1 00:00:00,000 --> 00:00:05,430 Hi, Welcome back, In this set of lectures we are talking about mechanism design. And 2 00:00:05,430 --> 00:00:09,438 the idea here, is that you want to use models to help us design institutions, and 3 00:00:09,438 --> 00:00:12,745 to also how to think about which institution we might use. In this 4 00:00:12,745 --> 00:00:16,754 particular lecture, we're going to talk about auctions, and how we auction things 5 00:00:16,754 --> 00:00:20,712 off. Now auctions are used in a lot of settings, they're used to auction off air 6 00:00:20,712 --> 00:00:24,520 waves, oil leases, there's even things like, wine auctions. And you go to these 7 00:00:24,520 --> 00:00:28,378 auctions, sometimes they have ascending bids, where people call out prices, and 8 00:00:28,378 --> 00:00:32,236 you keep bidding, until no one can bid anymore. Other times there's sealed bid 9 00:00:32,236 --> 00:00:36,095 auctions, where you just write down an amount. There's a third type of auction, 10 00:00:36,095 --> 00:00:40,139 that I'm going to talk about as well, called a. And price auction, which has a 11 00:00:40,139 --> 00:00:44,262 slightly more complicated set of rules. And when you auction something off, your 12 00:00:44,262 --> 00:00:48,127 objective is to get as much money as you can possibly get. And so that's what we'll 13 00:00:48,127 --> 00:00:51,992 talk about here, we'll talk about auctions from the perspective, of the person who's 14 00:00:51,992 --> 00:00:55,531 selling the thing off. And if you're selling the thing off, you want to think 15 00:00:55,531 --> 00:00:59,415 about, how can I make as much money as I possibly can. So, we're gonna talk about 16 00:00:59,415 --> 00:01:03,660 these three types of auctions, Ascending bid, second price and sealed price. Now 17 00:01:03,660 --> 00:01:07,741 again, an ascending bid is an auction where, we just keep calling out prices 18 00:01:07,741 --> 00:01:11,769 until an want, no one wants to stay in anymore. A second price auction is a 19 00:01:11,769 --> 00:01:16,068 sealed auction, where each person writes down an amount. The highest bid gets it, 20 00:01:16,068 --> 00:01:20,313 but they get it with the second highest bid. Okay, So it's sorta complicated. So, 21 00:01:20,313 --> 00:01:24,830 the highest bidder wins the good, but they only pay the second highest bid. And then 22 00:01:24,830 --> 00:01:29,402 finally a sealed bid auction, is everybody submits a bid and the highest bidder gets 23 00:01:29,402 --> 00:01:33,100 it, but they pay it at the amount that they bid. 'Kay, so let's start with 24 00:01:33,100 --> 00:01:36,712 ascending-bid auctions. Ascending-big auctions are pretty simple. Individuals 25 00:01:36,712 --> 00:01:40,324 keep calling out bids or there's an auctioneer, until no one's willing to go 26 00:01:40,324 --> 00:01:43,794 above a price, and whoever's bid the highest price gets it. So let's think 27 00:01:43,794 --> 00:01:47,599 about how that would work. You gotta think about how that would work, you gotta think 28 00:01:47,599 --> 00:01:50,967 about different types of behavioral models. [inaudible] said there's, sort of, 29 00:01:50,967 --> 00:01:54,334 three ways we can think about modeling people. One is, we can think of people 30 00:01:54,334 --> 00:01:57,790 being rational. The other is, we can thinking of people following psychological 31 00:01:57,790 --> 00:02:01,202 rules, having maybe some biases. And the third thing we can think about people 32 00:02:01,202 --> 00:02:04,835 being rule following. Having some sort of heuristic or rule of thumb that they use 33 00:02:04,835 --> 00:02:08,202 in different situations. So if we think about an ascending bid auction where 34 00:02:08,202 --> 00:02:11,702 somebody keeps calling out price. If I'm rational, I'm gonna [inaudible], if I've 35 00:02:11,702 --> 00:02:15,543 got some value, if it's worth $100 to me, I'm gonna keep bidding Until it gets up to 36 00:02:15,543 --> 00:02:19,751 $100. You know if, so if it's gonna sell for 90, that's where the 100 to be, then 37 00:02:19,751 --> 00:02:24,288 I'll bid 91. So I'll bid pretty much up to my value. What about these other two? What 38 00:02:24,288 --> 00:02:28,153 about psychological or rule following in this setting? Let's first do rule 39 00:02:28,153 --> 00:02:31,396 following. In this setting, a rule following bidder might have some rule 40 00:02:31,396 --> 00:02:35,096 like, I'm going to start off at half my value, and then I'm going to go up by five 41 00:02:35,096 --> 00:02:38,658 dollars, or two dollars. And there are some that are you know, fairly sub-stated 42 00:02:38,658 --> 00:02:42,267 [inaudible] about how they raise their bids. But at the end of the day, it seems 43 00:02:42,267 --> 00:02:46,012 like they're probably only going to bid up to their value. They wouldn't bid above 44 00:02:46,012 --> 00:02:49,575 their value, because then they're paying more then it's worth to them, and they 45 00:02:49,575 --> 00:02:53,001 probably wouldn't stop bidding at less then their value. However, their rule 46 00:02:53,001 --> 00:02:56,441 could determine how much they raise bids by, and things like that. Now for 47 00:02:56,441 --> 00:03:01,043 psychological bidder, here, a bunch of things could come. It could be that their 48 00:03:01,043 --> 00:03:05,586 initial bid is based on how much the previous goods sold for, or all sorts of 49 00:03:05,586 --> 00:03:10,306 things. But again, it's hard to imagine in this ascending bid auction, someone not 50 00:03:10,306 --> 00:03:14,967 bidding for something if it was going to sell for less than they wanted it for. 51 00:03:14,967 --> 00:03:19,816 It's also hard to imagine someone bidding more than they value something for. Well, 52 00:03:19,816 --> 00:03:24,481 maybe that's not that hard of it. Because you can image, in an ascending good 53 00:03:24,481 --> 00:03:29,268 action, that people could get, you know, frenzy. They could really want to win. So, 54 00:03:29,268 --> 00:03:33,871 even though something is valued at $100, to them, it might be that if they're 55 00:03:33,871 --> 00:03:38,720 winning it at 95 and then somebody else get 105 that they did 110 just for, you 56 00:03:38,720 --> 00:03:43,155 know, just for the thrill of winning. Once I was, I was talking to a real auctioneer 57 00:03:43,155 --> 00:03:46,977 recently at a charity auction. He said that he feels he can raise the amount of 58 00:03:46,977 --> 00:03:50,605 money, increase the amount of money that you get because he gets people all 59 00:03:50,605 --> 00:03:54,282 excited, and they get excited about winning. And they forget that even though 60 00:03:54,282 --> 00:03:58,152 they only want that vase for $100, they'll pay 150, just for the thrill of winning, 61 00:03:58,152 --> 00:04:01,732 for the thrill of the chase. So psychological models in this setting could 62 00:04:01,732 --> 00:04:05,554 actually lead to higher values. But let's start out by assuming that people are 63 00:04:05,554 --> 00:04:10,142 rational. So what's the outcome in a rescinding bid auction. The good just goes 64 00:04:10,142 --> 00:04:14,656 to whoever bid the most. So, fairly straight forward, how much is that person 65 00:04:14,656 --> 00:04:19,109 gonna pay? Well, they're probably gonna pay the value of the second highest 66 00:04:19,109 --> 00:04:23,924 bidder. Why's that? Because let's suppose that one person buys at 100 and another 67 00:04:23,924 --> 00:04:28,558 person buys at 70. So it starts out the bidding is at 40, and then 50, and then 68 00:04:28,558 --> 00:04:33,493 60, and then 70. And at 70, this person is gonna drop out. So this person who buys at 69 00:04:33,493 --> 00:04:37,558 100 shouldn't pay any more than 70. Yeah, they could make a mistake, if they, if 70 00:04:37,558 --> 00:04:41,289 their rule is to keep [inaudible] by ten, they could pay 80, but most of the time, 71 00:04:41,289 --> 00:04:45,207 you'd expect them to pay only a little bit over 70, only a little bit over the value 72 00:04:45,207 --> 00:04:50,064 of the second highest bidder. Okay, now let's look a second price auction. Totally 73 00:04:50,064 --> 00:04:54,593 different auction mechanism and we can compare the two. In a second price 74 00:04:54,593 --> 00:04:59,494 auction, everybody writes down a bid, whoever is the highest bid gets it but you 75 00:04:59,494 --> 00:05:04,396 pay the second highest price. So let's suppose there's three bidders. One bidder 76 00:05:04,396 --> 00:05:09,297 values it at, one puts in 90, one puts in 60, one puts in 70. So the winner is the 77 00:05:09,297 --> 00:05:14,260 one that bids 90 but they only pay 70, be cause they pay the second highest price. 78 00:05:14,260 --> 00:05:18,670 Totally straightforward Well, let's think about how you'd bid in this setting. You 79 00:05:18,670 --> 00:05:22,257 could be a rational bidder, a psychological bidder, or a rule-following 80 00:05:22,257 --> 00:05:26,253 bidder. Let's focus on the rational bidder to start with. Let's think about, how 81 00:05:26,253 --> 00:05:30,249 would you rationally bid in this setting? So let's suppose your value's 80. And 82 00:05:30,249 --> 00:05:34,246 let's for a moment suppose you bid your true value, you bid 80. But all we care 83 00:05:34,246 --> 00:05:38,345 about is the highest other bid. So if the highest other bid is 60, and you bid 80, 84 00:05:38,345 --> 00:05:42,509 you're gonna get it. Right? You're going to pay 60, so you're going to end up 85 00:05:42,509 --> 00:05:46,962 winning, in a sense, $twenty. Because you paid 60 and it was worth 80. Suppose the 86 00:05:46,962 --> 00:05:51,300 highest other bid is 75. If you bid 80, you get it, you pay 75, and so your net 87 00:05:51,300 --> 00:05:56,039 gain is going to be five. So let's suppose the highest other bid is 85. So you're no 88 00:05:56,039 --> 00:06:00,320 longer the highest bid. That means somebody else is going to get it. They're 89 00:06:00,320 --> 00:06:04,944 going to pay 80. You don't get it. So your value is zero. So your values are 25 and 90 00:06:04,944 --> 00:06:09,556 zero. Well let's suppose you think, maybe I should bid a little bit more, maybe I 91 00:06:09,556 --> 00:06:14,350 should bid 90. Well if you bid 90, and the highest other bid is 60, you're gonna get 92 00:06:14,350 --> 00:06:18,735 it for 60, and so your net is gonna be twenty. Now, why twenty? Twenty, because 93 00:06:18,735 --> 00:06:23,328 you valued it at 80, and you paid 60. So bidding 90 didn't hurt you anyway. You 94 00:06:23,328 --> 00:06:28,122 know, the fact, you did ten over your bid, your real value didn't cost you at all. 95 00:06:28,122 --> 00:06:33,098 Well, suppose the highest other bid is 75. Again you bid 90, but you only pay 75, and 96 00:06:33,098 --> 00:06:38,135 so your net is five just as it was before. But suppose the second the highest other 97 00:06:38,135 --> 00:06:42,930 bid is 85 and now you bid 90. Well, now you're gonna pay 85. You only value it at 98 00:06:42,930 --> 00:06:47,329 80, so you're gonna lose five. Notice you're worse off than you were before. Cuz 99 00:06:47,329 --> 00:06:51,423 before in that case, you didn't lose anything, and here you lose five. So it's 100 00:06:51,423 --> 00:06:55,685 fairly [inaudible] in a second price auction you don't wanna overbid. But do 101 00:06:55,685 --> 00:07:01,190 you want to under bid. Suppose you bid 70. Highest other bid is 60. You're gonna get 102 00:07:01,190 --> 00:07:07,425 it for 60. So your net is gonna be twenty. But, if the s econd highest bid is 75. And 103 00:07:07,425 --> 00:07:11,745 you bid 70. And you're not gonna get it, because they're gonna get it and they're 104 00:07:11,745 --> 00:07:16,011 only gonna pay 70. And you're gonna say, oh I wish I'da bid 80, or at least 76. So, 105 00:07:16,011 --> 00:07:20,547 you're only gonna get zero, whereas if you woulda bid 80, you'd have gotten it for 75 106 00:07:20,547 --> 00:07:24,650 and you would've made $five. And finally if the other highest other bid is 85, 107 00:07:24,650 --> 00:07:28,808 you're not gonna get it anyway and your payoff is zero. So what we see in the 108 00:07:28,808 --> 00:07:33,236 second price auction, is if you tell the truth you get 25 zero, if you over bid you 109 00:07:33,236 --> 00:07:37,502 get 25 minus five, and if you underbid you get twenty zero, zero. So the rational 110 00:07:37,502 --> 00:07:42,667 bidder, In this case, should be your true value. What about the other types of 111 00:07:42,667 --> 00:07:47,030 bitters? What if you're a rule following bitter? Well, the rule following bitter 112 00:07:47,030 --> 00:07:50,464 here. Could do a lot of things. The rule-following bidder could've. Say, will 113 00:07:50,464 --> 00:07:54,803 maybe I'm shade my bid, ten percent or they could over bid, it's hard to tell, so 114 00:07:54,803 --> 00:07:58,976 rule following bidder, may not play the optimal rule. They could, play it, over 115 00:07:58,976 --> 00:08:03,645 bid or under bid. The psychological bidder as well just going to be more variation we 116 00:08:03,645 --> 00:08:08,148 don't know if people are going to tell the truth or not but the interesting thing 117 00:08:08,148 --> 00:08:12,707 about this option is, is that weather or not the other people are irrational or not 118 00:08:12,707 --> 00:08:17,385 it's still optimal for you. If your rational to bid your true value. So the 119 00:08:17,385 --> 00:08:21,270 interesting thing here is, there's no sort of ratcheting up. Remember when you did 120 00:08:21,270 --> 00:08:25,012 that race to the bottom game, if other people were rational, then you wanted to 121 00:08:25,012 --> 00:08:28,513 start taking into account their irrationality. The interesting thing here 122 00:08:28,513 --> 00:08:32,302 in the second price auction is, even if other people are psychological, or other 123 00:08:32,302 --> 00:08:36,139 people are role based, you should still bid your true value. So what that's going 124 00:08:36,139 --> 00:08:39,833 to mean is that's going to lead a general tendency towards people being more 125 00:08:39,833 --> 00:08:43,286 rational. It doesn't mean we have to abandon the psychological and we're 126 00:08:43,286 --> 00:08:47,273 following Rules for thinking about how people behave. But it does mean that 127 00:08:47,273 --> 00:08:51,101 there's probability this general tendencies for people, over time at least 128 00:08:51,101 --> 00:08:55,554 to make ration al bids. So, let's think about this for a second. What happens in 129 00:08:55,554 --> 00:09:00,074 this auction? The outcome goes to the highest-valued bidder, and that person 130 00:09:00,074 --> 00:09:04,414 pays the second-highest price. That's the exact same thing we got in the 131 00:09:04,414 --> 00:09:08,561 ascending-bid auction. Okay, now let's go the, the sealed bid auction. This is, in 132 00:09:08,561 --> 00:09:12,491 some ways, even though the simplest, it's the most complicated. So now everybody 133 00:09:12,491 --> 00:09:16,572 puts in a bid. They're all sealed, and the highest bidder gets it, but they pay the 134 00:09:16,572 --> 00:09:20,199 highest price. So if there's three bidders, bidder one bids 90, bidder two 135 00:09:20,199 --> 00:09:24,180 bids 60, bidder three bids 70. Bidder one gets it at 90, but they, but she pays 90. 136 00:09:24,180 --> 00:09:28,969 She doesn't pay 70 she pays 90. So in this setting, it makes sense to do what? To 137 00:09:28,969 --> 00:09:33,940 shade, to bid a little bit less. So if we think about what a rational bidder should 138 00:09:33,940 --> 00:09:38,911 do, that person should shade a little bit. If we think about a psychological bidder, 139 00:09:38,911 --> 00:09:43,640 that person might also shade but they might, think, well other people are going 140 00:09:43,640 --> 00:09:48,308 to bid even numbers like 75 some are going to bid $75 and one cent. Now a rule 141 00:09:48,308 --> 00:09:53,259 following bidder in this case might shade by some fixed percentage. So think about a 142 00:09:53,259 --> 00:09:57,182 rational bidder, how they should bid, it's gonna depend on a bunch of things 143 00:09:57,182 --> 00:10:01,366 including the number of other people in the auction. Let's look at a simple case 144 00:10:01,366 --> 00:10:05,429 where there's just two. And one thing we know right away is the higher you bid, the 145 00:10:05,429 --> 00:10:09,500 more likely it is you're gonna win. So you wanna [inaudible] you wanna go under your 146 00:10:09,500 --> 00:10:13,231 value. But you also wanna get, you know, somewhat higher bids, 'cause then you're 147 00:10:13,231 --> 00:10:17,060 more likely to win. So we wanna think through how this logic plays out. So let's 148 00:10:17,060 --> 00:10:21,082 do a two bidder model. And let's suppose the value of the other bidder is a uniform 149 00:10:21,082 --> 00:10:24,814 distribution between zero and one. So remember, in a uniform distribution, it's 150 00:10:24,814 --> 00:10:28,497 equally likely to be any value between zero and one. Let's suppose the other 151 00:10:28,497 --> 00:10:32,957 bidder bids her true value. So if she bids her true value. What are the odds that you 152 00:10:32,957 --> 00:10:38,051 win if you bid 60 cents? We are gonna win if our value happens to be less than 60 153 00:10:38,051 --> 00:10:42,327 cents, and that's gonna happen 60 percent of the time. We can generalize this. 154 00:10:42,327 --> 00:10:47,284 Suppose you bid some amount, B, which is between zero and one. What are the odds 155 00:10:47,284 --> 00:10:52,679 that you win? Well again, you're probably, the odds that you win is just going to be 156 00:10:52,679 --> 00:10:57,812 B. So let's formalize this. Let's suppose the other person is bidding virtually 157 00:10:57,812 --> 00:11:03,207 badly, and think about what you should do. So V is your value, B is your bid. V minus 158 00:11:03,207 --> 00:11:08,340 B is your surplus. That's how much you'd win, if you win. So if your value is 90. 159 00:11:08,340 --> 00:11:15,033 And your bid was 30, and you won, you'd get 60. Right, that's how much you sort 160 00:11:15,033 --> 00:11:18,807 of, it's the difference between your value for the object and how much you bid, In 161 00:11:18,807 --> 00:11:23,158 this case though, these values are going to be at the interval 0,1, As are your 162 00:11:23,158 --> 00:11:27,733 bids. Now B, if you bid point six, is also your probability of winning. So if you bid 163 00:11:27,733 --> 00:11:31,582 a half, the probability of winning is a half. If you bid a quarter, the 164 00:11:31,582 --> 00:11:35,767 probability of winning is a quarter. So your expected winnings are just the 165 00:11:35,767 --> 00:11:40,397 probability of winning times your surplus. So that's just B times V minus D. All you 166 00:11:40,397 --> 00:11:45,083 want to do is maximize D times V minus B. Well if I multiply that out at B V minus B 167 00:11:45,083 --> 00:11:49,299 squared. Now, if you've had calculus, all you have to do is take the derivative to 168 00:11:49,299 --> 00:11:53,540 this, with respect to D, and that's gonna give you V minus two B equals zero, which 169 00:11:53,540 --> 00:11:58,020 we've got right here, and your optimal bid is to bid half your value. So if you think 170 00:11:58,020 --> 00:12:02,635 the other person's bidding her true value, you should bid half your value. And so 171 00:12:02,635 --> 00:12:07,266 let's think about this one again. So you're a rational bidder and you think, if 172 00:12:07,266 --> 00:12:12,253 the other person's bidding her true value, I should bid half my value. But that means 173 00:12:12,253 --> 00:12:17,121 the other person should probably also be bidding half of her value. If I'm bidding 174 00:12:17,121 --> 00:12:22,048 half my value and I'm rational, she should be bidding half her value. So let's think 175 00:12:22,048 --> 00:12:26,679 of, let's suppose she's bidding half her value, what should you do? If the other 176 00:12:26,679 --> 00:12:31,666 bidder bids half her value, now if I bid B the probability that I win is going to be 177 00:12:31,666 --> 00:12:37,947 2B. Why is that? Let's think about it. So suppose that I bid .25, If I did .25 I'm 178 00:12:37,947 --> 00:12:46,906 gonna win as long a s her value is less than .25 times two, because she's bidding 179 00:12:46,906 --> 00:12:53,018 half her value. So that means I'm gonna l, win half the time. So what we get is, the 180 00:12:53,018 --> 00:12:59,507 probability that I win if I get B is gonna be 2B, given that she's bidding half her 181 00:12:59,507 --> 00:13:03,768 value. So now we just do the same calculation. V is my value, B is my bid. 182 00:13:03,768 --> 00:13:08,631 So the difference between those two is how much I win. And now 2B is my probability 183 00:13:08,631 --> 00:13:13,318 of winning. So my winnings are gonna be 2B times VB. So if I write down that, and set 184 00:13:13,318 --> 00:13:18,182 the derivative again equal to zero, what I'm gonna get is that I again should bid V 185 00:13:18,182 --> 00:13:22,635 over two. Now if you don't know how to take derivatives, don't worry about it. 186 00:13:22,635 --> 00:13:27,498 All we're doing here is we're just using a little math to show that my [inaudible] 187 00:13:27,498 --> 00:13:32,009 bid again is gonna be V over two. Well this is great, because it says, if I bid 188 00:13:32,009 --> 00:13:36,605 half my value. And she bids half her value, we're both doing the optimal thing. 189 00:13:36,605 --> 00:13:41,399 So the optimal thing for each of us in this case, the rational thing to do, would 190 00:13:41,399 --> 00:13:46,134 be to bid half her value. So what's gonna happen is the highest value bidder is 191 00:13:46,134 --> 00:13:51,793 gonna get it. And they're gonna get it at half their value. Great, So let's look 192 00:13:51,793 --> 00:13:56,104 through all three of our auctions. In the sealed bit auction, the highest bidder 193 00:13:56,104 --> 00:14:00,087 gets it at half her value. In the ascending big auction, the highest value 194 00:14:00,087 --> 00:14:04,179 bidder gets it at the second highest value. And at the second price auction, 195 00:14:04,179 --> 00:14:09,074 the highest value bidder gets it, also at the second highest value. Notice this, 196 00:14:09,074 --> 00:14:14,803 though. Half of the highest bidder's value. If the highest bidder's value is 197 00:14:14,803 --> 00:14:20,728 60, half of their value is 30, and that's the expected value of the second highest 198 00:14:20,728 --> 00:14:25,643 bidder. Why's that, remember, let's think about it, we got this distribution of 199 00:14:25,643 --> 00:14:30,430 values and their uniform. So if I bid.6 and I win, that means that the other 200 00:14:30,430 --> 00:14:35,069 person's bid is somewhere in here. So what's, if it's somewhere in there, the 201 00:14:35,069 --> 00:14:39,827 expected value that would be halfway in between, which would be my bid over two. 202 00:14:39,827 --> 00:14:44,585 So half of my value, if I've got a uniform distribution, is excatly equal to the 203 00:14:44,585 --> 00:14:49,102 expected value of the second highest bidder. So wha t we get is, all three of 204 00:14:49,102 --> 00:14:54,162 these auctions seem to work about the same way. The highest value bidder gets it, and 205 00:14:54,162 --> 00:14:58,799 they get it at either the exact value of the second highest bidder, or at the 206 00:14:58,799 --> 00:15:02,943 expected value of the second highest bidder. If since, if you're auctioning it 207 00:15:02,943 --> 00:15:06,701 off, you don't know the exact value of the second Hindspitter. All you can expect to 208 00:15:06,701 --> 00:15:10,413 get is the expected value of the second Hindspitter, so it looks like all three of 209 00:15:10,413 --> 00:15:14,446 these things are the same. And in fact they are. So there's a theorem proven by 210 00:15:14,446 --> 00:15:18,786 Roger Myerson, and he, incidentally, he won a Nobel Prize for this work. So it's a 211 00:15:18,786 --> 00:15:23,181 fairly sophisticated theorem. That says if you have rational bidders, there's a Y 212 00:15:23,181 --> 00:15:27,631 class of auction mechanisms that includes sealed bids, second price, and ascending 213 00:15:27,631 --> 00:15:31,807 bid auctions, such that they get identical expected outcomes. So the expected 214 00:15:31,807 --> 00:15:36,257 outcomes in all three of those cases were highest bidder gets it at the expected 215 00:15:36,257 --> 00:15:41,029 value of the second highest bidder. And that's what we got and it's called the 216 00:15:41,029 --> 00:15:45,800 revenue equivalents here. So what the model tells us is, it doesn't matter how 217 00:15:45,800 --> 00:15:50,384 we auction things off, if voters are rational. So this is a really powerful 218 00:15:50,384 --> 00:15:55,465 theory, and here we see the value, one of the values of models. Because we might sit 219 00:15:55,465 --> 00:16:00,421 around and think, oh boy, ascending bid auctions are better. Seal bid auctions are 220 00:16:00,421 --> 00:16:05,501 better. Second price auctions are better. What this tells us is, if we have rational 221 00:16:05,501 --> 00:16:10,663 bidders, all three are equally good. But we may not have rational bidders. We could 222 00:16:10,663 --> 00:16:16,064 have psychological bidders, we could have rule following bidders, so here's where we 223 00:16:16,064 --> 00:16:20,274 take. Our model results, the revenue equivalence term, and we then try to bring 224 00:16:20,274 --> 00:16:24,590 our experience in and think something about the bidders in the auction. So let's 225 00:16:24,590 --> 00:16:28,690 suppose that we've got a bunch of really sophisticated bidders, so these are 226 00:16:28,690 --> 00:16:33,222 multinational firms bidding on oil leases. Well in that case, we can imagine they are 227 00:16:33,222 --> 00:16:37,602 probably fairly close to rational. And now we know that. Pretty much any auction 228 00:16:37,602 --> 00:16:41,526 method is going to give us the same revenue. And so we could s ay, well maybe 229 00:16:41,526 --> 00:16:45,555 it doesn't matter. Well now we may care about things like transparency. So for 230 00:16:45,555 --> 00:16:49,898 instance maybe we decide to have it be a sealed bid auction so we can actually see 231 00:16:49,898 --> 00:16:53,979 exactly how much people bid. And we know that, none of the, since the, all of the 232 00:16:53,979 --> 00:16:58,061 bidders are highly rational it's going to be okay, we're going to get the same 233 00:16:58,061 --> 00:17:02,528 revenue, and that way we'll see it. Let's suppose instead of having some charity 234 00:17:02,528 --> 00:17:06,911 auction we are auctioning off Something in the community, just for fun, and now, we 235 00:17:06,911 --> 00:17:10,458 know people maybe haven't participated in auction before, and it's somewhat 236 00:17:10,458 --> 00:17:14,241 confusing to them. And then, they may be suffering from some psychological biases, 237 00:17:14,241 --> 00:17:17,834 or they may just be following some simple rules. Well, in those settings, when 238 00:17:17,834 --> 00:17:21,583 you've got unsophisticated bidders. Let's think about the three auctions. In the 239 00:17:21,583 --> 00:17:25,390 sealed bid auction, they've gotta think about what are the distribution of other 240 00:17:25,390 --> 00:17:29,388 people's values. Well that could be really hard for them to do and they may make all 241 00:17:29,388 --> 00:17:33,100 sorts of mistakes. They may follow rules that don't make sense. They may suffer 242 00:17:33,100 --> 00:17:36,954 from psychological biases. What about the second price auction? Where you say that 243 00:17:36,954 --> 00:17:40,761 the highest bidder gets it at the second highest price. That may be confusing to 244 00:17:40,761 --> 00:17:44,709 people and they might not have any idea how it works. So what about. The ascending 245 00:17:44,709 --> 00:17:49,105 bid auction. This makes a lot of sense in that setting, because even if people are 246 00:17:49,105 --> 00:17:53,609 biased or if they are rule-following, it's still probably going to be the case that 247 00:17:53,609 --> 00:17:57,841 if the bid is lower than what they value it, that they'll probably bid. So that 248 00:17:57,841 --> 00:18:01,688 way, no one is going to. Do some silly thing and underbid, and not get something 249 00:18:01,688 --> 00:18:05,185 they want. And in addition, if we're trying to make as much money as we can, 250 00:18:05,185 --> 00:18:08,540 given that there could be some psychological bias in that people could 251 00:18:08,540 --> 00:18:12,320 just wanna win, we might even make more money by having an ascending bid auction. 252 00:18:12,320 --> 00:18:16,230 We're not gonna make more money in the sealed bid case. So what we see is if you 253 00:18:16,230 --> 00:18:20,091 have highly sophisticated people, maybe we go with sealed bid. Or maybe we go to 254 00:18:20,091 --> 00:18:24,148 second price cuz they can figure it out. If you got unsophisticated people maybe we 255 00:18:24,148 --> 00:18:27,862 go to the sending bid. For a couple reasons. One it's easier, and the other is 256 00:18:27,862 --> 00:18:31,235 maybe we get them sort of in a psychological frenzy, and we make more 257 00:18:31,235 --> 00:18:34,851 money. We have a powerful theorem, the revenue equivalence theorem, and that 258 00:18:34,851 --> 00:18:38,690 tells us it doesn't matter which auction mechanism we do, we use, If people are 259 00:18:38,690 --> 00:18:42,800 rational. But if we think about how people actually behave, we could then start to 260 00:18:42,800 --> 00:18:46,554 make some distinctions about what institution to auction things off might 261 00:18:46,554 --> 00:18:50,715 work best. And in some cases we might want a sealed bid. And in some cases we might 262 00:18:50,715 --> 00:18:54,495 want ascending. And in other cases we might want second price. So what we've 263 00:18:54,495 --> 00:18:58,464 seen here is we can write down models of auctions and we can develop some really 264 00:18:58,464 --> 00:19:02,530 profound results saying that it doesn't matter how you auction things off provided 265 00:19:02,530 --> 00:19:06,351 some conditions are met. So that's really nice. It sort of frees us up to think 266 00:19:06,351 --> 00:19:10,320 about other things. And it frees us up to think about how are people are actually 267 00:19:10,320 --> 00:19:14,288 going to behave. How much information do they have? How sophisticated are they? How 268 00:19:14,288 --> 00:19:18,305 many of them are there? And that can then, then we can use those criteria to decide 269 00:19:18,305 --> 00:19:21,980 which auctions we're going to use. As opposed to spending our time thinking 270 00:19:21,980 --> 00:19:25,850 about, well this auction is better than this auction on purely rational grounds. 271 00:19:25,850 --> 00:19:29,815 So we talked about what, why do we model. But why do we assume even rational actors? 272 00:19:29,815 --> 00:19:33,300 Remember, I said, benchmarks are good things. Remember I said Roger Myerson 273 00:19:33,300 --> 00:19:36,546 says, the one who's got the revenue equivalent theorum, that, assuming 274 00:19:36,546 --> 00:19:40,270 rational behavior's often a very good benchmark. Well, we saw that was the case 275 00:19:40,270 --> 00:19:44,217 here in options, because we see. If people are rational, doesn't matter what 276 00:19:44,217 --> 00:19:49,050 mechanism you use. Once we relax that assumption, then the mechanism may matter. 277 00:19:49,050 --> 00:19:53,897 But, now we know what criteria to use to think about choosing among auction 278 00:19:53,897 --> 00:19:59,333 mechanisms. So it's really useful. Models are really helpful. All right. Thank you.