耶鲁大学博弈论公开课 - 第3集 拍卖和获奖者的诅咒

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]

Where have my jars of coins got to? That isn’t very far. They’ve only been along one row. All right, we’ll whiz them along this row as fast as you can. Just shake and pass now. Everybody who has had access to those jars, can you please write down on your notebook, just write down, but don’t show it to your neighbor, write down for each of those two jars how many coins you think are in the small jar and how many coins you think are in the large jar. How many coins you think are in the small jar and how many coins you think are in the large jar. Keep passing it along. So today I want to talk about auctions. And just to put this in the context of the whole class, way back on the very first day the class we talked about different types of people playing games. We talked about evil gits versus indignant angels. And then for most of the course, really until this week, we’ve been assuming that you knew who it was you were playing You knew your own payoffs but you also knew who it was you were playing against or with But the new feature of this week has been that we looking at settings where you don’t necessarily know what are the payoffs of the other people involved in the game or strategic situation.

[译文 1]

我的硬币罐到哪里了？那不是很远。它们才刚经过一行。好吧，我们把它们沿着这一行尽可能快地传过去。现在开始摇晃传递。每个人接触过那些罐子的，请在你的笔记本上写下，不要给你的邻居看，写下这两个罐子中你认为小罐子里有多少硬币，大罐子里有多少硬币。继续传递。今天我想谈谈拍卖。把这放在整个课程的背景下回想，课程开始的第一天我们讨论了玩游戏的不同类型的人。我们讨论了邪恶的家伙与愤慨的天使。在课程的绝大部分时间里，实际上直到本周，我们都假设你知道你在和谁玩游戏。你知道自己的收益，但也知道你在和谁对抗或合作。但本周的新特点是，我们正在审视你可能不知道游戏中其他人的收益或策略情况的环境。

[段 2]

So in the signaling model we looked at last time, the different types of worker had different types of payoffs from going to get an MBA, from going to business school, and they yielded different payoffs to you if you hired them. So we had to model the game where you didn’t quite know the payoffs of the people you were playing against. And similarly, an auction, which is what we’re going to study today, is such a setting. Typically, in an auction, you are competing or playing with or against the other bidders. But typically, you don’t know something crucial about those other bidders. You don’t know how much they value the good in question. Typically, there’s a good up for sale, and you don’t know how much they value that good. So I want to start off by thinking about a little bit of this informational structure of auctions, And then we get into more detail as we go along And the first thing I want to distinguish are two extremes At one extreme I want to talk about common values And at the other extreme, I want to talk about private values. So the idea of a common value auction is that the good that is for sale ultimately has the same value for whoever buys it. Now that doesn’t mean they’re all going to be prepared to bid the same amount because they may not know what that value is.

[译文 2]

所以在我们上次看的信号模型中，不同类型的工人从攻读MBA、从读商学院中获得了不同类型的收益，如果你雇用他们，他们也会给你带来不同的收益。所以我们必须建模这样的游戏：你并不完全了解对手的收益。同样，我们今天要研究的拍卖就是这样一种情况。通常，在拍卖中，你在与其他竞拍者竞争或博弈。但通常，你不了解这些竞拍者的某些关键信息。你不知道他们对标的物的估价。通常，有一件待售商品，而你不知道他们对那件商品的估价程度。我想首先思考一下拍卖的信息结构，然后我们会逐渐深入细节。首先我想区分两个极端情况。一个极端是共同价值，另一个极端是私人价值。共同价值拍卖的理念是，待售商品对购买者来说最终具有相同的价值。但这并不意味着他们都准备出相同的金额，因为他们可能不知道那个价值是多少。

[段 3]

For example, imagine there’s an oil well. So there’s an oil well out there, there’s an oil reserve out there, and different companies are trying to estimate how much they want to bid for the right to draw oil out of this oil field. Each of them is going to make a little practice well and get some estimate of how much oil there is in the well. So they’re going to bid different amounts. But at the end of the day, what comes out of that well is the same for everybody. There is just one amount of oil in that well, and that oil is just worth one amount at the market price. So that a classic example of a common value auction The value of the good for sale the true value if you like is the same for all. And we’ll use the notation V to denote this common value that this object has. Now the other extreme is private value. And it’s really such an extreme it’s hard to think of good examples, but the idea is that the value of the good at hand is not only is it different for everybody, but my valuation of this good has no bearing whatsoever on your value for the good, and your value for the good has no bearing whatsoever on my value for the good.

[译文 3]

例如，假设有一口油井。那里有一口油井，有一片石油储备，不同的公司正试图估计他们愿意为开采权出价多少。他们每一方都会打一口试验井，获得对油井储量的一些估计。所以他们会出不同的金额。但最终，那口井产出的是相同的。只有一定量的石油在井里，而且那个石油在市场价格上只值一个金额。这是一个共同价值拍卖的经典例子。待售商品的价值——如果你愿意这样说的话是真实价值——对所有人都是相同的。我们用符号V来表示这个对象的共同价值。另一个极端是私人价值。这确实是一个很难想到好例子的极端情况，但理念是，手头商品的价值不仅对每个人都是不同的，而且我对这个商品的估价与你的估价完全无关，你对商品的估价也与我的估价完全无关。

[段 4]

So here’s a case where the value of the good, the ultimate value of the good in question, not only is it different for all, not only is it different for all, but moreover it’s completely idiosyncratic. And my value is irrelevant to you. Thank you. A value is irrelevant to you. So if you happen to buy this good, and you learn that, in fact, I valued a lot, that makes no difference to how happy you feel at having bought the good. Now, these are extremes, and most of reality lies between. I should give you a notation. let’s use V sub i to be the private values where i denotes the player in question. These are extremes and most things lie in between. So we already mentioned that on this extreme, close to this extreme, you could think about the oil wells. Oil wells are pretty much common value goods. There’s a certain amount of oil there and that’s all there is to it. However, even there, You could imagine that the different firms have different costs on extracting that oil, or these different firms have their machinery occupied to different extents in other wells that they’re digging. So even in that pure case seemingly perfect example of a common value it probably isn literally a common value Or these different firms have different distances between the wells and their refineries So the oil well is a good example of something that’s close to common value, but it isn’t really literally common value, probably in reality.

[译文 4]

所以这里有一种情况，商品的价值，标的物的最终价值，不仅对所有人都是不同的，不仅对所有人都是不同的，而且更重要的是，它是完全独特的。我的估价与你无关。谢谢你。估价与你无关。所以如果你碰巧买了这个商品，而你发现事实上我很重视它，这对你购买商品的幸福感毫无影响。现在，这些都是极端情况，而现实中的大多数事物介于两者之间。我应该给你们一个符号。让我用V下标i来表示私人价值，其中i表示相关参与者。这些是极端情况，大多数事物介于两者之间。我们已经提到过，在这个极端附近，接近这个极端，你可以想到油田。油田几乎是共同价值商品。那里有一定量的石油，仅此而已。然而，即使在那里，你也可以想象不同的公司在提取石油方面有不同的成本，或者这些公司在他们正在挖掘的其他油井上以不同的程度占用了他们的设备。所以即使在这个看似完美的共同价值的纯粹案例中，它可能并非字面上的共同价值。或者这些不同的公司在油井和炼油厂之间有不同的距离。所以油田是一个接近共同价值的好例子，但实际上可能并非字面上的共同价值。

[段 5]

One’s tempted to say that homes are private value. After all, my valuation, my happiness from living in my house, is not really affected by how happy you would feel living in my house. I don’t really care if you would like to live in my house or if you wouldn’t like to live in my house because I’m the person living in it. Is that right? But there’s a catch here. What’s the catch which makes homes not literally private value? What’s the catch? The catch is that at some point in time, I may want to resell my home. The home is a durable good. It’s a consumption good, my living in it. That’s a private value. But it’s also an investment good. I’m going to want to resell that home at some point when I’m kicked out of Yale or whatever. And then at that point which I sell it, I’m going to care a lot about how much you value it because that’s going to affect the price that I’m going to get at the end of the day So in the case of a home it somewhere between a private value and a common value It true that the consumption part might be private value but the investment component introduces common values So really for private values, for pure private values, we need to think about pure consumption goods.

[译文 5]

人们可能会说房屋是私人价值。毕竟，我对我住在房子里的幸福感，不会真正受到你住在我房子里会有多开心的影响。我真的不在乎你是否想住在我的房子里，或者你不想住在我的房子里，因为我是住在里面的人。对吗？但这里有一个陷阱。什么陷阱使得房屋并非字面上的私人价值？什么陷阱？陷阱是，在某个时候，我可能想转售我的房子。房屋是一种耐用品。它是一种消费品，我住在里面是私人价值。但它也是一种投资品。当我被赶出耶鲁大学或其他原因时，我想在某个时候转售那套房子。然后在我卖掉它的时候，我会非常关心你对它的估价，因为这将影响我最终能得到的价格。所以在房子的情况下，它介于私人价值和共同价值之间。消费部分可能是私人价值，这是真的，但投资成分引入了共同价值。所以对于私人价值，对于纯粹的私人价值，我们需要考虑纯粹的消费品。

[段 6]

Goods that I consume, they have no investment value, they have no resale value. So think about some good being sold on eBay. It’s a cake, say. It’s a cake. So if I buy it, once I’ve eaten it, I can’t re-sell it. I can’t have my cake and re-sell it. So think about pure consumption goods over here. And even in these pure consumption goods, I mustn’t get any psychological value out of thinking, I managed to get that cake and you didn’t. So the private value case is really an extreme thing, but it turns out to be a useful abstraction when we come to consider things further. All right, now where have my jars got to? Oh, plenty. Okay, so I can certainly, I’ve got certainly two rows I can play with here. Let’s talk about this auction for the jars. So what we going to do is we going to have people bid for the value in the jar They going to get they going to put forward a bid the highest bidder is going to win and what they going to win is the amount of money in the jar because what they going to pay is their bid So what is that? Is that a common value or a private value? That’s a common value. There is a certain amount of money in that jar.

[译文 6]

我消费的物品没有投资价值，没有转售价值。所以想象一下在eBay上出售的某件商品。比方说是一个蛋糕。如果我买了它，一旦我吃掉了，我就无法再出售它。我不能既保留蛋糕又转售它。所以在这里考虑纯粹的消费品。即使在这些纯粹的消费品中，我也不应该从心理上获得任何价值，比如想着我成功拿到了那个蛋糕而你没有。所以私人价值的情况确实是一个极端的事情，但当我们进一步考虑问题时，它被证明是一个有用的抽象概念。好吧，现在我的罐子到哪里了？哦，很多了。好吧，所以我肯定可以，我肯定有两排可以在这里玩。让我们谈谈这个关于罐子的拍卖。那么我们要做的是让人们对罐子里的价值进行投标。他们要提出一个出价，出价最高的人将获胜，他们将赢得的是罐子里的金额，因为他们将支付的是他们的出价。那是什么？是共同价值还是私人价值？这是共同价值。罐子里有一定数量的钱。

[段 7]

You don’t know what it is, but there is a certain amount of money in that jar and that’s the common value. So pretty much our jars of cayennes lie over here. They’re probably even a purer example than the oil well. All right. Now, let me get the first two rows of the class. So this row here and this row here, all of you have now had a chance to have a look at the jars. Let me just get you to write down, without looking at each other, write down on your notepad, You’ve already written down how many coins you can think in the jar. For the large jar, we’ll do the large jar first, write down your bid. Just so you can’t cheat later on, write down your bid. We’re playing this for real cash, right? So if you win, you’re going to have to pay me. So write down what you’re going to bid. Well, I might not hold it to you if it’s too crazy, but we’ll see. At least in principle, we’re playing for real cash. So write down your bid. Now, without changing your bid, show your neighbor your bid. All right. Now, what I’m going to do is, if I can just borrow Ali a second. Here’s some chalk. Let me go along the row and find out what those bids were.

[译文 7]

你们不知道里面有多少钱，但罐子里确实有一定数量的钱，这就是共同价值。所以我们这里的辣椒酱罐大致就是这样。它们甚至可能比油井更纯粹的例子。好了，现在让我看看前两排的同学。这一排和这一排，你们都已经有机会看过这些罐子了。让我请你们写下，不许看彼此，在你的笔记本上写下，你认为罐子里有多少硬币。大罐子，我们先做大罐子，写下你的报价。只是为了确保你们之后不能作弊，写下你的报价。我们是玩真的现金，对吧？所以如果你赢了，你得付钱给我。所以写下你要出的价格。嗯，如果太离谱我可能不会坚持让你付，但我们看看。至少原则上，我们是在玩真钱。所以写下你的报价。现在，不要改变你的报价，向你旁边的人展示你的报价。好了，我要做的就是，如果我能借用阿里一秒钟的话。这里有些粉笔。让我沿着这排走过去，看看那些报价是多少。

[段 8]

Do you want to record the bids? We’re going to record everybody’s bid. We’ll come back and talk about it afterwards. Where are those jars, by the way? Let’s have a look at the jar. Where’s the jar gone? Who’s got the large jar there? Hold up the large jar so everyone can see it. That’s the bid. It’s coins in a Sainsbury’s pesto jar. Seems to be quite good. All right. Okay, so I won’t bother with names today. I’m just going to get your bids. All right. Everyone’s written down a bid? No one’s going to cheat? All right. So what is your bid? $4.50. $4.50. $3.00. Sound that so everyone can hear All right I going to pass this along so $3.80. Shout louder than that. What was it? $3.80. $3.80, go on. $4. $4 again. $2.09. $2.09. $3. $1.60. $2.01. Sorry? The last one was what? 201. 201 here? That was after a 160 though. That was after a 160. All right. Sorry. Eighty-nine cents. Eighty-nine cents. This is for the big jar? The big jar. 140. 140. All right. We get a second row’s worth of people. 141. 141. 150. 150. $3. $3. $2. $2. $4.50. $4.50. $5. $5, we’re getting some high ones now. One cent. One cent. Okay. What’s wrong with my jaw? Okay. All right, pass that along. Eighty. That was an 80 150 150 159 A dollar A dollar A dollar 20 A dollar 20 And three more A dollar 50 A dollar 50 Two dollars All right, we have lots of bids and the winner is, the last one was two dollars.

[译文 8]

你们要记录报价吗？我们会记录每个人的报价。之后我们再回来讨论。顺便问一下，那些罐子在哪里？让我们看看那个罐子。罐子去哪了？谁拿着大罐子？举起来让大家都看到。那就是报价。是 Sainsbury’s 香蒜酱罐里的硬币。看起来确实不错。好了，好了，所以我今天就不记名字了。我只是要你们报价。好了，每个人都写下了报价吗？没有人会作弊吧？好了，你的报价是多少？$4.50。$4.50。$3.00。大声说出来让大家都听到。好了，我要把这个传下去所以 $3.80。大声点。多少？$3.80。$3.80，继续。$4。又是 $4。$2.09。$2.09。$3。$1.60。$2.01。抱歉？最后一个是多少？201。这里是 201？但那是 160 之后的。那是 160 之后的。好了，抱歉。89 美分。89 美分。这是大罐子的吗？大罐子。140。140。好了，我们收集到第二排的人了。141。141。150。150。$3。$3。$2。$2。$4.50。$4.50。$5。$5，我们现在看到一些高报价了。1 美分。1 美分。好了，我下巴怎么了？好了，好了，把那个传下去。80。那是 80 150 150 159 1 美元 1 美元 1 美元 20 1 美元 20 还有三个 1 美元 50 1 美元 50 2 美元 好了，我们有很多报价，获胜者是，最后一个是 2 美元。

[段 9]

I’ve actually forgotten how many coins were in here. Let me just remind myself. This was the large jar, right? Okay, now I know again. Okay, all right, so who’s our winner there? I’ve got a 4.50 here. There’s a 5. Professor Ben Polak There’s a 5. Okay, so here’s our winner. Who’s our winner? Okay, so let’s have our winner stand up a second. All right, so now a round of applause for our winner, So, I don’t want to put it in the jar. All right. Now, let’s talk about how people bid and why they bid that amount. Okay? So, let’s start with our winner. All right? Let’s start with our winner. All right. So, why did you bid $5? It looked like there could be about $5 in there. All right. So, I’ve forgotten your name. My name is? Ashley So Ashley is saying she bid roughly because it looked like there was about in there Plus you get the jar Plus you get the jar I not throwing in the jar Okay all right So let just sample a few other people and see what they say What did you say again? I said $1.60 because I didn’t want to overestimate it because then I’d have to pay you more than I’d get. All right. So what was your estimate? My estimate was about $180 to $200.

[译文 9]

我实际上已经忘记里面有多少硬币了。让我提醒一下自己。这是大罐子，对吧？好了，我现在又想起来了。好了，谁是我们的获胜者？我这里有 $4.50。有一个 $5。Ben Polak 教授那里有个 $5。好了，这里是我们的获胜者。谁是我们的获胜者？好了，让我们的获胜者站起来一下。好了，为我们的获胜者鼓掌。所以，我不想把它放进罐子里。好了，现在让我们谈谈人们是如何报价的，以及他们为什么报那个价。好吧？让我们从我们的获胜者开始。好吧？让我们从我们的获胜者开始。好了，你为什么报 $5？因为看起来里面大概有 $5。好了，我忘记你叫什么名字了。你叫什么？Ashley 所以 Ashley 说她大致报了这个价因为看起来里面大概有那么多钱，加上你还能得到这个罐子。加上你还能得到这个罐子，我不打算把罐子扔掉。好了好吧，让我们只抽样几个人看看他们怎么说。你又说了什么？我说 $1.60 因为我不想高估它，因为那样我付给你的钱会比我的更多。好了，你的估计是多少？大约 $180 到 $200。

[段 10]

All right. So I did under that. So your estimate was $180 to $200, and you bid around $160. That person next to you? Well, I guessed three, and same reasoning. I thought they would probably be about $4, and then I valued it like $1. All right, so you thought there was about $4 worth of coin, and you actually bid? Three. Three, all right. So all of you actually wrote down initially how many coins you thought were in there, right? Is that right? Let’s just get some idea of the distribution of those. So how many people thought there was less than a dollar in there? No shame here, just raise your hands. How many people thought there was between a dollar and a dollar fifty? How many people thought there was between a dollar fifty and two dollars? There’s some people at the back right there. How many people thought there was between two dollars and two How many people thought there was between $1.50 and $2? There’s some people at the back right there. How many people thought there was between $2 and $2.50? How many people thought there was between $2.50 and $3? How about more than $3.50? Clearly the people who bid high did. So we have a whole range of estimates there, a wide range of estimates, a wide range of bids, and people are saying things like, well, I thought there was this many coins in there.

[译文 10]

好了，所以我在那个以下。所以你的估计是 $180 到 $200，你报了大约 $160。挨着你的人呢？嗯，我猜了 3 美元，同样的理由。我觉得大概可能有 $4，然后我给它估值为 $1。好了，所以你觉得大概有 $4 价值的硬币，你实际报了？3。3，好了。所以你们所有人实际上最初都写下了你们认为里面有多少硬币，对吧？是这样吗？让我们了解一下这些估计的分布情况。有多少人认为里面不到 1 美元？这里没有羞耻感，举手。有多少人认为在 1 美元到 1.50 美元之间？有多少人认为在 1.50 美元到 2 美元之间？后面有一些人。多少人认为在 2 美元到 2.50 美元之间？有多少人认为在 2.50 美元到 3 美元之间？超过 $3.50 的呢？显然是那些报高价的人。所以我们看到了一系列估计，各种各样的估计，各种各样的报价，人们说类似这样的话，呃，我认为里面有这么多的硬币。

[段 11]

Maybe I shaded down a little bit from the number of coins I thought was in there because I want to make some profit on this. Is that right? That’s kind of the explanation I’m hearing from people. And what I want to suggest is that’s not a very good way to bid in this auction. So let’s repeat what I think people did. And people can contradict me if this is wrong. I think most people, they shook this thing. they waited a bit, they figured out there was, let’s say, 350 worth of pennies in there, and then they said, okay, 350, so I’ll bid, I don’t know, 340, 330, something like that. All right So what wrong with that What wrong with that All right Well first of all to reveal that there something wrong with it let me tell you how many coins were in there Now, in the larger jar, there was $2.07. $2.07. How many of you bid more than $2.07? Actually, we can see that here. Let’s just raise your hands. Quite a few of you. All right? So what we see here is a number of people, including our winner, bid a lot more than the number of coins in the jar. All right? What we find by a lot is that the winning bid was much, much greater than the true value.

[译文 11]

也许我对我认为的硬币数量打了一点折扣，因为我想要在这上面赚点钱。是这样吗？这就是我从人们那里听到的解释。而我想建议的是，这不是一个在这种拍卖中报价的好方法。让我们重复一下我认为人们做了什么。如果我说的不对，人们可以反驳我。我认为大多数人，他们摇了摇这个东西，等了一会儿，他们算出大概有 350 个硬币在里面，然后他们说，好，350，所以我报，我不确定，340，330，类似这样的。好了，这样做有什么问题？这样做的有什么问题？好了，首先，为了揭示这样做有问题，让我告诉你们里面有多少硬币。现在，大罐子里有 $2.07。$2.07。你们有多少人报价超过 $2.07？实际上，我们可以从这里看到。举起手来。你们很多人。好吧？那么我们在这里看到的是，包括我们的获胜者在内的一些人，报的价远高于罐子里的硬币数量。好吧？我们所说的"远"是获胜者的报价远远大于真实价值。

[段 12]

And this is a common phenomenon in common value auctions. It’s such a common phenomenon that it has a name. The name is the winner’s curse. It’s the winner’s curse. And the main lesson of the first half of today is going to be let figure out why there exists a winner curse let try and avoid falling into a winner curse and maybe let even figure out how to do better All right? So let’s try and think through why it is we fall into a winner’s curse. All right. All right. So one way to think about this is to think about naive bidding in this context. So suppose people’s strategy was actually to bid their estimate. Now I know that isn’t what people did. Most people shaded their estimate a little bit. But most people bid pretty close to their estimate. What’s going to happen in that instance is what? People are going to bid essentially what they think it’s worth and we just saw that fully half of you, I think half of the people we sampled, overestimated the number of coins in there. Is that right? Let’s just have that show of hands. How many people, raise your hand again, let’s be honest, if you thought there was more than 207 in there? Maybe roughly a half, maybe a little bit less than a half of you overestimated the number number of coins in there Now what that going to mean It going to mean all of those people who have this overestimate are going to overbid But we can be a little bit more general and a little bit more rigorous about this.

[译文 12]

这在共同价值拍卖中是一种常见现象。这种现象非常普遍，以至于它有一个名字。这个名字叫"赢家诅咒"。就是"赢家诅咒"。今天前半部分的主要课程就是让我们弄清楚为什么存在赢家诅咒，让我们尝试避免陷入赢家诅咒，也许甚至让我们弄清楚如何做得更好。好了？让我们试着思考为什么我们会陷入赢家诅咒。好了。好了。所以一种思考方式是考虑在这种情境下的朴素报价。假设人们的策略实际上是按他们的估计来报价。我知道这不是人们所做的。大多数人对他们的估计打了一点折扣。但大多数人报价非常接近他们的估计。在这种情况下会发生什么？人们基本上会按他们认为的价值来报价，而我们刚刚看到，我们抽样的人中有一半，我认为是有一半的人高估了里面的硬币数量。是这样吗？让我们举手确认。有多少人，诚实地说，如果你认为里面有超过 207 个硬币？大概有一半，也许比一半少一点，你们高估了硬币数量。现在这意味着什么？它意味着所有那些有高估的人都会过度报价。但我们可以对此更加笼统一些，更加严谨一些。

[段 13]

Let’s try and be a little bit more general. So first of all, let’s just make sure we understand what the payoffs are in this auction. The payoff this auction is what? You get the true value, you get the number of coins, number of pennies in the jar minus your bid if you are the highest and you get zero otherwise. I think it’s straightforward. We all understand that’s what the value is. And what do people do? People try to estimate. This is not a mistake. People try to estimate how many coins were in the jar. Now, in fact, the true number of coins in the jar was V, which turned out to be 207. But when people estimate it, they don’t get it exactly right, neither here, where you’re shaking the jar, nor in the case of these oil samples. So what they actually estimate is But when people estimate it, they don’t get it exactly right, neither here, where you’re shaking the jar, nor in the case of these oil samples. So what they actually estimate, each person forms an estimate, which we could call yi. And this yi we could think of as being the truth plus noise. So let’s call it epsilon i. Let’s even put a tilde on it to make it clear it’s a random term. So for some people, epsilon i is going to be a positive amount, which means they’re going to overestimate the number of coins in the jar.

[译文 13]

好的，让我们尝试稍微更一般化一点。首先，让我们确保理解这个拍卖中的收益是什么。这个拍卖的收益是什么？如果你是最高出价者，你得到真实价值，即罐子里的硬币数量减去你的出价；否则你得到零。我认为这很直接。我们都理解这就是价值所在。人们会怎么做？人们会尝试估计。这不是错误。人们会尝试估计罐子里有多少硬币。事实上，罐子里的真实硬币数量是 V，最终是 207。但当人们估计时，他们不会完全准确，无论是现在你们摇晃罐子，还是在这些石油样本的情况下。所以他们实际估计的是每个人都形成一个估计，我们可以称之为 yi。这个 yi 可以看作是真实值加上噪声。所以我们称之为 epsilon i。我们甚至给它加上一个波浪号以明确表示这是一个随机项。所以对一些人来说，epsilon i 将是一个正值，这意味着他们会高估罐子里的硬币数量。

[段 14]

And for some people, epsilon i is going to be a negative amount, which means they’re going to underestimate the number of coins in the jar. Everyone agree with that? That’s not a controversial statement, right? Everyone okay with that? So let’s think about the distribution of these yi’s. Let’s draw a picture that has on the horizontal axis all the different estimates that people could form of the number of coins on the jar. And let anchor this by v So here v And here is going to be the if you like the probability of getting that estimate So the frequency or probability of estimating yi given that vi is there. So I don’t know what the shape of this distribution is, but my guess is it’s kind of bell shaped. Is that right? Probably, it probably looks something like this. That’s implausible. And we can actually test this if we had time. We could actually go around all of you and get you to report what your estimates were, and we could plot that distribution and see if it is bell-shaped. But my guess is it’s reasonable to assume it’s bell-shaped. There’s some central tendency to estimate something close to the truth. If I’d drawn this correctly, I’d have its highest point at v. I haven’t quite drawn it correctly. It’s probably roughly symmetric. Okay, so now suppose that people’s bidding strategy is pretty much what they reported.

[译文 14]

对一些人来说，epsilon i 将是一个负值，这意味着他们会低估罐子里的硬币数量。大家都同意吗？这不是一个有争议的陈述，对吧？大家都明白吗？那么让我们想想这些 yi 的分布。让我们画一幅图，横轴上是人们对罐子中硬币数量的各种可能估计。以 v 为锚点。这是给定 vi 的情况下获得该估计的概率。所以我不知道这个分布的形状，但我的猜测是它大致呈钟形。对吗？可能，它大概看起来像这样。这不太合理。实际上我们可以测试这个，如果有时间的话。我们可以走遍你们所有人，让你们报告你们的估计是什么，然后我们可以绘制那个分布，看看它是否是钟形的。但我的猜测是，假设它是钟形的是合理的。有一个中心趋势，倾向于估计接近真实值。如果我画得正确的话，它的最高点应该在 v 处。我画得不太正确。它大概大致对称。好的，那么现在假设人们的出价策略基本上是他们所报告的那样。

[段 15]

People are going to bid roughly their estimate of the number of coins in the jar. So suppose people bid B roughly equal to Y So I know people are going to shade a little bit but let ignore that for now People are bidding roughly equal to YI. So what’s going to happen here? Who’s going to win? Who’s going to win? If this is the way in which the YIs emerge naturally in life, there’s a true VI, and then people make some estimate of it, which is essentially V plus noise, who’s going to end up being the winner? The winner of the auction. It’s going to be the person who has the highest estimate. So there’s really a lot of people. The winner isn’t going to be the person who estimated it correctly at V. The winner’s going to be way out here somewhere. The winner’s going to be way up in the right-hand tail. the winner will then be the i whose yi is the biggest is the maximum And the problem with this is the person whose yi is the biggest has what They have the biggest error. The person whose yi is the max, i.e. epsilon i is the max. And that’s exactly what happened. When we did estimates just now, One was the person who, Ashley, who had estimated that it would be roughly, maybe a little bit more than $5 worth of coins in there.

[译文 15]

人们会大致按照他们对罐子中硬币数量的估计来出价。所以假设人们出价 B 大约等于 yi。我知道人们会稍微压低一点，但让我们暂时忽略这一点。人们出价大约等于 yi。那么这里会发生什么？谁会赢？谁会赢？如果这就是 yi 在生活中自然出现的方式，有一个真实的 vi，然后人们做出一些估计，本质上是 V 加上噪声，那么谁会成为拍卖的赢家？拍卖的赢家将是估计值最高的人。所以这里有很多人。赢家不会是估计正确为 V 的人。赢家将远远在这里的某个地方。赢家将在右尾的上方。赢家将是 yi 最大的那个 i，即最大值，这就是问题所在。yi 最大的那个人有什么？他们有最大的误差。yi 最大的那个人，即 epsilon i 是最大的。事情就是这样发生的。当我们刚才做估计时，有一个人，Ashley，她估计罐子里大概有略多于 5 美元价值的硬币。

[段 16]

So I’m guessing, if that’s right, that no one else estimated more than $5 in these two rows. Is that correct? No one estimated more than $5. So the person who had the highest estimate bid the most, which was pretty close to her estimate, and that caused her to lose money. He ends up owing me whatever it is, 193, which I will collect afterwards. So the winner’s curse is caused by this. It’s caused by if people bid taking into account their own estimate and only their own estimate of the number of coins in the jar or the amount of oil in the oil well, then the winner ends up being the person with the highest estimate, which means the person with the highest error. So notice what this leads to. On average, the bid, the winning bid, is going to be much, much bigger than the truth. Is that right? The biggest error is typically going to be way out in this right tail, and that’s going to mean people are going to lose money. All right, so this phenomenon is very general because common value auctions are very general. I already mentioned the oil fields. In the early period after World War II, when the US government started auctioning out the rights to drill oil in the Gulf, in the Gulf of Mexico, early on it was observed that these companies, the winning companies, the companies who won the bid each time, was losing money.

[译文 16]

所以我猜，如果是这样的话，这两排中没有人估计超过 5 美元。对吗？没有人估计超过 5 美元。所以估计最高的人出了最高价，这大约接近她的估计，而这导致她亏钱。他最终欠我 193 美元，不管是多少，之后我会收取。所以赢家的诅咒是由此引起的。如果人们出价时只考虑他们自己对罐子里硬币数量或油井中石油数量的估计，那么赢家最终是估计最高的人，这意味着有最大误差的人。注意这导致什么。平均而言，出价和赢家的出价将比真实值大得多。对吗？最大的误差通常会在右尾很远的地方，这意味着人们会亏钱。好的，所以这个现象非常普遍，因为共同价值拍卖非常普遍。我已经提到了油田。在二战后的早期时期，当美国政府开始在墨西哥湾拍卖钻探权时，早期观察到这些公司，赢家，每次赢得出价的公司都在亏损。

[段 17]

It was great for the government, but these companies were consistently losing money They were consistently overbidding Be careful It wasn that the companies as a whole were overbidding it was that the winning bid was overbidding It was the winner curse Now over time, companies figured this out, and they figured out that they shouldn’t bid as much, and this effect went away. But you also see this effect in other places where naive bidders are involved. So for example, those people who’ve been following the baseball free agent markets, I think you could argue, someone could do an empirical test of this, you could argue that the winning bids on free agents in the baseball free agent market end up being horrible overbids for the same reason. The team who has the highest idiosyncratic estimate of the person’s value ends up hiring that player, but the highest idiosyncratic value tends to be too high. And similarly, perhaps more importantly, if you look at IPOs, initial public offerings of companies, they tend to sell too high. There’s a very, this one, the baseball one, I haven’t got the data, but the IPOs we know that IPO, there’s a tendency for IPOs, initial public offerings of companies, to have too high a share price and for those shares to fall back after a while. Maybe a little bit of initial enthusiasm but then they fall back And why Again the people with the highest estimate of the value of the company end up winning the company and if they not sophisticated about the way they bid then they overbid All right?

[译文 17]

这对政府来说是好事，但这些公司持续亏损。它们持续出价过高。注意，这不是说这些公司整体上出价过高，而是说赢家的出价过高。这就是赢家诅咒。随着时间的推移，公司们意识到了这一点，他们意识到不应该出那么高的价，这种效应消失了。但你也可以在其他有天真投标人的地方看到这种效应。例如，那些一直在关注棒球自由球员市场的人，我认为你可以论证，有人可以做实证检验，你可以说棒球自由球员市场上的赢得出价最终是糟糕的超额出价，原因相同。对他的价值有最高特有估计的球队最终会签下那个球员，但最高的特有价值往往太高了。同样，也许更重要的是，如果你看 IPO，即公司的首次公开募股，它们的售价往往太高了。这有一个非常，这个棒球的我没有数据，但 IPO 我们知道 IPO，有一种趋势，公司的首次公开募股会有太高的股价，之后这些股价会回落。可能是一些最初的热情但然后回落。为什么？同样，对公司价值有最高估计的人最终赢得了公司，如果他们对出价方式不成熟，他们就会出价过高。对吗？

[段 18]

All right, so this is a serious problem out there, and it raises the problem, it raises the issue, well, how should I correct this? I might, in life, be involved in an auction as a bidder for something that has a common value element. How should I think about how I should bid? We’ve learned how we shouldn’t bid. We shouldn’t just bid my estimate minus a little. So how should we think about it? Now to walk us towards that, let me try and think a little bit more about the information that’s out there. Let’s go back to our oil well example. Each of these oil companies drills a test well in the oil fields. and from this test well, each of them gets an estimate of yi. You can imagine someone doing a test drill into my jar of coins, and when they do this test drill into this jar of coins, they form an estimate yi. And suppose that your estimate of the number of coins in the jar, or the number of oil in the oil well suppose that your particular one is equal to 150 Then if I then asked you the question not to bid but I asked you the question how many coins do you think are in the jar, your answer would be 150. That would be your best estimate.

[译文 18]

好的，所以这是一个严重的问题，它提出了这个问题，提出了一个问题，我应该如何纠正这个问题？在生活中，我可能作为投标人参与一个具有共同价值元素的拍卖。我应该如何思考我应该怎么出价？我们已经学会了不应该怎么出价。我们不应该只是用我的估计减去一点。那么我们应该怎么想呢？为了引导我们朝那个方向，让我试着再多思考一下那里的信息。让我们回到我们的油井例子。每个这样的石油公司在油田钻了一口测试井。从这口测试井，每个公司得到一个 yi 的估计。你可以想象有人对我的硬币罐做一次测试钻探，当他们对这个硬币罐做测试钻探时，他们形成一个估计 yi。假设你对罐子里的硬币数量，或者油井里的石油数量的估计恰好等于 150。那么如果我问你问题，不是让你出价，而是我问你你觉得罐子里有多少硬币，你的回答会是 150。那将是你的最佳估计。

[段 19]

But suppose I then told you that your neighbor, let’s go back to Ashley again. So Ashley’s estimate was, let’s say it was 150. It wasn’t, but let’s say it was 150. And suppose I went to her neighbor and asked her neighbor, and her neighbor said, actually, I think there’s only 130 in there. So suppose Ashley now knows that she did a little test. She thinks there’s 150. But she now knows that her neighbor has done a similar test, and he thinks there’s only 130. Now what should be Ashley’s estimate of the number of coins in the jar? Well, somewhere in between, right? So probably somewhere between 150 and 130, maybe about 140, but certainly lower than 150. Is that right? Is that right? So if I told you that someone else had an estimate that was 20 lower than yours, that would cause you to lower your belief about how many coins was in the jar. Now let’s push this a little harder. Suppose I told you not that your neighbor had an estimate of 130, but just that your neighbor had an estimate that was lower than 150. I’m not going to tell you exactly what your neighbor estimates. I’m just going to tell you that his estimate is lower than yours. So your initial belief was there was 150 coins in this jar, but now I know that my neighbor thinks there’s fewer than 150.

[译文 19]

但假设我告诉你，你的邻居，让我们再回到Ashley那里。所以Ashley的估计是，比如说150。不是150，但假设是150。假设我去找她的邻居问她，她的邻居说，实际上我觉得里面只有130。所以假设Ashley现在知道她做了一点测试。她认为有150。但她现在知道她的邻居做了类似的测试，他觉得只有130。那么Ashley对罐子里硬币数量的估计应该是多少呢？嗯，在两者之间，对吧？所以可能在150和130之间，大概140左右，但肯定低于150。对吗？是这样吗？所以如果我告诉你有人的估计比你低20，那就会让你降低对罐子里硬币数量的信念。现在让我们更进一步。假设我告诉你的不是你邻居的估计是130，而只是你邻居的估计比150低。我不打算告诉你你邻居具体估计了多少。我只是要告诉你，他的估计比你的低。所以你最初的信念是罐子里有150枚硬币，但现在我知道我的邻居认为少于150枚。

[段 20]

Do you think your belief is still 150, or is it lower? Who thinks it’s gone up? It hasn’t gone up, right? Who thinks it’s gone down? It’s gone down. I don’t know exactly by how much to pull it down, but the fact that I know that my neighbor has a lower estimate than me suggests that I should have a lower estimate than 150 Now suppose I tell you something more dramatic Suppose I go to Ashley and say your initial estimate was actually it wasn 150 it was wasn it Let do it So your initial estimate was 500 pennies right And I’m not going to tell you what your neighbor’s estimate was, I’m not going to tell you what your neighbor’s neighbor’s estimate was, but I’m going to tell you that every single person in the row, in the two rows, other than you, had an estimate lower than $5. So Ashley’s estimate was $5, but I’m now going to tell her that every single person in the room had a lower estimate than hers. So what I’m going to tell her is that YJ is less than YI for all J, for all the other people. Now I claim that if you tell me that everybody else, there were probably what 30 other people there, has an estimate lower than mine, everyone else, what should I now estimate?

[译文 20]

你认为你的信念还是150，还是降低了？谁认为它上升了？它没有上升，对吧？谁认为它下降了？它下降了。我不知道具体要降低多少，但我知道我邻居的估计比我低这一事实表明我应该有一个低于150的估计。现在假设我告诉你更戏剧性的事情。假设我去找Ashley说，你最初的估计实际上不是150，它是——让我们这样做——你最初的估计是500枚硬币，对吧。我不打算告诉你你邻居的估计是多少，我也不会告诉你你邻居的邻居估计是多少，但我会告诉你，除了你之外，这一排、两排里的每一个人都有一个低于5美元的估计。所以Ashley的估计是5美元，但现在我要告诉她，房间里每个人的估计都比她低。所以我要告诉她的是，对于所有其他人J，YJ都小于YI。现在我声称，如果你告诉我所有其他人，大概还有30个人，有一个比我低的估计，每个其他人，那我现在应该估计多少？

[段 21]

What should happen to my estimate? It’s going to come down a lot. It going to come down a lot Is that right If my estimate was but I know everybody else not just one person but everybody else had a lower estimate then my guess of the number of coins in the jar has come down a whole lot But what But that exactly what Ashley knows as soon as she found out that she’s won the auction. If people are bidding their values, if people are bidding people are bidding their estimates, then as soon as Ashley discovers she’s won, she’s going to say, oh bother, I now know that my estimate was too high. She makes something more extravagant than bother, but at the very least she might say, oh bother, I now know that everyone else had a lower estimate than me, and therefore my estimate of $5 is too high. So what’s going to happen is if people start bidding their or close to their estimates, then once they’ve won, they’re going to learn exactly this. They’re going to learn that everyone else’s estimate was lower than theirs, and they’re going to regret their choices. It can’t be a good idea, it can’t be an equilibrium, for people to make choices which they’re going to regret if they win That crazy So we need to think about how to correct for that So how do we correct for it Now let talk about this a little bit harder Each of you, when you’re bidding for this jar of coins, I claim you only really care about how many coins were in the jar in one circumstance.

[译文 21]

我的估计应该发生什么变化？它会大幅下降。它会大幅下降。对吗？如果我的估计是，但我知道所有人，不只是一个人，而是所有人都有一个更低的估计，那么我对罐子里硬币数量的猜测就会大幅下降。但是——但这正是Ashley一旦发现自己赢得了拍卖就知道了的事情。如果人们按照他们的价值投标，如果人们投标——人们按照他们的估计投标，那么一旦Ashley发现她赢了，她会说，哦糟了，我现在知道我的估计太高了。她会说比"糟了"更夸张的话，但至少她可能会说，哦糟了，我现在知道每个人的估计都比我低，因此我5美元的估计太高了。所以会发生的事情是，如果人们开始按照他们的估计投标，或者接近他们的估计投标，那么一旦他们赢了，他们就会确切地了解到这一点。他们会知道每个人的估计都比他们低，他们会后悔他们的选择。让人们做出如果赢了就会后悔的选择不可能是个好主意，不可能是均衡。所以我们需要考虑如何纠正这一点。那么我们如何纠正它呢？现在让我们更深入地谈谈。当你们每个人为这罐硬币投标时，我声称你只在一种情况下真正关心罐子里有多少硬币。

[段 22]

What’s the only circumstance in which you care at all How many coins are in the jar? If you win. I claim you only care how many coins are in the jar, or how much oil is in the well, if you win, if your bid is the winning bid. And if your bid is the winning bid, what do you know? You know that your estimate was the highest estimate in the room, at least if this equilibrium has the property that bids are increasing in estimates, which is not much to expect. So you know… in this case, you would have we have an estimate, yi, that was at least as big as yj for all the other people in the room. So where are we? You only care how many coins are in the jar if you win, and if you win you know your estimate was the highest. So what’s the relevant estimate? The relevant estimate of the number of coins in the jar for you when you’re bidding, The relevant estimate is not how many coins do I think is in this jar, that’s the naive thing. The relevant estimate is how many coins do I think is in this jar given my shaking of it and given the fact that I have won the auction, or given the supposition that I might win the auction.

[译文 22]

你在什么情况下根本不关心罐子里有多少硬币？只有当你赢了的时候。我声称，只有当你赢了，如果你的出价是最高出价，你才会关心罐子里有多少硬币，或者油井里有多少油。如果你的出价是最高出价，你知道什么？你知道你的估计是房间里最高的估计，至少如果这个均衡具有出价随估计递增的特性，这不是什么过分的要求。所以你知道……在这种情况下，你的估计yi至少和其他房间里所有人的估计yj一样大。那么我们处于什么位置？你只有在赢了的时候才关心罐子里有多少硬币，如果你赢了，你知道你的估计是最高的。那么相关的估计是什么？当你投标时，对你来说罐子里硬币数量的相关估计不是我认为这罐里有多少硬币，这是天真的想法。相关的估计是，考虑到我摇晃了它，考虑到我赢得了拍卖，或者考虑到我可能赢得拍卖，我认为这罐里有多少硬币。

[段 23]

So the relevant estimate in bidding the relevant estimate when bidding is how many coins do I think are there given my initial guess, yi, and given that yi is bigger than yj. Now notice this is kind of a weird thing. It’s a counterfactual thing. I don’t know, at the time at which I’m bidding, I don’t know that I’m going to win. But nevertheless, I should bid as if I knew I was going to win because I only care in the certain sense which I win. So the way in which I should estimate the number of coins in the jar, and indeed the way in which I should bid is I should bid the number of coins I would think were in the jar if I won Say that again I should bid the number of coins I would think were in the jar if my bid ended up being the winning bid So the lesson here is bid as if you know you win Bid as if you know you win. Now why is that a good idea? Let’s go back to this case of now you discover you’ve won. Provided you bid as if you know you won, when you win you’re not going to be disappointed because you already took that information into account. But if you bid not as if you won, you fail to take into account the possibility of winning, then winning is going to come as a shock to you and cause regret.

[译文 23]

所以投标时相关的估计，投标时的相关估计是，考虑到我的初始猜测yi，考虑到yi大于yj，我认为那里有多少硬币。现在注意这有点奇怪的事情。这是一个反事实的事情。我不知道，在我投标的时候，我不知道我会赢。但尽管如此，我应该好像我知道我会赢那样投标，因为只有在某种意义上我赢了的时候我才关心。所以我应该估计罐子里硬币数量的方式，实际上我应该投标的方式是，我应该投标如果我赢了我会认为罐子里有多少硬币。再说一遍，我应该投标如果我的出价最终成为最高出价，我会认为罐子里有多少硬币。所以这里的教训是，好像你知道你会赢那样投标。好像你知道你会赢那样投标。为什么这是个好主意？让我们回到这个你发现你赢了的情况。只要你好像知道你会赢那样投标，当你赢的时候你不会失望，因为你已经把那个信息考虑进去了。但如果你不是好像你赢了那样投标，你没有考虑到赢的可能性，那么赢了就会像一个冲击一样到来并引起后悔。

[段 24]

So the only way to prevent this ex post regret, the only way to bid optimally is to bid as if you know you’re going to win. Estimate the number of coins not on your own sample, but on the belief that your sample is the biggest sample. Yeah, there’s a question. Go I don understand what the difference is between bidding as if you know you win and what if you won right Because if you bid, like whenever you bid, you’re bidding the number that you think, oh, well, I think there are this many coins in the jar, so if I win, I don’t want to bid too many so that I don’t lose, right? So how is that different from bidding as if you know you win versus when it’s too long? Good, okay, good, good, good. So how is it different to say bidding as if I know I win? So it’s bidding. Okay, so let me try and say it again. So what you’re going to do is you’re going to think of the following thought experiment. Suppose you told me I won. Suppose you told me I won. Now how many coins do I think are in the jar? Let me bid that amount. So before we even do the bid, let’s do the following thought experiment. You’re figuring out how many coins you think are there.

[译文 24]

所以防止这种事后后悔的唯一方法，投标最优的唯一方法就是好像你知道你会赢那样投标。不要基于你自己的样本估计硬币数量，而是基于你的样本是最大样本的信念来估计。是的，有个问题。请说——我不明白，好像你知道你会赢那样投标和如果你赢了的区别是什么——因为无论什么时候你投标，你都是在投标你认为的数字，哦，好吧，我认为罐子里有这么多硬币，所以如果我赢了，我不想投太多以至于我输了，对吧？所以这和好像你知道你会赢那样投标有什么不同呢？好的，嗯，好的，好的。那么说好像我知道我会赢有什么不同呢？所以这就是投标。好的，让我试着再说一遍。所以你要做的是你要考虑以下思想实验。假设你告诉我我赢了。假设你告诉我我赢了。现在我认为罐子里有多少硬币？让我按那个数额投标。所以在我们做投标之前，让我们做以下思想实验。你在计算你认为那里有多少硬币。

[段 25]

Now I say, suppose it turns out that your estimate’s the highest estimate. Now how many coins do you think are there? That’s what you should bid. I’m arguing that being told that your estimate’s the highest is going to drag down that estimate a long way. But the key idea here is if you bid as if you know you win, then you won’t regret winning. That’s what you want to avoid. Professor Ben Polak Professor Peter Salgo Professor Peter Salgo Professor Peter Salgo group of people. Let me get people to shout these out fairly quickly. We move on to these two rows. Write down your bid on the smaller jar now, on the smaller jar. All right. This is your bid, not your estimate. Write down your bid on the smaller jar. All right, as fast as we can go, all right, just shout out a number. Forty cents. Forty cents. One dollar. One dollar. One dollar twenty. One dollar twenty. One fifty. One fifty. Ninety-eight cents. $98. $1. $1. $0.90. $0.90. $0.75. $0.75. $1.60. $1.60. $1.50. $1.50. Okay I going to pass this in so I go to the other side Keep shouting them out 95 cents 80 80 50 50. 75. 125. 125. 150. Buck 30. Buck 30. 125. 125. 109. 109. 115. 115 and? 80. 80. Did I get everybody? All right. 80 was the last one.

[译文 25]

好，我再说一遍，假设你的估算是最高的估算。你觉得那里有多少枚硬币？这就是你应该报的价。我主张，如果你被告知自己的估算是最高的，这会大大拉低那个估算。但关键的想法是，如果你按照好像知道自己会赢的方式来报价，那么你不会后悔赢了。这正是你要避免的情况。Ben Polak教授、Peter Salgo教授、Peter Salgo教授、Peter Salgo教授这些人。让我让大家相当快地喊出这些。我们继续到这两排。现在在较小的罐子上写下你的报价，在较小的罐子上。好。这是你的报价，不是你的估算。在较小的罐子上写下你的报价。好，尽可能快地，好，就喊出一个数字。四十美分。四十美分。一美元。一美元。一美元二十。一美元二十。一美元五十。一美元五十。九十八美分。$98。$1。$1。$0.90。$0.90。$0.75。$0.75。$1.60。$1.60。$1.50。$1.50。好，我要把这个传过去，所以我到另一边继续喊它们出来。九十五美分。八十。八十。五十。五十。七十五。一百二十五。一百二十五。一百五十。三十美分。三十美分。一百二十五。一百二十五。一百零九。一百零九。一百一十五。一百一十五还有吗？八十。八十。我每个人都收到了吗？好。八十是最后一个。

[段 26]

All right. So, okay, the bids came down partly because the jar was smaller, of course, which is cheating. But let me just tell you, let’s find out who the winner was, first of all. So 160 is the winner. 160 is the winner. And it turns out that the number of coins in this jar was 148. All right, so what happened here? I think people took into account, people did lower their bids below the estimate. Let’s just check, actually. So who is my 160 person? So stand up my 160 person. So how many coins did you think were in there? 160. Professor Ben Polak 160, okay. So your name is? Robert. Professor Ben Polak So Robert thought there was one you bid 160 Yes Professor Ben Polak All right how many coins do you think was in there 160 Professor Ben Polak 160 I not doing well here am I I doing well here All right Okay fine Okay So what am I trying to convince you to do here? What am I trying to convince you to do? All right. So let me find some other bidders. So what did you bid? $1. $1. How many coins do you think were in there? $125. $125. Okay. So how many of you, be honest now, how many of you bid significantly below your estimate? Raise your hands, have you bid below your estimate?

[译文 26]

好的。好的，报价下降部分是因为罐子变小了，当然，这算是在作弊。但让我先告诉大家，让我们先找出谁是赢家。所以160是赢家。160是赢家。结果这个罐子里的硬币数量是148。好，这里发生了什么？我认为人们考虑到了，人们确实把报价降低到了估算以下。让我们检查一下，实际上。那么谁是我的160这个人？站起来，我的160这个人。你认为那里有多少枚硬币？160。Ben Polak教授160，好的。那么你叫什么名字？Robert。Ben Polak教授所以Robert认为有一个你报价160是的Ben Polak教授好的你认为那里有多少枚硬币160Ben Polak教授160我这里做得不好是吧我这里做得很好好的好的好吧好的那么我在这里想说服你做什么？我在这里想说服你做什么？好的。让我找一些其他的竞标者。那么你报了什么价？$1。$1。你认为那里有多少枚硬币？$125。$125。好的。那么你们中有多少人，说实话，有多少人你们的报价明显低于你们的估算？举起手来，你们的报价低于你们的估算了吗？

[段 27]

Good, so we’re learning something. I feel like this is the 24th lecture, I should be able to teach you something. So the idea here is, in a common value auction, you need to shade your bid considerably. In fact, most of these bids, even though you were shading your bid considerably, most of you didn’t shade it enough. So even taking this into account, even taking into account the lesson of the day, even with that into account, a number of you are still overbidding. So what’s the takeaway lesson? If you’re in a common value auction, a common value auction, you need to bid as if you have been told that your estimate is the highest estimate That means you need to shade your estimate a lot If you don’t do this, you’ll win a lot of auctions and you’ll be very unhappy. All right? All right, now we’re not done here. All right, let me move forward by moving away now just from common value auctions. So far we’ve focused on common value auctions and we’ve focused on a particular structure of auction, but I also want to talk about different types of auction themselves. Because one phenomenon you’re seeing out there a lot these days is that people run different structures of auctions. And auctions are getting more and more important in the US economy. It used to be that auctions were something you thought of as a pretty rare event and You see them when people are selling cattle, and you see them when people were selling art, but that was pretty much it.

[译文 27]

好的，所以我们学到了一些东西。我感觉这是第24场讲座，我应该能够教你们一些东西。所以这里的想法是，在共同价值拍卖中，你需要相当大地压低你的报价。事实上，尽管你们已经相当大地压低了你们的报价，但你们中的大多数人都没有压得足够低。所以即使考虑到这一点，即使考虑到今天的教训，即使考虑到这一点，你们中的一些人仍然在过度出价。所以要点是什么？如果你是处在一个共同价值拍卖中，一个共同价值拍卖中，你需要表现得好像被告知你的估算是最高估算那样来出价。这意味着你需要大幅压低你的估算。如果你不这样做，你会赢得很多拍卖，但你会非常不开心。好的？好的，我们还没有结束。好的，让我从共同价值拍卖中走出来继续前进。到目前为止，我们专注于共同价值拍卖，我们专注于一种特定的拍卖结构，但我也想谈谈拍卖本身的不同类型。因为你最近看到的一个现象是，人们运行不同结构的拍卖。而且拍卖在美国经济中变得越来越重要。过去拍卖被认为是一件相当罕见的事情，你会看到它们在人们出售牛的时候，你会看到它们在人们出售艺术品的时候，但仅此而已。

[段 28]

But now you see auctions everywhere. We see auctions on eBay. We see auctions for the Spectrum. Pretty much everything is auctioned these days. So auctions are becoming important. In fact, at Yale this year, we had a class solely devoted to auctions. We’re having one day of this class for auction. Everything is auctioned these days. So auctions are becoming important. In fact, at Yale this year, we had a class solely devoted to auctions. We’re having one day of this class for auctions, but they had a whole 24 lectures on auctions. It’s that important. And one thing we should realize is that there are lots of different types of auction. So let’s talk about four different types of auction. Let’s call them A, B, C, and D. So the first type of auction is a first price sealed bid auction. And that’s what we just did. Everybody wrote down their bid on a piece of paper. And the winner was the person with the highest bid, and they paid their bid. Ashley in the first case, Jonathan in the second, Robert in the second one. So a first price sealed bid auction is what we just did and that’s a typical auction you might see, for example, in house sales. Here’s another type of auction though. So this sounds crazy but let me write it up anyway You can imagine a second price sealed bid auction So what happens in a second price sealed bid auction Everybody writes down their bid.

[译文 28]

但现在你到处都能看到拍卖。我们在eBay上看到拍卖。我们在Spectrum上看到拍卖。这些天几乎所有东西都在拍卖。所以拍卖变得越来越重要。事实上，在耶鲁大学今年，我们有一门专门讲授拍卖的课程。我们这门课用一天来讲拍卖。这些天几乎所有东西都在拍卖。所以拍卖变得越来越重要。实际上，耶鲁大学今年开设了一门专门研究拍卖的课程。我们用其中一天讲授拍卖，但他们整整用了24场讲座来讲授拍卖。拍卖就是如此重要。我们应该认识到，拍卖有很多不同类型。让我们讨论四种不同的拍卖类型。我们称之为A、B、C和D。第一种拍卖类型是第一价格密封投标拍卖。这就是我们刚才做的。每个人在一张纸上写下他们的出价。赢家是出价最高的人，他们支付他们的出价。第一种情况是Ashley，第二种是Jonathan，第二种是Robert。所以第一价格密封投标拍卖就是我们刚才做的，这是一种典型的拍卖，你可能会在房屋销售中看到。不过还有另一种拍卖类型。这听起来很疯狂，但无论如何让我写下来。你可以想象一个第二价格密封投标拍卖。所以在第二价格密封投标拍卖中会发生什么？每个人写下他们的出价。

[段 29]

Each player writes down their bid. The highest bidder gets the good. So that’s the same as before. But now, instead of paying the bid that they wrote down, they pay the second highest bid. The idea is the winner pays the second bid. The winner is the person with the highest bid, but they pay the second bid. So that seems crazy, doesn’t it? Seems a bit crazy. These are sometimes called vickery auctions. and Vickery won the Nobel Prize, so they can’t be that crazy. We’ll come back and talk about it. Here’s two other kinds of auction. We can think about an ascending open auction. So this is what you all think of when we say auction This is what happens at a cattle auction or an art auction in which people are shouting out bids One way to think about this is if we were bidding something if we were auctioning off something in the class today is that everybody who is still in the auction would raise their hands, and as the bid got higher and higher, some of you would start dropping out. Is that right? And eventually, when there’s only one hand left, that person would win the auction. Is that right? So that’s a version of an ascending open auction. Everybody raises their hand when the price is zero, and as the price goes up, hands go down until there’s only one hand left.

[译文 29]

每个参与者写下他们的出价。最高出价者得到物品。所以这和之前一样。但现在，他们不是支付他们写下的出价，而是支付第二高的出价。这个想法是赢家支付第二高的出价。赢家是出价最高的人，但他们支付第二高的出价。这似乎很疯狂，不是吗？看起来有点疯狂。这些有时被称为Vickery拍卖。而Vickery获得了诺贝尔奖，所以他们不可能那么疯狂。我们会回过头来讨论它。还有两种其他类型的拍卖。我们可以想到一种上升开放式拍卖。这就是你们所有人当我们说拍卖时想到的。这就是在牲畜拍卖或艺术品拍卖中发生的事情，人们在那里喊出出价。一种思考方式是，如果我们在课堂上拍卖某样东西，每个仍在拍卖中的人都会举起手来，随着出价越来越高，你们中的一些人会开始退出。对吗？最终，当只剩一只手时，那个人就会赢得拍卖。对吗？所以这是上升开放式拍卖的一个版本。每个人在价格为零时举起手来，随着价格上涨，手会放下直到只剩一只手。

[段 30]

But we can also imagine another crazy auction, which is a descending open auction. So how does a descending open auction, or I should just say, this is the kind of, this open, extending one is what you typically see on eBay. What is a descending open auction? And ascending Oakland auction is the same idea almost, except instead of starting the prices at zero and going up, I’ll start the price at infinity and go down. So now, if I start the price at infinity, none of you have your hands up, I hope. And as the price goes down, eventually, one of you is going to raise their hands and then you get that good and pay that amount So this auction happens in the real world It used to happen in a place called Filene Basement When I was a graduate student struggling to have enough money, there was a place in Boston called Filene’s Basement which would sell clothing in this way. So you’d go and pick out the suits you needed for your horrible job interview, and the price would come down each week, and you’d hope that no one bought it before you did. Sometimes it’s called a Dutch auction. Here’s four kinds of auctions. Two of them seem pretty familiar. A and C sound like familiar kind of auctions that you’re used to seeing, and B and D seem a little weird.

[译文 30]

但我们也可以想象另一种疯狂的拍卖，那就是下降开放式拍卖。所以下降开放式拍卖是怎样的，或者我应该说，这种开放的、延伸的形式是你在eBay上通常看到的。什么是下降开放式拍卖？上升式奥克兰拍卖几乎是相同的想法，只是不是从零开始价格上涨，而是从无穷大开始价格下降。所以现在，如果我从无穷大的价格开始，我希望你们没有人举手。随着价格下降，最终，你们中会有一个人举起手来，然后你得到那件物品并支付那个金额。所以这种拍卖在现实世界中发生过。它曾经发生在一个叫做Filene Basement的地方。当我是一名研究生，为没有足够的钱而挣扎时，波士顿有一个叫做Filene’s Basement的地方，它会以这种方式出售服装。所以你会去挑选你可怕的工作面试所需的西装，价格每周都会下降，你希望没有人比你先买走它。有时它被称为荷兰式拍卖。这就是四种拍卖。其中两种看起来相当熟悉。A和C听起来像你习惯看到的那种熟悉的拍卖，而B和D看起来有点奇怪。

[段 31]

The first thing I want to convince you of is that B and D are not as weird as they seem. auction. So let’s look at these crazy auctions. The first thing I want to claim is that auction D is really the same as auction A. So just remind us of what those two auctions are. Auction A is exactly the auction we just did for the coins. Everybody writes down their bid. So just to remind us of what those two auctions are. Auction A is, it’s exactly the auction we just did for the coins. Everybody writes down their bid, we open all the envelopes, and the winner is the person with the highest bid written down, and they pay that. The descending open auction, nobody bids, nobody bids, nobody bids, nobody bids, suddenly, suddenly, somebody bids, and then they pay that amount. Why are those two auctions the same? Well, think about that descending bid, that descending open auction. During that descending open auction, each of you may have written down in your head, it’s useful to think of it this way, you’ve written down in your head the number at which you’re going to raise your hand. Is that right? So there I am as a graduate student waiting for my suit to come down in price so I can afford it, and I know what that number is, and that, from your point of view, the other potential wearers of this suit, from your point of view, that’s a sealed bid for me.

[译文 31]

我想让你们相信的第一件事是，B和D并没有看起来那么奇怪。拍卖。让我们来看看这些奇怪的拍卖。我首先要声明的是，拍卖D实际上和拍卖A是一样的。所以让我们回顾一下这两个拍卖是什么。拍卖A正是我们刚才做硬币的那个拍卖。每个人都写下自己的出价。所以提醒一下这两个拍卖是什么。拍卖A就是，我们刚才做硬币的那个拍卖。每个人都写下自己的出价，我们打开所有的信封，赢家是出价最高的那个人，他们支付那个金额。降价式公开拍卖，没人出价，没人出价，没人出价，没人出价，突然，突然，有人出价了，然后他们支付那个金额。为什么这两个拍卖是一样的？嗯，想想那个降价式出价，那个降价式公开拍卖。在那个降价式公开拍卖期间，你们每个人可能都在心里记下了一个数字，用这种方式思考会很有帮助，你们在心里记下了自己要举手的那个数字。对吧？我是作为一个研究生等着我的西装价格降到我能买得起的时候，我知道那个数字是多少，而从你们的角度来看，其他可能买这件西装的人，从你们的角度来看，那对我来说就是一个密封投标。

[段 32]

At the end of the day, whoever has that highest intended bid, that highest sealed bid, will end up winning the suit, and they pay their bid So from a strategic point of view the descending open auction and the sealed first price auction are the same thing The person who has the highest bid, the highest strategy, wins and they pay their bid. You don’t get to see anyone else’s strategy until it’s too late. So D is equal to A. What about B and D? So I claim that B and D are not the same, but they’re very closely related. Sorry, B and C. So C is what? C is our eBay auction. It’s our classic auction you’re all used to playing on eBay. And B is this slightly crazy thing where we all write down bids, and the winner is the person who has the highest bid, but they only pay the second amount. Now why am I saying that’s the same as our eBay auction, in some ways? Well, then think about the eBay auction. Here you are playing the eBay auction. So all of you have your hands up, meaning you’re still in, and the price is going up. Price is going up over time, and all of you that have your hands up you still in Each of you has some strategy in mind which is what The strategy is when am I going to lower my hand What the highest price I willing to pay or high price I going to pay for this object?

[译文 32]

最终，无论谁有那个最高的预期出价，那个最高的密封投标，最终都会赢得这件西装，并且他们支付自己的出价。所以从策略的角度来看，降价式公开拍卖和密封式第一价格拍卖是一样的。拥有最高出价、最高策略的人获胜，他们支付自己的出价。在太晚之前你看不到任何其他人的策略。所以D等于A。B和D呢？我声称B和D并不一样，但它们密切相关。对不起，B和C。C是什么？C是我们的eBay拍卖。这是你们都在eBay上玩的那种经典拍卖。B是有点疯狂的东西，我们所有人都写下出价，赢家是出价最高的人，但他们只支付第二高的金额。为什么我说这在某些方面和我们的eBay拍卖一样？嗯，想想eBay拍卖。你们正在玩eBay拍卖。所以你们所有人都举手，意味着你们还在里面，价格在上涨。价格随着时间上涨，你们所有举手的人都还在里面。每个人心里都有某种策略，策略是我什么时候要放下手？我愿意为这件物品支付的最高价格是多少？

[段 33]

So your strategy in the classic eBay auction is, the price at which I lower my hand. Who wins in that open ascending auction? The person who has the highest intended bid. The person whose hand is up at the end is the person whose intended bid is the highest. But what amount do they pay? When does the auction stop? When does the auction stop? It stops when the second to last hand goes down. So if I’m the winning bid in an open ascending auction, my hand is still up. You don’t know what I was willing to pay. What I’m actually going to pay is the price of the last person whose hand went down. I’m going to pay the bid of the person whose amount they’re going to pay is the second highest amount. That make sense? So in an ascending open auction, the winner, the person who has the highest intended bid actually pays the amount highest intended bid of the second highest player So an ascending open auction is structurally very similar to these seal bid auctions which is really why these seal bid auctions are interesting, these second price seal bid auctions are interesting. Now having said that, they’re not exactly the same, and the reason they’re not exactly the same is that if in fact the good for sale has common value, then we might learn something by the fact that the hands are up.

[译文 33]

所以你在经典eBay拍卖中的策略是，我放下手的那个价格。谁在那个公开升价拍卖中获胜？有最高预期出价的人。最后还举着手的人就是预期出价最高的人。但他们支付多少？拍卖什么时候停止？拍卖什么时候停止？它停止于倒数第二只手放下的时候。所以如果我在公开升价拍卖中获胜，我的手还举着。你不知道我愿意支付什么。我实际要支付的是最后那个放下手的人的价格。我要支付的是那个人的出价，也就是第二高的金额。明白了吗？因此在公开升价拍卖中，赢家，也就是有最高预期出价的人，实际上支付的是第二高玩家的最高预期出价的金额。因此公开升价拍卖在结构上与这些密封投标拍卖非常相似，这正是为什么这些密封投标拍卖有趣，为什么这些第二价格密封投标拍卖有趣。不过话虽如此，它们并不完全相同，它们不完全相同的原因是，如果待售物品实际上有共同价值，那么我们可能通过手还举着这件事学到一些东西。

[段 34]

So the fact that people’s hands are still up in the open auction, whereas you can’t see what people are doing in the sealed auction, makes these not identical. But there’s clearly a close similarity between them. Now let’s ask, I guess, the question people have been wondering about, which is, how should I bid at eBay? We figured out that for a common value auction, if you’re going to reset, you know, the common value auction on eBay, for example, if the good you’re buying is a good you’re later on going to want to resell, in that case, we already know that you should shade your estimate of the value considerably. So let’s go to the other extreme. Let’s consider a private value. a private value auction. There’s no common value here at all, and let’s Let’s assume that this auction is either second price sealed bid or open ascending. To summarize, it’s either what we call B or what we call C. There you are, you’re bidding on eBay and it’s a private value good. There’s nothing interesting about how much anyone else values this thing. So what’s your value? Your value is Vi. You might bid Bi. So this is your value. Your bid is Bi. And what’s your payoff? So our payoff is Vi minus it not minus Bi what it minus It going to be minus let call it bj bar and I say what it is in a minute So your payoff is the value of the good to you minus this thing I’m going to call bj bar, which I’ll say what it is in a minute, if you win.

[译文 34]

所以公开拍卖中人们的手还举着，而你看不到密封拍卖中人们在做什么，这使得它们并不完全相同。但它们之间显然有密切的相似性。现在我想问问，我想大家一直在想知道的问题，那就是，我应该在eBay上怎么出价？我们已经弄清楚，对于共同价值拍卖，如果你要重新估值，你知道，eBay上的共同价值拍卖，例如，如果你购买的商品是之后你想要转卖的商品，在这种情况下，我们已经知道你应该相当大地压低你对价值的估计。所以让我们走向另一个极端。让我们考虑私人价值。私人价值拍卖。这里根本没有共同价值，让我们假设这个拍卖要么是第二价格密封投标，要么是公开升价。总而言之，它要么是我们所说的B，要么是我们所说的C。你在那里，你在eBay上竞拍，而这是一个私人价值商品。关于其他人对这东西估值多少没有什么有趣的。那么你的价值是多少？你的价值是Vi。你可能会出Bi。所以这是你的价值。你的出价是Bi。你的收益是什么？所以我们的收益是Vi减去，不是减去Bi，而是减去，让我称之为bj̄，我一会儿会说什么。所以你的收益是商品对你的价值减去这个东西，我称之为bj̄，如果你是赢家的话。

[段 35]

So if ba is highest. and it’s 0 otherwise. Is that right? So what’s BJ bar? BJ bar is the highest other bid. So if my bid is the highest, my final payoff is the value of the good to me minus the highest other bid, the second highest bid, in other words. So question, how should I bid either on eBay here or for that matter in a second price steel bid auction? What’s the right way to bid in these auctions? Should I bid my value Should I bid under my value Let have a poll Who thinks you should bid over your value You only going to pay the second price so who thinks you should pay over your value Who thinks you should bid over your value Who thinks you should bid your value? Who thinks you should bid under your value? All right, everyone knows this. That’s good, that’s good. Okay, good, good, good, good. That’s correct. So the optimal thing to do is bid your value. Bid your value. value. Actually we can do better than that. We can show, we haven’t got time now, but we can show that bidding your value in a second place option is a weakly dominant strategy. So setting Bi equal to Vi is weakly dominant. dominant. It’s a weakly dominant strategy. So it’s really a very good idea.

[译文 35]

所以如果ba是最高的。否则就是0。对吧？那么bj̄是什么？bj̄是最高的另一个出价。所以如果我的出价是最高的，我的最终收益是商品对我的价值减去最高的另一个出价，也就是第二高的出价。那么问题，我应该在eBay上还是说在第二价格密封投标拍卖中怎么出价？这些拍卖中正确的出价方式是什么？我应该按我的价值出价吗？我应该低于我的价值出价吗？让我们做个民调。谁认为你应该高于你的价值出价？你只会支付第二价格，所以谁认为你应该支付高于你的价值？谁认为你应该高于你的价值出价？谁认为你应该按你的价值出价？谁认为你应该低于你的价值出价？好吧，每个人都知道这个。这是好的，这是好的。好的，好的，好的，好的。这是正确的。所以最优的做法是按你的价值出价。按你的价值出价。实际上我们可以做得比这更好。我们可以证明，我们现在没有时间，但我们可以证明在第二价格选项中按你的价值出价是一个弱占优策略。所以设定Bi等于Vi是弱占优的。它是一个弱占优策略。所以这真的是一个非常好的主意。

[段 36]

So there’s nothing subtle about bidding on eBay if it’s truly a private value auction. You’re going to stay in until it hits your value and then you’re going to drop out. I’ll leave proving that as an exercise What about if we switch from the second price auction or eBay to a first price auction, so now your payoff is Vi minus your own bid if you win and 0 otherwise. So the first price auction, going to get your value minus your own bid if you win and zero otherwise. Now how should you bid? This is a private value auction, so you don’t have to worry anymore about the winner’s curse. But nevertheless, how should you bid? Should you bid more than your value? Should you bid the same as your value? Or should you bid less than your value? Who thinks you should bid more than your value? Is there a poll? Who thinks you should bid your value? Who thinks you should bid less than your value? The answer is here, you should bid less than your value. Let’s see why. Bid less than Vi. Why? Because if you bid Vi, even if you win the auction, what’s going to be your payoff? 0. If you lose the auction, you get 0. If you win the auction, you get 0. If you bid less than Vi, if you shade your bid a bit, going to be your payoff?

[译文 36]

所以如果在eBay上竞拍真的是私人价值拍卖的话，没有什么微妙的讲究。你会一直留在里面直到价格达到你的价值，然后你就退出。我把证明这一点留作练习。如果从第二价格拍卖或eBay转换到第一价格拍卖会怎样？那么现在你的收益是Vi减去你自己的出价（如果你赢的话），否则就是0。所以第一价格拍卖，如果你赢的话，你会得到你的价值减去你自己的出价，否则就是0。现在你应该怎么出价？这是一个私人价值拍卖，所以你不必再担心赢家诅咒了。但尽管如此，你应该怎么出价？你应该高于你的价值出价吗？你应该和你的价值一样出价吗？还是你应该低于你的价值出价？谁认为你应该高于你的价值出价？有民调吗？谁认为你应该按你的价值出价？谁认为你应该低于你的价值出价？答案在这里，你应该低于你的价值出价。让我们看看为什么。低于Vi出价。为什么？因为如果你出价Vi，即使你赢了拍卖，你的收益是多少？0。如果你输掉拍卖，你得到0。如果你赢了拍卖，你得到0。如果你低于Vi出价，如果你稍微压低你的出价，你的收益会是多少？

[段 37]

Zero. If you lose the auction, you get zero. If you win the auction, you get zero. If you bid less than VI, if you shade your bid a bit, then if you win, which will happen with some probability, you’ll make some surplus. So here it’s flipped around. Here it turns out that bidding your value in the first price auction is weakly dominated. All right, where are we? We haven’t got much time. We want to get one more thing out of the class. So where are we here? What we’ve argued is in a second price auction, you’re going to bid your value, but the winner is only going to pay the second price. In a first price auction, you’re going to shade your bid under your value. You’re going to trade off two things. The two things you going to trade off are as you raise your bid you increase your chance of winning the auction but you get less surplus if you win So the first price auction is a classic trade marginal benefit and marginal cost The marginal benefit of raising your bid is you increase the probability of winning. The marginal cost is you’ll get less surplus if you win. But in summary, in the second price auction, I bid, quote, truthfully my value, but if I win, I only pay the second price.

[译文 37]

零。如果你输掉拍卖，你就得到零。如果你赢得拍卖，你也得到零。如果你出价低于你的真实价值，稍微压低一下出价，那么如果你赢了——这会有一定概率发生——你会获得一些剩余。这里情况就反过来了。在一级价格拍卖中，按照你的价值出价是弱被支配的。好了，我们说到哪里了？我们时间不多了。我们想从这节课中再讲一点东西。我们说到哪里了？我们论证的是，在二级价格拍卖中，你会按照你的价值出价，但赢家只需要支付第二高的价格。在一级价格拍卖中，你会压低你的出价，低于你的价值。你需要在两件事之间权衡。你提高出价会增加赢得拍卖的概率，但赢得后获得的剩余会减少。所以一级价格拍卖是经典的边际收益和边际成本的权衡。提高出价的边际收益是增加获胜概率。边际成本是赢得后你会获得更少的剩余。但总的来说，在二级价格拍卖中，我按我的价值如实出价，但如果我赢了，我只支付第二价格。

[段 38]

In the first price auction, I bid less than my value, but I pay what I bid if I win. And that leads us to the natural question. Which of these two auctions, at least in expectation, is going to raise more money? Let me make some assumptions. Let’s assume that it’s a purely private value environment. and let’s assume that these, let’s also assume that these values are completely independent, that my value is statistically completely independent of your value, they’re just completely idiosyncratic. And let assume that we all kind of basically similar except for that So we going to assume independence symmetry private values Most simple thing you can imagine And let ask the question again. Suppose I’m selling the good now. Would I rather sell this as a second price auction in which at least you’ll bid your values, but the winner will only pay the second value? Or would I rather sell it as a first price auction in which you’re all going to shade your values because of this effect of trying to get some surplus, but at least the winner will actually pay what they bid, which is going to generate more revenue for me. Let’s have a poll. Who thinks I’ll get more revenue from a second price auction? Who thinks I’ll get more revenue from a first price auction? This is the last poll of the class.

[译文 38]

在一级价格拍卖中，我出价低于我的价值，但如果我赢了，我支付我出的价格。这引导我们思考一个自然的问题。这两种拍卖方式，至少在期望值上，哪个会产生更多收入？让我做一些假设。假设这是一个纯私人价值环境。我们还假设这些价值是完全独立的，我的价值在统计上完全独立于你的价值，它们完全是特异性的。我们假设除了这一点外大家基本上是相似的。我们假设独立性、对称性、私人价值。这是你能想象的最简单的情况。让我们再次提出这个问题。假设我现在要出售这件商品。我更愿意将它作为二级价格拍卖来出售吗？在二级价格拍卖中至少你们会按价值出价，但赢家只需支付第二高的价格？还是我更愿意将它作为一级价格拍卖来出售？在这种拍卖中你们都会压低你们的出价，因为这种试图获得一些剩余的效果，但至少赢家实际上会支付他们出的价格，这会为我产生更多收入。让我们做一个投票。谁认为我会从二级价格拍卖中获得更多收入？谁认为我会从一级价格拍卖中获得更多收入？这是这节课的最后一次投票。

[段 39]

We can surely get no extensions here. Let’s try it again. No extensions. Last poll of the class. Last poll of the whole course. Who thinks you get more, I’m going to expect more revenue from a second price auction in which people will bid their values but only get the second price And who thinks they get more revenue from a first price auction in which people pay what they bid but they all shade their bids There a slight majority of a second price So here’s a great theorem. Provided we’re in the setting I said, pure private value, absolutely independent, and my value is completely statistically independent of your value, we’re all basically similar. Independent, symmetric private value. Both of those type of auctions we mentioned, the first price auction and the second price auction, And indeed, any other kind of auction which has the property that in equilibrium the person with the highest value ends up winning the good, any such auction, in expectation, yields exactly the same revenue. In expectation. The first price auction, the second price auction, or any other silly old auction you come up with, at least it has the property that in equilibrium the highest value wins. All of them generate the same revenue. expectation. But to find out why, you’re going to have to take another class in game three, because we’re done and I will see you at the review session.

[译文 39]

我们这里肯定得不到任何扩展。让我们再试一次。没有扩展。课堂上的最后一次投票。整个课程的最后一次投票。谁认为你会得到更多收入——我预期从二级价格拍卖中获得更多收入？在二级价格拍卖中人们会按他们的价值出价，但只会得到第二价格。谁认为他们会从一级价格拍卖中获得更多收入？在这种拍卖中人们支付他们出的价格，但他们都会压低他们的出价。选择二级价格的人略占多数。这是一个很棒的定理。只要我们处于我所说的设定中，纯私人价值、完全独立，我的价值在统计上完全独立于你的价值，我们基本上都是相似的。独立、对称、私人价值。我们提到的这两种拍卖，一级价格拍卖和二级价格拍卖，确实，任何其他类型的拍卖只要具有这样的特性：在均衡中价值最高的人最终赢得商品，任何这样的拍卖，在期望值上都会产生完全相同的收入。在期望值上。一级价格拍卖、二级价格拍卖，或者你想出的任何其他愚蠢的拍卖方式，至少它具有这样的特性：在均衡中最高价值者获胜。所有这些都会产生相同的期望收入。但要找出为什么，你得参加博弈论三的另一门课，因为我们要结束了，复习课上见。