个游戏？

[段 51]

What should we have used? Backward induction. How many of you used backward induction? Be honest. So what’s the point here? The point is this. Five minutes ago, I said the most important thing you’ll ever learn at Yale is backward induction. Then I distracted you with some fairly irrelevant nonsense. And five minutes later, nobody used backwood. induction. So the main lesson from today, the lesson we’re going to pick up on Wednesday, is to use something. What are we going to use? All right, we’ll see you on Wednesday.

[译文 51]

我们应该用什么？逆向归纳法。你们有多少人用了逆向归纳法？诚实回答。那么重点是什么？重点是这样的。五分钟前，我说你们在耶鲁学到的最重要的东西是逆向归纳法。然后我用一些相当无关紧要的废话分散了你们的注意力。五分钟后，没有人用逆向归纳法。所以今天的主要教训，我们周三要继续讨论的教训，就是用一些东西。我们要用什么？好的，我们周三见。