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← 24. Asymmetric information: auctions and the winner's curse

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Showing Revision 1 created 07/12/2012 by Amara Bot.

  1. Professor Ben Polak:
    Where have my jars of coins
  2. got to?
    That isn't very far.
  3. They've only been on one row?
    Well whiz them along this row
  4. as fast as you can.
    Just shake and pass now.
  5. Everybody who has had access to
    those jars, can you please write
  6. down on your notebook--just
    write down,
  7. but don't show it to your
    neighbor--write down for each of
  8. those two jars how many coins
    you think are in the small jar
  9. and how many coins you think are
    in the large jar.
  10. How many coins you think are in
    the small jar and how many coins
  11. you think are in the large jar?
    Keep passing it along.
  12. All right, so today I want to
    talk about auctions.
  13. And just to put this in the
    context of the whole class,
  14. way back on the very first day
    of the class,
  15. we talked about different types
    of people playing games.
  16. We talked about evil gits
    versus indignant angels,
  17. and then for most of the
    course,
  18. really until this week,
    we've been assuming that you
  19. knew who it was you were
    playing.
  20. You knew your own payoffs but
    you also knew whom it was you
  21. were playing against or with.
    But the feature,
  22. the new feature of this week,
    has been that we're looking at
  23. settings where you don't
    necessarily know what are the
  24. payoffs of the other people
    involved in the game or
  25. strategic situation.
    So in the signaling model we
  26. looked at last time,
    the different types of worker
  27. had different types of payoffs
    from going to get an MBA,
  28. from going to business school,
    and they yielded different
  29. payoffs to you if you hired
    them.
  30. So we had to model the game
    where you didn't quite know the
  31. payoffs of the people you were
    playing against.
  32. Similarly, an auction--this is
    what we're going to study
  33. today--is such a setting.
  34. Typically, in an auction,
    you are competing or playing
  35. with or against the other
    bidders.
  36. But typically you don't know
    something crucial about those
  37. other bidders.
    You don't know how much they
  38. value the good in question.
    So there's a good up for sale,
  39. and you don't know how much
    they value that good.
  40. So I want to start off by
    thinking about a little bit of
  41. the informational structure of
    auctions and then we'll get into
  42. more detail as we go along.
    The first thing I wanted to
  43. distinguish are two extremes.
    At one extreme I want to talk
  44. about "common values" and at the
    other extreme I want to talk
  45. about "private values."
    So the idea of a common value
  46. auction is that the good that is
    for sale ultimately has the same
  47. value for whoever buys it.
    Now that doesn't mean they're
  48. all going to be prepared to bid
    the same amount because they may
  49. not know what that value is.
    For example,
  50. imagine an oil well.
    So there's an oil well out
  51. there.
    There's an oil reserve out
  52. there, and different companies
    are trying to estimate how much
  53. they want to bid for the right
    to draw oil out of this oil
  54. field.
    Each of them is going to make a
  55. little practice well and get
    some estimate of how much oil
  56. there is in the well,
    so they're going to bid
  57. different amounts.
    But at the end of the day what
  58. comes out of that well is the
    same for everybody.
  59. There is just one amount of oil
    in that well,
  60. and that oil is just worth one
    amount at the market price.
  61. So that's a classic example of
    a common value auction.
  62. The value of the good for sale,
    the true value if you like,
  63. is the same for all.
    We'll use the notation V to
  64. denote this common value that
    this object has.
  65. Now, the other extreme is
    private value and it's really
  66. such an extreme it's hard to
    think of good examples.
  67. But the idea is that the value
    of the good at hand,
  68. not only is it different for
    everybody,
  69. but my valuation of this good
    has no bearing whatsoever on
  70. your value for the good,
    and your value for the good has
  71. no bearing whatsoever on my
    value for the good.
  72. So here's a case where the
    value of the good,
  73. the ultimate value of the good
    in question,
  74. not only is it different for
    all, but, moreover,
  75. it's completely idiosyncratic
    and my value is irrelevant to
  76. you.
    So if you happen to buy this
  77. good and you learn that in fact,
    I valued it a lot,
  78. that makes no difference to how
    happy you feel at having bought
  79. the good.
    Now, these are extremes and
  80. most of reality lies between.
    I should give you the notation.
  81. Let's use V_i to be
    the private values where i
  82. denotes the player in question.
    These are extremes and most
  83. things lie in between.
    So we already mentioned that on
  84. this extreme,
    close to this extreme,
  85. you could think about the oil
    wells.
  86. Oil wells are pretty much
    common value goods.
  87. There's a certain amount of oil
    there and that's all there is to
  88. it.
    However, even there you could
  89. imagine that the different firms
    have different costs on
  90. extracting that oil or these
    different firms have their
  91. machinery occupied to different
    extents in other wells that
  92. they're digging.
    So even in that pure case,
  93. that seemingly perfect example
    of a common value,
  94. it probably isn't literally a
    common value.
  95. Or these different firms have
    different distances between the
  96. wells and their refineries.
    So the oil well is a good
  97. example of something that's
    close to common value but it
  98. isn't really literally common
    value, probably,
  99. in reality.
    One's tempted to say that homes
  100. are private value,
    after all, my valuation,
  101. my happiness from living in my
    house is not really affected by
  102. how happy you would feel living
    in my house.
  103. I don't really care if you
    would like to live in my house
  104. or if you wouldn't like to live
    in my house because I'm the
  105. person living in it.
    Is that right?
  106. But there's a catch here.
    What's the catch which makes
  107. homes not literally private
    value?
  108. What's the catch?
    The catch is that at some point
  109. in time I may want to resell my
    home.
  110. The home is a durable good.
    It's a consumption good,
  111. my living in it,
    that's a private value.
  112. But it's also an investment
    good, I'm going to want to
  113. resell that home at some point
    when I'm kicked out of Yale or
  114. whatever,
    and then at that point at which
  115. I sell it, I'm going to care a
    lot about how much you value it
  116. because that's going to affect
    the price that I'm going to get
  117. at the end of the day.
    So in the case of a home,
  118. it's somewhere between a
    private value and a common
  119. value.
    It's true that the consumption
  120. part might be private value,
    but the investment component
  121. introduces common values.
    So really for private values,
  122. for pure private values,
    we need to think about pure
  123. consumption goods.
    Goods that I consume,
  124. they have no investment value,
    they have no resale value.
  125. So think about some good being
    sold on eBay.
  126. It's a cake, say.
    So if I buy it,
  127. once I've eaten it,
    I can't resell it.
  128. I can't have my cake and resell
    it.
  129. So think about pure consumption
    goods over here.
  130. And even in these pure
    consumption goods I mustn't get
  131. any psychological value out of
    thinking I managed to get that
  132. cake and you didn't.
    So the private value case is
  133. really an extreme thing,
    but it turns out to be a useful
  134. abstraction when we come to
    consider things further.
  135. Now, where have my jars got to?
    So I've got certainly two rows
  136. I can play with here.
    Let's talk about this auction
  137. for the jars.
    So what we're going to do is
  138. we're going to have people bid
    for the value in the jar.
  139. They're going to put forward a
    bid.
  140. The highest bidder is going to
    win, and what they're going to
  141. win is the amount of money in
    the jar, but what they're going
  142. to pay is their bid.
    So what is that?
  143. Is that a common value or a
    private value?
  144. That's a common value.
    There is a certain amount of
  145. money in that jar.
    You don't know what it is,
  146. but there is a certain amount
    of money in that jar and that's
  147. the common value.
    So pretty much our jars of
  148. coins lie over here.
    They're probably even a purer
  149. example than the oil well.
    All right, now let me get the
  150. first two rows of the class,
    so this row here and this row
  151. here.
    All of you have now had a
  152. chance to have a look at the
    jars.
  153. Let me just get you to write
    down, without looking at each
  154. other, write down on your
    notepads--you've already written
  155. down how many coins you think
    are in the jar.
  156. For the large jar--we'll do the
    large jar first--write down your
  157. bid.
    Just so you can't cheat later
  158. on, write down your bid.
    We're playing this for real
  159. cash, so if you win you're going
    to have to pay me.
  160. So write down what you're going
    to bid.
  161. Well I might not hold it to you
    if it's too crazy,
  162. we'll see, but at least in
    principle we're playing for real
  163. cash.
    So write down your bid,
  164. without changing your bid show
    your neighbor your bid.
  165. Now, what I'm going to do
    is--if I can just borrow Ale a
  166. second--here's some chalk.
    Let me go along the row and
  167. find out what those bids were.
    Ale you want to record the bids?
  168. So we're going to record
    everybody's bid and we'll come
  169. back and talk about it
    afterwards.
  170. Where are those jars by the way?
    Let's have a look at
  171. the--Where's the jar gone?
    Whose got the large jar there?
  172. Yeah the woman in the corner.
    Hold up that large jar so that
  173. everyone can see it.
    That's the bid.
  174. It's coins in a Sainsbury's
    pesto jar.
  175. Sainsbury's pesto turns out to
    be quite good.
  176. All right, so I won't bother
    with names today.
  177. I'm just going to get your bids.
    Everyone's written down a bid.
  178. No one's going to cheat?
    So what is your bid?
  179. Student: $4.50.
    Professor Ben Polak:
  180. $4.50.
    Student: $3.00.
  181. Professor Ben Polak:
    Shout it out so everyone can
  182. hear.
    Student: $3.00.
  183. Student: $4.00.
    Student: $.99.
  184. Professor Ben Polak: All
    right, I'm going to pass this
  185. along so?
    Student: $.80.
  186. Student: $3.80.
    Professor Ben Polak:
  187. Shout louder than that,
    what was it?
  188. Student: $3.80.
    Professor Ben Polak:
  189. $3.80, go on.
    Student: $4.00.
  190. Professor Ben Polak:
    $4.00 again.
  191. Student: $2.09.
    Professor Ben Polak:
  192. $2.09.
    Student: $3.00.
  193. Student: $1.60.
    Student: $2.01.
  194. Professor Ben Polak:
    Sorry, the last one was what?
  195. Student: $2.01.
    Professor Ben Polak:
  196. $2.01 here, that was after $1.60
    though.
  197. Student: $.89.
    Professor Ben Polak:
  198. $.89.
    Student: This is for the
  199. big jar?
    Professor Ben Polak: The
  200. big jar.
    Student: $1.40.
  201. Professor Ben Polak:
    $1.40, all right.
  202. Now we get a second row's worth
    of people.
  203. Student: $1.41.
    Professor Ben Polak:
  204. $1.41.
    Student: $1.50.
  205. Professor Ben Polak:
    $1.50.
  206. Student: $3.00.
    Professor Ben Polak:
  207. $3.00.
    Student: $2.00.
  208. Professor Ben Polak:
    $2.00.
  209. Student: $4.50.
    Professor Ben Polak:
  210. $4.50.
    Student: $5.00
  211. Professor Ben Polak:
    $5.00, we're getting some high
  212. ones now.
    Student: $.01.
  213. Professor Ben Polak:
    $.01, okay.
  214. What's wrong with my jar?
    Okay.
  215. All right, pass that along.
    Student: $.80.
  216. Professor Ben Polak:
    That was an $.80.
  217. Student: $1.50.
    Professor Ben Polak:
  218. $1.50.
    Student: $1.59.
  219. Student: $1.00.
    Professor Ben Polak:
  220. $1.00.
    Student: $1.20.
  221. Professor Ben Polak:
    $1.20 and three more.
  222. Student: $1.50.
    Student: $1.50.
  223. Student: $2.00.
    Professor Ben Polak: All
  224. right, so we have lots of bids
    and the winner is?
  225. The last one was $2.00.
    I've actually forgotten how
  226. many coins were in here.
    Let me just remind myself.
  227. This was the large jar right?
    Okay now I know again.
  228. All right, so who is our winner
    there?
  229. We've got a $4.50 here,
    there's a $5.00.
  230. Okay so here's our winner,
    who's our winner?
  231. Let's have our winner stand up
    a second.
  232. So now a round of applause for
    our winner.
  233. Now, let's talk about how
    people bid, and why they bid
  234. that amount.
    Okay, so let's start with our
  235. winner.
    So why did you bid $5.00?
  236. Student: It looked like
    there could about $5.00 in
  237. there.
    Professor Ben Polak: All
  238. right, so I've forgotten your
    name, your name is?
  239. Student: Ashley.
    Professor Ben Polak: So
  240. Ashley is saying she bid roughly
    $5.00 because it looked like
  241. there was about $5.00 in there.
    Student: Plus you get
  242. the jar.
    Professor Ben Polak:
  243. Plus you get the jar,
    I'm not sure I'm throwing in
  244. the jar.
    Let's just sample a few other
  245. people and see what they say.
    What did you say again?
  246. Student: I said $1.60
    because I didn't want to over
  247. estimate it because then I'd
    have to pay you more than I'd
  248. get.
    Professor Ben Polak: All
  249. right, so what was your
    estimate?
  250. Student: My estimate was
    about $1.80 to $2.00 so I bid
  251. under that.
    Professor Ben Polak: So
  252. your estimate was $1.80 to $2.00
    and you bid around $1.60.
  253. Person next to you?
    Student: Well I guess
  254. $3.00 and same reasoning.
    I thought there would probably
  255. be about $4.00 and then I valued
    it at like $1.00.
  256. Professor Ben Polak: All
    right, so you thought there was
  257. about $4.00 worth of coin and
    you actually bid?
  258. Student: $3.00.
    Professor Ben Polak:
  259. $3.00 all right,
    so all of you actually wrote
  260. down initially how many coins
    you thought were in there,
  261. right?
    Is that right?
  262. Let's just get some idea of the
    distribution of those.
  263. So how many people thought
    there was less than $1.00 in
  264. there?
    Raise your hand:
  265. no shame here,
    just raise your hands.
  266. How many people thought there
    was between $1.00 and $1.50?
  267. How many people thought there
    was between $1.50 and $2.00?
  268. How many people thought there
    was between $2.00 and $2.50?
  269. How many people thought there
    was between $2.50 and $3.00?
  270. How about more than $3.50?
    Clearly the people who bid high
  271. did.
    So we have a whole range of
  272. estimates there,
    a wide range of estimates,
  273. a wide range of bids.
    And people are saying things
  274. like: well, I thought there was
    this many coins in there.
  275. Maybe I shaded down a little
    bit from the number of coins I
  276. thought was in there because I
    want to make some profit on
  277. this, is that right?
    That's kind of the explanations
  278. I'm hearing from people.
    What I want to suggest is
  279. that's not a very good way to
    bid in this auction.
  280. So let's just repeat what I
    think people did,
  281. and people can contradict me if
    this is wrong.
  282. I think most people,
    they shook this thing.
  283. They weighed it a bit.
    They figured out there was,
  284. let's say, $3.50 worth of
    pennies in there.
  285. And then they said,
    okay $3.50, so I'll bid $3.40,
  286. $3.30 something like that.
    So what's wrong with that?
  287. Well first of all,
    to reveal that there's
  288. something wrong with it,
    let me tell you how many coins
  289. were in there.
    In the larger jar there was
  290. $2.07.
    How many of you bid more than
  291. $2.07?
    Just raise your hands.
  292. Quite a few of you, all right.
    So what we see here is a number
  293. of people, including our winner,
    bid a lot more than the number
  294. of coins in the jar.
    What we find,
  295. by a lot, is that the winning
    bid was much,
  296. much greater than the true
    value.
  297. This is a common phenomenon in
    common value auctions.
  298. It's such a common phenomenon
    that it has a name.
  299. The name is the "winner's
    curse."
  300. It's the winner's curse.
    And the main lesson of the
  301. first half of today is going to
    be: let's figure out why there
  302. exists a winner's curse;
    let's try and avoid falling
  303. into a winner's curse;
    and maybe let's even figure out
  304. how to do better.
    So let's try and think through
  305. why it is we fall into a
    winner's curse.
  306. So one way to think about this
    is to think about naïve
  307. bidding in this context.
    So suppose people's strategy
  308. was actually to bid their
    estimate.
  309. I know that isn't what people
    did.
  310. Most people shaded their
    estimate a little bit.
  311. But most people bid pretty
    close to their estimate.
  312. What's going to happen in that
    instance is what?
  313. People are going to bid
    essentially what they think it's
  314. worth, and we just saw that
    fully half of you--I should say
  315. half the people we
    sampled--overestimated the
  316. number of coins in there.
    Is that right?
  317. Let's just have that show of
    hands.
  318. How many people,
    raise your hands again,
  319. let's be honest,
    if you thought there was more
  320. than $2.07 in there.
    So maybe roughly a half,
  321. maybe a little less than a half
    of you overestimated the number
  322. of coins in there.
    Now, what's that going to mean?
  323. It's going to mean all of those
    people who have this
  324. overestimate are going to
    overbid.
  325. But we can be a little bit more
    general and a little bit more
  326. rigorous about this.
    So let's try and be a little
  327. bit more general.
    So first of all,
  328. let's just make sure we
    understand what the payoffs are
  329. in this auction.
    The payoff in this auction is
  330. what?
    You get the true value,
  331. you get the number of
    coins--the number of pennies in
  332. the jar--minus your bid,
    if you are the highest;
  333. and you get 0 otherwise.
    I think it's straightforward,
  334. we all understand that's what
    the value is.
  335. And what do people do?
    People tried to estimate--this
  336. is not a mistake--people tried
    to estimate how many coins were
  337. in the jar.
    Now, in fact,
  338. the true number of coins in the
    jar was V which turned out be
  339. $2.07.
    But when people estimate it,
  340. they don't get it exactly
    right, neither here where you're
  341. shaking the jar,
    nor in the case of these oil
  342. samples.
    So what they actually
  343. estimate--each person forms an
    estimate, which we could call
  344. Y_i--and this
    Y_i we could think of
  345. as being the truth plus noise.
    So let's call it
  346. ε_i.
    Let's even put a tilde on it to
  347. make it clearer that it's a
    random term.
  348. So for some people
    ε_i is going to
  349. be a positive amount,
    which means they're going to
  350. overestimate the number of coins
    in the jar.
  351. And for some people
    ε_i is going to
  352. be a negative amount,
    which means they're going to
  353. underestimate the number of
    coins in the jar.
  354. Everyone agree with that?
    That's not a controversial
  355. statement, everyone okay with
    that?
  356. So let's think about the
    distribution of these
  357. Y_i's.
    Let's draw a picture that has
  358. on the horizontal axis all the
    different estimates that people
  359. could form of the number of
    coins in the jar.
  360. And let's anchor this by V,
    so here's V.
  361. And here is going to be,
    if you like,
  362. the probability of getting that
    estimate: so the frequency or
  363. probability of estimating
    Y_i given that
  364. V_i is there.
    So I don't know what the shape
  365. of this distribution is but my
    guess is it's kind of bell
  366. shaped.
    Is that right?
  367. So it probably looks something
    like this.
  368. That seem plausible?
    We could actually test this if
  369. we had time.
    We could actually go around all
  370. of you and get you to report
    what your estimates were,
  371. and we could plot that
    distribution and see if it is
  372. bell shaped.
    But my guess is,
  373. it's reasonable to assume its
    bell shaped.
  374. There's some central tendency
    to estimate something close to
  375. the truth.
    If I'd drawn this correctly I'd
  376. have its highest point at V.
    I haven't quite drawn it
  377. correctly.
    It's probably roughly symmetric.
  378. Okay, so now suppose that
    people's bidding strategy is
  379. pretty much what they reported.
    People are going to bid roughly
  380. their estimate of the number of
    coins in the jar.
  381. So suppose people bid
    B_i roughly equal to
  382. Y_i.
    So I know people are going to
  383. shade a little bit,
    but let's ignore that for now.
  384. So people are bidding roughly
    equal to Y_i.
  385. So what's going to happen here?
    Who's going to win?
  386. If this is the way in which the
    Y_i's emerge naturally
  387. in life--there's a true V and
    then people make some estimate
  388. of it which is essentially V
    plus noise--who's going to end
  389. up being the winner,
    the winner of the auction?
  390. It's going to be the person who
    has the highest estimate.
  391. So if there's really a lot of
    people the winner isn't going to
  392. be the person who estimated it
    correctly at V.
  393. The winner's going to be way
    out here somewhere.
  394. The winner is going to be way
    up in the right hand tail.
  395. Why?
    Because the winner will then be
  396. the i who's Y_i is the
    biggest, the maximum.
  397. The problem with this is the
    person whose Y_i is
  398. the biggest has what?
    They have the biggest error:
  399. the person whose Y_i
    is the max, i.e.,
  400. ε_i is the max.
    And that's exactly what
  401. happened.
    When we did estimates just now
  402. the person who won was the
    person, Ashley,
  403. who had estimated there to be
    roughly (maybe a little bit more
  404. than) $5.00 worth of coins in
    there.
  405. So I'm guessing,
    is this right,
  406. that no one else estimated more
    than $5.00 in these two rows,
  407. is that correct?
    No one estimated more than
  408. $5.00.
    So the person who had the
  409. highest estimate bid the most,
    which is pretty close to her
  410. estimate, and that caused her to
    lose money.
  411. She ends up owing me whatever
    it is, $1.93,
  412. which I will collect
    afterwards.
  413. So the winner's curse is caused
    by this.
  414. It's caused by:
    if people bid taking into
  415. account their own estimate and
    only their own estimates of the
  416. number of coins in the jar or
    the amount of oil in the oil
  417. well,
    then the winner ends up being
  418. the person with the highest
    estimate, which means the person
  419. with the highest error.
    So notice what this leads to.
  420. On average, the winning bid is
    going to be much,
  421. much bigger than the truth.
    Is that right?
  422. The biggest error is typically
    going to be way out in this
  423. right tail and that's going to
    mean people are going to lose
  424. money.
    All right, so this phenomenon
  425. is very general because common
    value auctions are very general.
  426. I already mentioned the oil
    fields.
  427. In the early period after World
    War II when the U.S.
  428. Government started auctioning
    out the rights to drill oil in
  429. the gulf, in the Gulf of Mexico,
    early on, it was observed that
  430. these companies,
    the winning companies,
  431. the companies who won the bid
    each time was losing money.
  432. It was great for the
    government, but these companies
  433. were consistently losing money,
    they were consistently
  434. overbidding.
    Be careful, it wasn't that the
  435. companies as a whole were
    overbidding.
  436. It was that the winning bid was
    over bidding:
  437. it was the winner's curse.
    Over time, companies figured
  438. this out and they've figured out
    that they shouldn't bid as much,
  439. and this in fact went away.
    But you also see this effect in
  440. other places where naïve
    bidders are involved.
  441. So for example,
    those people who have been
  442. following the baseball free
    agent market,
  443. I think you could argue
    that--someone can do an
  444. empirical test of this--you
    could argue that the winning
  445. bids on free agents in the
    baseball free agent market end
  446. up being horrible overbids for
    the same reason.
  447. The team who has the highest
    idiosyncratic estimate of the
  448. person's value ends up hiring
    that player,
  449. but the highest idiosyncratic
    value tends to be too high.
  450. Similarly, perhaps more
    importantly, if you look at
  451. IPO's, initial public offerings
    of companies,
  452. they tend to sell too high.
    The baseball one I haven't got
  453. the data, but the IPO's we know
    that there's a tendency for
  454. IPO's,
    initial public offerings of
  455. companies, to have too high a
    share price and for those shares
  456. to fall back after awhile.
    There may be a little bit of
  457. initial enthusiasm,
    but then they fall back.
  458. Why?
    Again, the people with the
  459. highest estimates of the value
    of the company end up winning
  460. the company,
    and if they're not
  461. sophisticated about the way they
    bid then they overbid.
  462. So this is a serious problem
    out there and it raises the
  463. issue: well, how should I
    correct this?
  464. I might, in life,
    be involved in an auction as a
  465. bidder for something that has a
    common value element.
  466. How should I think about how I
    should bid?
  467. We've learned how we shouldn't
    bid.
  468. We shouldn't just bid my
    estimate minus a little.
  469. So how should we think about it?
    Now, to walk us towards that
  470. let me try and think about a
    little bit more about the
  471. information that's out there.
    Let's go back to our oil well
  472. example.
    Each of these oil companies
  473. drills a test well in the oil
    field, and from this test well
  474. each of them gets an estimate of
    Y_i.
  475. So you can imagine someone
    doing a test drill into my jar
  476. of coins, and when they do this
    test drill into this jar of
  477. coins they form an estimate
    Y_i.
  478. And suppose that your estimate
    of the number of coins in the
  479. jar or the amount of oil in the
    oil well,
  480. suppose that your particular
    one is equal to 150.
  481. Then, if I then asked you the
    question--not to bid--but I
  482. asked you the question how many
    coins do you think are in the
  483. jar.
    Your answer would be 150.
  484. That would be your best
    estimate.
  485. But suppose I then told you
    that your neighbor,
  486. let's go back to Ashley again.
    So Ashley's estimate was,
  487. let's say, it was 150--it
    wasn't, but let's say it was
  488. 150.
    And suppose I went to her
  489. neighbor and asked her neighbor.
    And her neighbor said:
  490. actually, I think there's only
    130 in there.
  491. So suppose Ashley now knows
    that she did a little test,
  492. she thinks there's 150.
    But she now knows that her
  493. neighbor has done a similar test
    and he thinks there's only 130.
  494. Now what should be Ashley's
    estimate of the number of coins
  495. in the jar?
    Somewhere in between;
  496. so probably somewhere between
    150 and 130, maybe about 140,
  497. but certainly lower than 150.
    Is that right?
  498. So if I told you that someone
    else had an estimate that was 20
  499. lower than yours that would
    cause you to lower your belief
  500. about how many coins was in the
    jar.
  501. Now let's push this a little
    harder.
  502. Suppose I told you not that
    your neighbor had an estimate of
  503. 130, but just that your neighbor
    had an estimate that was lower
  504. than 150.
    I'm not going to tell you
  505. exactly what your neighbor
    estimates, I'm just going to
  506. tell you that his estimate is
    lower than yours.
  507. So your initial belief was
    there was 150 coins in this jar,
  508. but now I know that my neighbor
    thinks there's fewer than 150.
  509. Do you think your belief is
    still 150 or is it lower?
  510. Who thinks it's gone up?
    It hasn't gone up.
  511. Who thinks it's gone down?
    It's gone down.
  512. I don't know exactly by how
    much to pull it down,
  513. but the fact that I know that
    my neighbor has a lower estimate
  514. than me suggests that I should
    have a lower estimate than 150.
  515. Now I'm going to tell you
    something more dramatic.
  516. Suppose I go to Ashley and say
    your initial estimate
  517. was--actually it wasn't 150,
    it was $5.00--so let's do it.
  518. So your initial estimate was
    500 pennies.
  519. And I'm not going to tell you
    what your neighbor's estimate
  520. was.
    I'm not going to tell you what
  521. your neighbor's,
    neighbors estimate was.
  522. But I'm going to tell you that
    every single person in the row,
  523. in the two rows other than you,
    had an estimate lower than
  524. $5.00.
    So Ashley's estimate was $5.00,
  525. but I'm now going to tell her
    that every single person in the
  526. room had a lower estimate than
    hers.
  527. So what I'm going to tell her
    is that Y_j <
  528. Y_i for all_
    j,_ for all the
  529. other people.
    But I claim that if you tell me
  530. that everybody else--there were
    probably what,
  531. 30 other people there--has an
    estimate lower than
  532. mine--everyone else--what should
    I now estimate?
  533. What should happen to my
    estimate?
  534. It's going to come down a lot,
    is that right?
  535. If my estimate was $5.00 but I
    know everybody else,
  536. not just one person,
    but everybody else had a lower
  537. estimate,
    then my guess of the number of
  538. coins in the jar has come down a
    whole lot.
  539. But what?
    But that's exactly what Ashley
  540. knows as soon as she found out
    that she's won the auction.
  541. If people are bidding their
    values--sorry not their
  542. values--if people are bidding
    their estimates,
  543. then as soon as Ashley
    discovers she's won,
  544. she's going to say:
    oh bother, I now know that my
  545. estimate was too high.
    She may say something more
  546. extravagant than bother,
    but at the very least,
  547. she is going to say:
    oh bother,
  548. I now know that everyone else
    had a lower estimate than me,
  549. and therefore my estimate of
    $5.00 is too high.
  550. So what's going to happen is if
    people start bidding their
  551. estimates or close to their
    estimates,
  552. then once they've won,
    they're going to learn exactly
  553. this.
    They're going to learn that
  554. everyone else's estimate was
    lower than theirs and they're
  555. going to regret their choices.
    It can't be a good idea--it
  556. can't be an equilibrium--for
    people to make choices which
  557. they're going to regret if they
    win.
  558. That's crazy.
    So we need to think about how
  559. to correct for that.
    So how do we correct for it?
  560. Now let's talk about this a
    little bit harder.
  561. Each of you,
    in your bidding for this jar of
  562. coins, I claim you only really
    care about how many coins were
  563. in the jar, in one circumstance.
    What's the only circumstance in
  564. which you care at all how many
    coins are in the jar?
  565. If you win.
    I claim you only care how many
  566. coins are in the jar,
    or how much oil is in the well,
  567. if you win, if your bid is the
    winning bid.
  568. If your bid is the winning bid
    what do you know?
  569. You know that your estimate was
    the highest estimate in the room
  570. (at least if this equilibrium
    has the property that bids are
  571. increasing in estimates per se,
    which is not much to expect).
  572. So you know in this case,
    you would have an estimate
  573. Y_i that was at least
    as big as Y_j for all
  574. the other people in the room.
  575. So where are we?
    You only care how many coins
  576. are in the jar if you win,
    and if you win you know your
  577. estimate was the highest.
    So what's the relevant estimate?
  578. The relevant estimate of the
    number of coins in the jar for
  579. you when you're bidding,
    the relevant estimate is not
  580. how many coins do I think is in
    this jar, that's the naïve
  581. thing.
    The relevant estimate is:
  582. how many coins do I think is in
    this jar given my shaking of it
  583. and given the fact that I
    have won the auction,
  584. given the supposition that I
    might win the auction.
  585. So the relevant estimate when
    bidding is how many coins do I
  586. think are there given my initial
    guess,
  587. Y_i,
    and given that Y_i is
  588. bigger than Y_j.
    Now, notice this is kind of a
  589. weird thing.
    It's a counter factual thing.
  590. I don't know at the time at
    which I'm bidding,
  591. I don't know that I'm going to
    win.
  592. But nevertheless,
    I should bid as if I knew I was
  593. going to win,
    because I only care in the
  594. circumstance in which I win.
    So the way in which I should
  595. estimate the number of coins in
    the jar, and indeed,
  596. the way in which I should bid
    is, I should bid the number of
  597. coins I would think were in the
    jar if I won [correction:
  598. less a few].
    Say that again,
  599. I should bid [correction:
    fewer than]
  600. the number of coins I would
    think were in the jar if my bid
  601. ends up being the winning bid.
    So the lesson here is,
  602. bid as if you know you win.
    Now why is that a good idea?
  603. Let's go back to this case of
    now you discover you've won.
  604. Provided you bid as if you know
    you won, when you win you're not
  605. going to be disappointed because
    you already took that
  606. information into account.
    But if you bid not as if you
  607. won, you failed to take into
    account the possibility of
  608. winning,
    then winning's going to come as
  609. a shock to you and cause regret.
    So the only way to prevent this
  610. ex-post regret,
    the only way to bid optimally,
  611. is to bid as if you know you're
    going to win.
  612. Estimate the number of coins
    not on your own sample but on
  613. the belief that your sample is
    the biggest sample.
  614. Question?
    Student: I don't
  615. understand what the difference
    is between bidding,
  616. sorry,
    I don't understand what the
  617. difference is between bidding as
    if you know you win and what if
  618. you won right?
    Because if you bid,
  619. like whenever you bid,
    you're bidding the number that
  620. you think,
    oh well, I think there are this
  621. many coins in the jar,
    so if I win I don't want to bid
  622. too many so that I don't lose,
    right?
  623. Professor Ben Polak:
    Good.
  624. Student: So how is that
    different from bidding as if you
  625. know you win versus if you won?
    Professor Ben Polak:
  626. Good question.
    So how is it different to say
  627. bidding as if I know I win?
    Let me try and say it again.
  628. So what you're going to do is
    you're going to think of the
  629. following thought experiment.
    Suppose you told me I won,
  630. now how many coins do I think
    are in the jar?
  631. Let me bid that amount.
    So before we even do the bid,
  632. let's do the following thought
    experiment.
  633. You're figuring out how many
    coins you think are there.
  634. Now I say, suppose it turns out
    that your estimate's the highest
  635. estimate, now how many coins do
    you think are there?
  636. That's what you should bid
    [correction: minus a little].
  637. I'm arguing that being told
    that your estimate's the highest
  638. is going to drag down that
    estimate a long way.
  639. But the key idea is if you bid
    as if you know you win then you
  640. won't regret winning and that's
    what you want to avoid.
  641. You want to avoid the winner's
    curse.
  642. Now let's see how that goes on,
    let me swap places with Ale
  643. again.
    And let's see if we can
  644. actually very quickly just do
    one row on the second jar.
  645. So this is the yellow mic.
    So same group of people,
  646. let me get people to shout
    these out fairly quickly so that
  647. we move on.
    So these two rows,
  648. write down your bid on the
    smaller jar now.
  649. This is your bid,
    not your estimate.
  650. Write down your bid on the
    smaller jar.
  651. As fast as we can go,
    just shout out a number.
  652. Student: $.40.
    Professor Ben Polak:
  653. $.40.
    Student: $1.00.
  654. Professor Ben Polak:
    $1.00.
  655. Student: $1.20.
    Professor Ben Polak:
  656. $1.20.
    Student: $1.50.
  657. Professor Ben Polak:
    $1.50.
  658. Student: $.98.
    Professor Ben Polak:
  659. $.98.
    Student: $1.00.
  660. Professor Ben Polak:
    $1.00.
  661. Student: $.90.
    Professor Ben Polak:
  662. $.90.
    Student: $.75.
  663. Professor Ben Polak:
    $.75.
  664. Student: $1.60.
    Professor Ben Polak:
  665. $1.60.
    Student: $1.50.
  666. Professor Ben Polak:
    $1.50.
  667. Student: $1.40.
    Professor Ben Polak:
  668. $1.40, okay I'm going to pass
    this in, so I'll go to the other
  669. side.
    Keep shouting them out.
  670. Student: $.95.
    Student: $.80.
  671. Professor Ben Polak:
    $.80.
  672. Student: $.50.
    Professor Ben Polak:
  673. $.50.
    Student: $.75.
  674. Student: $1.25.
    Professor Ben Polak:
  675. $1.25.
    Student: $1.50.
  676. Student: $1.30.
    Professor Ben Polak:
  677. $1.30.
    Student: $1.25.
  678. Professor Ben Polak:
    $1.25.
  679. Student: $1.09.
    Professor Ben Polak:
  680. $1.09.
    Student: $1.15.
  681. Professor Ben Polak:
    $1.15 and?
  682. Student: $.80.
    Professor Ben Polak:
  683. $.80, did I get everybody?
    $.80 was the last one.
  684. So okay the bids came down
    partly because the jar was
  685. smaller of course,
    which is cheating.
  686. But let me just tell you--let's
    find out who the winner was
  687. first of all.
    So $1.60 is the winner and it
  688. turns out that the number of
    coins in this jar was $1.48.
  689. So what happened here?
    I think people took into
  690. account--people did lower their
    bids below the estimates.
  691. Let's just check actually,
    so who was my $1.60 person?
  692. Stand up my $1.60 person,
    so how many coins did you think
  693. were in there?
    Student: $1.60.
  694. Professor Ben Polak:
    $1.60, your name is?
  695. Student: Robert.
    Professor Ben Polak: So
  696. Robert thought there was,
    hang on, you bid $1.60,
  697. how many coins did you think
    was in there?
  698. Student: $1.60.
    Professor Ben Polak:
  699. $1.60, I'm not doing well here
    am I?
  700. So what am I trying to convince
    you to do here?
  701. Let me find some other bidders,
    so what did you bid?
  702. Student: $1.00.
    Professor Ben Polak:
  703. $1.00, how many coins do you
    think were in there?
  704. Student: $1.25.
    Professor Ben Polak:
  705. $1.25, okay, so how many of
    you--be honest now--how many of
  706. you bid significantly below your
    estimate?
  707. So raise your hands,
    how many of you bid below your
  708. estimate?
    Good, so we're learning
  709. something.
    I feel like this is the
  710. twenty-fourth lecture,
    I should be able to teach you
  711. something.
    Okay, so the idea here is:
  712. in a common value auction you
    need to shade your bid
  713. considerably.
    In fact, most of these bids,
  714. even though you were shading
    your bid considerably,
  715. most of you didn't shade it
    enough.
  716. So even taking this into
    account, even taking into
  717. account the lesson of the day,
    even with that into account,
  718. a number of you are still
    overbidding.
  719. So what's the take away lesson?
    If you're in a common value
  720. auction, you need to bid as if
    you have been told that your
  721. estimate is the highest
    estimate.
  722. That means you need to shade
    your estimate a lot.
  723. If you don't do this you'll win
    a lot of auctions,
  724. and you'll be very unhappy.
    All right, now we're not done
  725. here, let me move forward by
    moving away now just from common
  726. value auctions.
    So far we've focused on common
  727. value auctions and we've focused
    on a particular structure of
  728. auction.
    But I also want to talk about
  729. different types of auctions
    themselves because one
  730. phenomenon you're going to be
    seeing out there a lot these
  731. days is that people run
    different structures of
  732. auctions.
    And auctions are getting more
  733. and more important in the U.S.
    economy.
  734. It used to be that auctions
    were something you thought of as
  735. a pretty rare event.
    You'd see them when people were
  736. selling cattle,
    and you'd see them people were
  737. selling art but that was pretty
    much it.
  738. But now you see auctions
    everywhere.
  739. We see auctions on eBay.
    We see auctions for the
  740. spectrum.
    Pretty much everything is
  741. auctioned these days.
    So auctions are becoming
  742. important.
    In fact, at Yale this year,
  743. we had a class solely devoted
    to auctions.
  744. We're having one day of this
    class devoted to auctions,
  745. but they had a whole 24
    lectures on auctions,
  746. it's that important.
    One thing we should realize is
  747. that there are lots of different
    types of auctions.
  748. So let's talk about four
    different types of auctions.
  749. Let's call them A, B, C, and D.
    So the first type of auction is
  750. a first-price,
    sealed-bid auction.
  751. And that's what we just did.
    Everybody wrote down their bid
  752. on a piece of paper.
    And the winner was the person
  753. with the highest bid,
    and they paid their bid:
  754. Ashley in the first case,
    Jonathon in the second--Robert
  755. in the second one.
    So a first-priced sealed-bid
  756. auction is what we just did,
    and that's a typical auction
  757. you might see,
    for example,
  758. in house sales.
    Here's another type of auction
  759. though.
    So this sounds crazy,
  760. but let me write it up anyway.
    You could imagine a
  761. second-price sealed-bid auction.
    So what happens in a
  762. second-price,
    sealed-bid auction?
  763. Everybody writes down their
    bid, each player writes down
  764. their bid.
    The highest bidder gets the
  765. goods so that's the same as
    before.
  766. But now instead of paying the
    bid that they wrote down,
  767. they pay the second highest
    bid.
  768. So the idea is the winner pays
    the second bid.
  769. The winner is the person with
    the highest bid,
  770. but they pay the second bid.
    So that seems crazy doesn't it?
  771. It seems a bit crazy.
    These are sometimes called
  772. Vickrey auctions.
    And Vickrey won the Nobel
  773. Prize, so it can't be that
    crazy.
  774. We'll come back and talk about
    it.
  775. Here's two other kinds of
    auctions.
  776. We can think about an ascending
    open auction.
  777. So this is what you all think
    of when we say auction.
  778. This is what happens at a
    cattle auction or an art
  779. auction, in which people are
    shouting out bids.
  780. One way to think about this is,
    if we were auctioning off
  781. something in the class today,
    is that everybody who is still
  782. in the auction would raise their
    hands, and,
  783. as the bid got higher and
    higher, some of you would start
  784. dropping out.
    And eventually,
  785. when there's only one hand
    left, that person would win the
  786. auction.
    Is that right?
  787. So that's a version of an
    ascending open auction.
  788. Everybody raises their hands
    when the price is 0 and,
  789. as the price goes up,
    hands go down until there's
  790. only one hand left.
    But we can also imagine another
  791. crazy auction,
    which is a descending open
  792. auction.
    So how does a descending open
  793. auction--So I should just say
    this open ascending one is what
  794. you typically see on eBay.
    What's a descending open
  795. auction?
    A descending open auction is
  796. the same idea,
    almost, except instead of
  797. starting the prices at 0 and
    going up,
  798. I'll start the price at
    infinity and go down.
  799. So now, if I start the price at
    infinity, none of you have your
  800. hands up I hope.
    And then as the price goes
  801. down, eventually one of you is
    going to raise their hands,
  802. and then you get that good and
    pay that amount.
  803. So this auction happens in the
    real world.
  804. It used to happen in a place
    called Filene's Basement.
  805. When I was a graduate student
    struggling to have enough money,
  806. there was a place in Boston
    called Filene's Basement,
  807. which would sell clothing in
    this way.
  808. So you go and pick out the
    suits you needed for your
  809. horrible job interview,
    and the price would come down
  810. each week, and you'd hope that
    no one bought it before you did.
  811. Sometimes it's called a Dutch
    auction.
  812. So here's four kinds of
    auctions.
  813. Two of them seem pretty
    familiar.
  814. So A and C sound like familiar
    kind of auctions that you're
  815. used to seeing,
    and B and D seem a little
  816. weird.
    So the first thing I want to
  817. convince you of is that B and D
    are not as weird as they seem.
  818. So let's look at these crazy
    auctions.
  819. The first thing I want to claim
    is that auction D is really the
  820. same as auction A.
    So let's just remind ourselves
  821. what those two auctions are.
    Auction A is--it's exactly the
  822. auction we just did for the
    coins.
  823. Everybody writes down their bid.
    We open all the envelopes.
  824. And the winner is the person
    with the highest bid written
  825. down, and they pay that.
    The descending open auction:
  826. nobody bids,
    nobody bids,
  827. nobody bids,
    nobody bids,
  828. suddenly somebody bids,
    and then they pay that amount.
  829. Why are those two auctions the
    same?
  830. Well, think about that
    descending open auction.
  831. During that descending open
    auction, each of you may have
  832. written down in your head--it's
    useful to think of it this
  833. way--you've written down in your
    head the number at which you're
  834. going to raise your hand.
    Is that right?
  835. So when I was a graduate
    student waiting for my suit to
  836. come down in price so I can
    afford it,
  837. and I know what the number is,
    and from your point of view,
  838. that's a sealed bid for me.
    At the end of the day whoever
  839. has that highest intended bid,
    that highest sealed bid,
  840. will end up winning the suit
    and they'll pay their bid.
  841. So from a strategic point of
    view the descending open auction
  842. and the sealed first price
    auction are the same thing.
  843. The person who has the highest
    bid, the highest strategy,
  844. wins.
    And they pay their bid.
  845. You don't get to see anyone
    else's strategy until it's too
  846. late.
    So D is equal to A.
  847. What about B and D?
    So I claim that B and D are not
  848. the same but they're very
    closely related.
  849. Sorry B and C.
    So C is what?
  850. C is our eBay auctions,
    our classic auction you're all
  851. used to playing on eBay.
    And B is this slightly crazy
  852. thing where we all write down
    bids and the winner is the
  853. person who has the highest bid
    but they only pay the second
  854. amount.
    Now why am I saying that's the
  855. same as our eBay auction in some
    ways?
  856. Well let's think about the eBay
    auction.
  857. Here you are playing the eBay
    auction, so all of you have your
  858. hands up meaning you're still
    in, and the price is going up.
  859. The price is going up over
    time, and all of you have your
  860. hands up, you're still in.
    Each of you has some strategy
  861. in mind which is what?
    The strategy is when am I going
  862. to lower my hand?
    What's the highest price I'm
  863. going to pay for this object?
    So your strategy in the classic
  864. eBay auction is:
    the price at which I lower my
  865. hand.
    Who wins in that open ascending
  866. auction?
    The person who has the highest
  867. intended bid.
    The person whose hand is up at
  868. the end is the person whose
    intended bid is the highest.
  869. But what amount do they pay?
    When does the auction stop?
  870. It stops when the second to
    last hand goes down.
  871. So if I'm the winning bid in an
    open ascending auction my hand
  872. is still up.
    You don't know what I was
  873. wiling to pay.
    What I'm actually going to pay
  874. is the price of the last person
    whose hand went down.
  875. I'm going to pay the bid of the
    person whose amount that they
  876. were going to pay is the second
    highest amount.
  877. Does that make sense?
    So in an ascending open auction
  878. the winner, the person who has
    the highest intended bid,
  879. actually pays the highest
    intended bid of the second
  880. highest player.
    So an ascending open auction is
  881. structurally very similar to
    these sealed bid auctions,
  882. which is really why the sealed
    bid auctions are interesting.
  883. Now, having said that,
    they're not exactly the same,
  884. and the reason they're not
    exactly the same is that if in
  885. fact the good for sale has
    common value then we might learn
  886. something by the fact that the
    hands are up.
  887. So the fact that people's hands
    are still up in the open
  888. auction, whereas you can't see
    what people are doing in the
  889. sealed auction,
    makes these not identical,
  890. but there's clearly a close
    similarity between them.
  891. Now, let's ask,
    I guess, the question you've
  892. been wondering about,
    which is how should I bid at
  893. eBay?
    We figured out that for the
  894. common value auction on eBay,
    for example,
  895. if the good you're buying is a
    good you're later on going to
  896. want to resell,
    in that case we already know
  897. that you should shade your
    estimate of the value
  898. considerably.
    So let's go to the other
  899. extreme.
    Let's consider a private value
  900. auction.
    There's no common value here at
  901. all and let's assume that this
    auction is either second-price
  902. sealed-bid or open ascending.
    To summarize,
  903. it's either what we call B or
    what we call C.
  904. So there you are,
    you're bidding on eBay,
  905. and it's a private value good:
    there's nothing interesting
  906. about how much anyone else
    values this thing.
  907. So what's your value?
    Your value is V_i.
  908. You might bid B_i.
    So this is your value.
  909. Your bid is B_i.
    And what's your payoff?
  910. Your payoff is V_i
    minus--it's not minus
  911. B_i.
    What's it minus?
  912. It's going to be minus
    B_jbar,
  913. and I'll say what it is in a
    minute.
  914. So your payoff is:
    the value of the good to you
  915. minus this thing I'm going to
    call B_jbar (which
  916. I'll say what it is in a minute)
    if you win,
  917. so if B_i is highest.
    And it's 0 otherwise.
  918. Is that right?
    So what's B_jbar?
  919. B_jbar is the highest
    other bid.
  920. So if my bid is the highest,
    my final payoff is the value of
  921. the good to me minus the highest
    other bid, the second highest
  922. bid, in other words.
    So question,
  923. how should I bid either on eBay
    here or for that matter in a
  924. second-priced,
    sealed-bid auction:
  925. what's the right way to bid in
    these auctions?
  926. Should I bid my value?
    Should I bid under my value?
  927. Let's have a poll.
    Who thinks you should bid over
  928. your--you're only going to pay
    the second price--so who thinks
  929. you should pay over your value?
    Who thinks you should bid over
  930. your value?
    Who thinks you should bid your
  931. value?
    Who thinks you should bid under
  932. your value?
    Everyone knows this that's
  933. good, okay good,
    that's correct.
  934. So the optimal thing to do is
    bid your value.
  935. Actually we can do better than
    that, we can show--we haven't
  936. got time now--but we can show
    that bidding your value in a
  937. second price auction is a weakly
    dominant strategy.
  938. So setting B_i =
    V_i is weakly
  939. dominant.
    It's a weakly dominant
  940. strategy:.
    so it's really a very good idea.
  941. So there's nothing subtle about
    bidding on eBay if it's truly a
  942. private value auction.
    You're going to stay in until
  943. it hits your value and then
    you're going to drop out.
  944. I'll leave proving that as an
    exercise.
  945. What about if we switch from
    the second price auction,
  946. or eBay, to a first-price
    auction?
  947. So now your payoff is
    V_i minus your own bid
  948. if you win and 0 otherwise.
    So the first price auction
  949. you're going to get your value
    minus your own bid if you win,
  950. and 0 otherwise.
    Now how should you bid?
  951. Remember this is a private
    value auction,
  952. so you don't have to worry
    anymore about the winner's
  953. curse.
    But nevertheless,
  954. how should you bid?
    Should you bid more than your
  955. value?
    Should you bid the same as your
  956. value?
    Or should you bid less than
  957. your value?
    Who thinks you should bid more
  958. than your value?
    Let's have a poll.
  959. Who thinks you should bid your
    value?
  960. Who thinks you should bid less
    than your value?
  961. Yeah, the answer is:
    here you should bid less than
  962. your value.
    Let's see why.
  963. Bid less than V_i.
    Why?
  964. Because if you bid
    V_i,
  965. even if you win the auction,
    what's going to be your payoff?
  966. 0.
    If you lose the auction you get
  967. 0, if you win the auction you
    get 0.
  968. If you bid less than
    V_i,
  969. if you shade your bid a bit,
    then, if you win,
  970. which will happen with some
    probability, you'll make some
  971. surplus.
    So here it's flipped around.
  972. Here it turns out that bidding
    your value in the first-price
  973. auction is weakly dominated.
    All right, where are we.
  974. We haven't gotten much time.
    We want to get one more thing
  975. out of the class,
    so where are we here?
  976. What we've argued is:
    in a second-price auction
  977. you're going to bid your value,
    but the winner's only going to
  978. pay the second price.
    In a first price auction you're
  979. going to shade your bid under
    your value.
  980. You're going to trade off two
    things.
  981. The two things you're going to
    trade off are:
  982. as you raise your bid,
    you'll increase your chance of
  983. winning the auction,
    but you'll get less surplus if
  984. you win.
    So the first-price auction is a
  985. classic trade off:
    marginal benefit and marginal
  986. cost.
    The marginal benefit of raising
  987. your bid is you increase the
    probability of winning.
  988. The marginal cost is you'll get
    less surplus if you win.
  989. But in summary,
    in the second-price auction I
  990. bid "truthfully my value," but
    if I win I only pay the second
  991. price.
    In the first price auction I
  992. bid less than my value but I pay
    what I bid if I win.
  993. That leads us to the natural
    question.
  994. Which of these two auctions,
    at least in expectation,
  995. is going to raise more money?
    Let's make some assumptions.
  996. Let's assume that it's a purely
    private value environment.
  997. And let's also assume that
    these values are completely
  998. independent, that my value is
    statistically completely
  999. independent of your value:
    they're just completely
  1000. idiosyncratic.
    Let's assume that we're all
  1001. kind of basically similar except
    for that.
  1002. So I'm going to assume
    independence,
  1003. symmetry, private values:
    most simple thing you can
  1004. imagine.
    Let's ask the question again.
  1005. So I'm selling the good now,
    would I rather sell this as a
  1006. second-price auction in which at
    least you'll bid your values but
  1007. the winner will only pay the
    second value;
  1008. or would I rather sell it as a
    first price auction in which
  1009. you're all going to shade your
    values because of this effect of
  1010. trying to get some surplus,
    but at least the winner will
  1011. actually pay you what they bid.
    Which is going to generate more
  1012. revenue for me?
    Let's have a poll.
  1013. Who thinks I should sell
    it--Who thinks I'll get more
  1014. revenue from a second price
    auction?
  1015. Who thinks I'll get more
    revenue from a first price
  1016. auction?
    This is the last poll of the
  1017. class.
    We can surely get no
  1018. abstentions here.
    Let's try it again,
  1019. no abstentions:
    last poll of the class,
  1020. last poll of the whole course.
    Who thinks I can expect more
  1021. revenue from a second price
    auction in which people will bid
  1022. their values but I only get the
    second price?
  1023. Who thinks I get more revenue
    from a first price auction in
  1024. which people pay what they bid,
    but they all shade their bids?
  1025. There's a slight majority of
    the second price.
  1026. So here's a great theorem.
    Provided we're in the setting I
  1027. said--pure private value,
    absolutely independent,
  1028. my value is completely
    statistically independent of
  1029. your value, and we're all
    basically similar--independent,
  1030. symmetric, private value--both
    of those type of auctions we
  1031. mentioned, the first price
    auction and the second price
  1032. auction,
    and indeed, any other kind of
  1033. auction which has the property
    that in equilibrium,
  1034. the person with the highest
    value ends up winning the good.
  1035. Any such auction in expectation
    yields exactly the same revenue,
  1036. in expectation.
    The first price auction,
  1037. the second price auction--or
    any other silly old auction you
  1038. come up with,
    at least it has the property
  1039. that in equilibrium,
    the highest value wins--all of
  1040. them generate the same revenue
    in expectation.
  1041. But to find out why,
    you're going to have to take
  1042. another class in Game Theory.
    We're done and I will see you
  1043. at the review session.