1 00:00:00,000 --> 00:00:04,527 Hi. In our final lecture on mechanism design, we're gonna talk about how we can 2 00:00:04,527 --> 00:00:09,402 use mechanisms to decide whether or not we should fund public projects. Now to think 3 00:00:09,402 --> 00:00:13,813 about a public project, what we're thinking about is some outlay of funds to 4 00:00:13,813 --> 00:00:18,340 buy something from which everybody is gonna benefit from it. So, a private good 5 00:00:18,340 --> 00:00:23,100 would be something like this sweater, or a chair, or a pen, it's something that just 6 00:00:23,100 --> 00:00:27,685 one individual is gonna use. If we think about a public project, you think about 7 00:00:27,685 --> 00:00:31,992 something like a road or a park, where everybody can use it. The example I'm 8 00:00:31,992 --> 00:00:36,461 gonna use for this particular lecture is the example of getting a coffee machine 9 00:00:36,461 --> 00:00:40,765 for an office, because if you get a coffee machine, everybody can use it. So one 10 00:00:40,765 --> 00:00:45,176 coffee machi, machine can serve a whole bunch of people. So here's the idea. Let's 11 00:00:45,176 --> 00:00:49,470 suppose there's three people and person one would be willing to contribute $40. 12 00:00:49,470 --> 00:00:53,709 It's worth $40 to her to have a coffee machine. Person two would be willing to 13 00:00:53,709 --> 00:00:58,058 contribute $50. And person three would be willing to contribute $twenty. So if you 14 00:00:58,058 --> 00:01:02,993 add all these things up. You get a $110, so you'd be collecting [inaudible] between 15 00:01:02,993 --> 00:01:07,747 $110, and the machine only cost 80, which is great. But here's the problem. The 16 00:01:07,747 --> 00:01:12,627 problem is these values, the 40, the 50, the twenty, they're private information. 17 00:01:12,627 --> 00:01:17,318 No one knows those before the fact. And so, what you've got is, you've got a 18 00:01:17,318 --> 00:01:22,326 classic case of hidden information. People value the coffee mach--, machine some 19 00:01:22,326 --> 00:01:26,105 amount. But we'd like to get them to reveal that information so we can decide 20 00:01:26,105 --> 00:01:30,107 whether or not to buy the coffee machine. Because it could be that they do not value 21 00:01:30,107 --> 00:01:33,681 it enough. That person one values it at twenty that person two values it at 22 00:01:33,681 --> 00:01:37,398 twenty, and person three values it at twenty. So the total value is only 60, and 23 00:01:37,398 --> 00:01:40,972 the coffee machine costs 80, so it?s not worth doing. So the challenge from a 24 00:01:40,972 --> 00:01:44,593 design standpoint is to figure out how we get people to reveal their hidden 25 00:01:44,593 --> 00:01:48,474 information. So again it comes down to a question of [inaudible] compatibility. So 26 00:01:48,474 --> 00:01:52,860 what we're going to talk about her e is a mechanism called a Pivot Mechanism. And 27 00:01:52,860 --> 00:01:56,972 this was designed really by three people, Clark, Groves, and Vicry. So this is 28 00:01:56,972 --> 00:02:01,358 sometimes called the Clark-Groves-Vicry Pivot Mechanism. We'll just sort of call 29 00:02:01,358 --> 00:02:05,853 it the Pivot Mechanism. He's how it works; you only have to pay the marginal amount. 30 00:02:05,853 --> 00:02:10,129 So you pay the minimal amount that you would have to pay given other people's 31 00:02:10,129 --> 00:02:14,570 bids in order to make the project viable. So if without you, people are willing to 32 00:02:14,570 --> 00:02:18,944 pay 60 dollars and it costs 80. Then you only have to pay twenty. If without you, 33 00:02:18,944 --> 00:02:23,402 people are willing to pay $70 and it cost 80, then you only have to pay ten. So it 34 00:02:23,402 --> 00:02:28,027 is, you only have to pay that amount that would make it viable if you threw in that 35 00:02:28,027 --> 00:02:32,374 much money. And this creates an incentive for you to tell the truth, because it 36 00:02:32,374 --> 00:02:36,776 doesn't hurt you to say how much you really valued the project, cuz you're only 37 00:02:36,776 --> 00:02:41,047 going to pay your marginal amount, whether it's $twenty or whether it's $ten. So, 38 00:02:41,047 --> 00:02:45,080 here's formally how the Clark Groves Vicry mechanism works. Each person claims a 39 00:02:45,080 --> 00:02:48,915 value. Now this, the real value is hidden information, but they're gonna claim a 40 00:02:48,915 --> 00:02:53,046 value. And the whole idea behind mechanism design is to get them to claim their true 41 00:02:53,046 --> 00:02:57,079 value. So each person claims a value, and if the sum of those values is bigger than 42 00:02:57,079 --> 00:03:01,013 the cost, if everybody's claiming values that add up to more than the cost, since 43 00:03:01,013 --> 00:03:04,848 we're gonna share this coffee machine, then we go ahead and do the project and 44 00:03:04,848 --> 00:03:09,590 buy the coffee machine. Now, how much do people pay? Well, person one is just gonna 45 00:03:09,590 --> 00:03:14,656 pay the cost, minus the bids of the other two people, the values of the other two 46 00:03:14,656 --> 00:03:19,514 people. Or if the [inaudible] are bigger than the cost, Person one is going to pay 47 00:03:19,514 --> 00:03:24,525 nothing because the project should be done without Person one contributing anything. 48 00:03:24,525 --> 00:03:29,049 So, that's it. That's all there is to the mechanism. Let's see how it works. So 49 00:03:29,049 --> 00:03:33,352 let's again go to our example where there's three people. Person one buys at 50 00:03:33,352 --> 00:03:37,711 40, person two at 50 and person three at twenty and the cost is 80 dollars. So 51 00:03:37,711 --> 00:03:42,353 again if we add these three things up we are gonna get 110 dollars. So clearly you 52 00:03:42,353 --> 00:03:47,182 wanna buy the coffee machine because they value at 100 and it only cost 80. But how 53 00:03:47,182 --> 00:03:52,793 do we decide how much each person should pay? Again, the rule is, each person's 54 00:03:52,793 --> 00:03:58,476 just gonna pay that cost, which is $80, minus the values of the other two people. 55 00:03:58,476 --> 00:04:04,013 So if we look at person one, the cost is $80. The other two people added, added 56 00:04:04,013 --> 00:04:09,160 together, 50+20 is 70. So that means person one is just gonna pay $ten. What we 57 00:04:09,160 --> 00:04:13,268 want to figure out is, does it make sense for person one to tell the truth. So if 58 00:04:13,268 --> 00:04:17,221 this is the mechanism, should person one say 40 dollars or should they say 50 59 00:04:17,221 --> 00:04:21,431 dollars or should they say twenty dollars. Well let's think, let's suppose the cost 60 00:04:21,431 --> 00:04:25,641 is 80 and person one values it at 40, and let's suppose that they claim a value of 61 00:04:25,641 --> 00:04:29,646 40, so in this trial we're gonna submit they're actually claiming the truth. So 62 00:04:29,646 --> 00:04:33,805 let's think through all the possibilities, so one possibility is that some of the 63 00:04:33,805 --> 00:04:37,758 other people's is only 30. So, if some of the other people's 30, and they claim 40, 64 00:04:37,758 --> 00:04:41,644 that only adds up to 70, so they're not gonna pay anything. >> Cuz the project's 65 00:04:41,644 --> 00:04:45,634 not gonna get done, and so they're not going to make anything. Now, if the other 66 00:04:45,634 --> 00:04:49,675 people, some of their bids is 40, and our person claims 40, then they're going to 67 00:04:49,675 --> 00:04:53,716 pay 40, and they're going to break even. And they're going to pay $40, and they're 68 00:04:53,716 --> 00:04:57,502 going to get a project for $40, so, you know, whether you do it or not really 69 00:04:57,502 --> 00:05:01,594 doesn't matter. Let's suppose that some of the others is $45 though. So the others 70 00:05:01,594 --> 00:05:05,687 bids, or values, add up to 45. This person claims 40. They're only going to have to 71 00:05:05,687 --> 00:05:09,677 pay 35, right? Because 45 plus 35 adds up to 80, which is our cost, And, so on net 72 00:05:09,677 --> 00:05:13,811 they're going to come out five ahead. >> And then finally, let's look at some of 73 00:05:13,811 --> 00:05:17,814 the others as ninety. Well now, their claim value is forty, they're not gonna 74 00:05:17,814 --> 00:05:22,298 pay anything because they're not gonna pay anything and they're gonna come up forty 75 00:05:22,298 --> 00:05:26,408 ahead. So if they claim that you value, sometimes the project doesn't get done, 76 00:05:26,408 --> 00:05:30,358 sometimes it gets done and they're indifferent, sometimes it gets done and 77 00:05:30,358 --> 00:05:34,361 you make a little money, sometimes you don't have to pay anything. Now let's 78 00:05:34,361 --> 00:05:38,684 suppose they decide to cheat a little bit, and to claim a value of only thirty. So 79 00:05:38,684 --> 00:05:42,544 you're gonna say, oh, no, I want forty, in the shade. Well now if the sum of the 80 00:05:42,544 --> 00:05:46,699 others is 30 the project doesn't get done and then it'll pay anything Because the 81 00:05:46,699 --> 00:05:51,320 project isn't done. If someone else is 40 and they did 30, again that adds up to 70. 82 00:05:51,320 --> 00:05:55,270 So that's less than the cost and the project doesn't get done, And because some 83 00:05:55,270 --> 00:05:59,220 of the others is 45 and they'd done 30, that's only 75. So it's a third time the 84 00:05:59,220 --> 00:06:03,120 project doesn't get done. But in the case where, that some of the others was 90, 85 00:06:03,120 --> 00:06:07,170 then the project gets done and they don't pay anything. So if you compare that to 86 00:06:07,170 --> 00:06:10,770 the case where they tell the truth, they're worse off in these two cases 87 00:06:10,770 --> 00:06:14,820 because when the sum of the others is 45, if they'd have told the truth, they only 88 00:06:14,820 --> 00:06:18,770 would have paid 35 and they'd have come out five ahead. But when the sum of the 89 00:06:18,770 --> 00:06:25,511 others is 45 and they. A 30 that only adds up to 75, And the product doesn't get done 90 00:06:25,511 --> 00:06:29,491 and they're worse off. They are getting nothing when they could've gotten a plus 91 00:06:29,491 --> 00:06:34,076 five. So it seems pretty clear you don't wanna under claim, because if you under 92 00:06:34,076 --> 00:06:38,843 claim, the project could not get done in cases where you'd like to get done. What 93 00:06:38,843 --> 00:06:43,335 about over claiming? Well, let's think. Suppose the value is 40, now I claim 50. 94 00:06:43,335 --> 00:06:47,946 Well, if the sum of the others is 30, and I claim 50, 50+30 adds up to 80, which is 95 00:06:47,946 --> 00:06:52,650 the cost. That means I'm gonna have to pay 50, and I'm out ten. Now in the other 96 00:06:52,650 --> 00:06:57,782 cases I'm going to only pay 40 or less, so I'm just the same as if I told the truth, 97 00:06:57,782 --> 00:07:02,480 but in this one case I'm worse off. So what we see is if I look at the three 98 00:07:02,480 --> 00:07:06,793 cases, do I tell the truth where I get zero, zero, five and 40. Where I 99 00:07:06,793 --> 00:07:12,526 understate, I get 00040 and when I overstate I get minus 100540. What you see 100 00:07:12,526 --> 00:07:18,335 is, I'm best off telling the truth. What the Clark-iii mechanism does, which is 101 00:07:18,335 --> 00:07:23,885 fantastic, it's a way to; induce people to tell the truth. So, this is again what we 102 00:07:23,885 --> 00:07:27,757 call the 'Incentive Compatibility'. Each person has an incentive under the 103 00:07:27,757 --> 00:07:32,001 mechanism we had provided the rational, to give their true value. So that's great, 104 00:07:32,001 --> 00:07:36,244 totally great, and we think well, this is a fantastic mechanism. And let's see how 105 00:07:36,244 --> 00:07:40,328 it plays out. Let's say there's a case where person one has a value of thirty, 106 00:07:40,328 --> 00:07:44,518 person two has a value of thirty, and person three has a value of thirty. So the 107 00:07:44,518 --> 00:07:49,482 other two people. Have values of 60. The total cost is 90. So that means person one 108 00:07:49,482 --> 00:07:54,688 is gonna pay 30, person two is gonna pay 30 and person three is gonna pay 30 for a 109 00:07:54,688 --> 00:07:59,639 total revenue of 90, which is great. It costs 90 and we're gonna get revenue of 110 00:07:59,639 --> 00:08:04,401 90. So this mechanism not only gives people the truth to reveal, but in this 111 00:08:04,401 --> 00:08:09,274 case it actually raises enough money to pay for the project. Now, notice that's 112 00:08:09,274 --> 00:08:14,121 not always gonna be true. Let's go back to our example of 40, 50, and twenty. In this 113 00:08:14,121 --> 00:08:18,791 case, how much is person one gonna pay? Person one is gonna pay 80 minus the sum 114 00:08:18,791 --> 00:08:23,561 of the other two people's bids, which is just gonna be $ten. >> Person two is going 115 00:08:23,561 --> 00:08:28,051 to pay 80 minus the sum of the other two people's bid, which is one and three, 116 00:08:28,051 --> 00:08:32,484 which is $60. So they're going to pay $twenty. And person three is going to pay 117 00:08:32,484 --> 00:08:37,033 80 minus the sum of the other people's bids, but that's 90. So the most you can 118 00:08:37,033 --> 00:08:41,873 make see you can't pay, can't make someone pay negative amount. So they're not going 119 00:08:41,873 --> 00:08:46,422 to pay anything. So in this case the total revenue is only $30. So now we have a 120 00:08:46,422 --> 00:08:50,796 problem, we got people to truthfully reveal, everybody gives their own value, 121 00:08:50,796 --> 00:08:55,285 but. You don't raise enough money to pay for the project. So to pay for the project 122 00:08:55,285 --> 00:08:59,650 we have to have some other way of paying for the project. Possible taxing people, 123 00:08:59,650 --> 00:09:03,796 But if we tax people, that could cause them to change their value assessment. 124 00:09:03,796 --> 00:09:08,270 Because the thing is now they have less money than they had before. So what we see 125 00:09:08,270 --> 00:09:12,417 is, the [inaudible] mechanism work sorta, [inaudible] some of the [inaudible] 126 00:09:12,417 --> 00:09:16,727 funding the project. But it doesn't work perfectly because it's not balanced, in 127 00:09:16,727 --> 00:09:21,073 the sense that you ca n't fully pay for the project. See cause what we we'd like a 128 00:09:21,073 --> 00:09:24,774 mechanism to do, when there's public project setting, we'd like it to be 129 00:09:24,774 --> 00:09:28,751 efficient by that I mean we'd like it to be the case that you always get. The 130 00:09:28,751 --> 00:09:31,794 project if it's worth it. So you always, you only do the project if it's 131 00:09:31,794 --> 00:09:35,309 worthwhile, so you can have an efficient outcome. You'd like it to be the case that 132 00:09:35,309 --> 00:09:38,824 it makes sense for people to always join, so that you are not coercing people into 133 00:09:38,824 --> 00:09:41,910 doing it, that you have to join if you don't want to. You'd like it to be 134 00:09:41,910 --> 00:09:45,425 incentive compatible, so that people tell the truth. And then finally, you'd like it 135 00:09:45,425 --> 00:09:49,013 to be balanced, like to be able to pay for the project. What you can show is that 136 00:09:49,013 --> 00:09:53,129 that's impossible. So there's no mechanism that'll do this. So what you can do is you 137 00:09:53,129 --> 00:09:56,706 can sort of do second best. You can sacrifice one of these things. And the 138 00:09:56,706 --> 00:10:00,773 thing you can sacrifice in the [inaudible] victory mechanism is that it's balanced. 139 00:10:00,773 --> 00:10:04,448 Now, there's other mechanisms that sacrifice other restrictions in order to 140 00:10:04,448 --> 00:10:08,172 get this to work. So it'd be balanced, but they won't necessarily satisfy the 141 00:10:08,172 --> 00:10:11,994 condition that no one's coerced to join. It could be that you have to join the 142 00:10:11,994 --> 00:10:15,571 project, and sometimes you end up worse off than if you said, I'm not even 143 00:10:15,571 --> 00:10:19,588 participating at all. So what we learn from mechanism design by writing models 144 00:10:19,588 --> 00:10:23,939 where we say okay here's the values that people have and think about how we induce 145 00:10:23,939 --> 00:10:28,134 them to tell the truth, you learn what is possible to accomplish and what is not 146 00:10:28,134 --> 00:10:31,821 possible to accomplish. Okay. So when we think about mechanism design, which we 147 00:10:31,821 --> 00:10:35,314 should in some sense, two fundamental issues we're trying to overcome. One is 148 00:10:35,314 --> 00:10:39,083 hidden action. We may not see what people do. So what we'd like to do is write down 149 00:10:39,083 --> 00:10:42,576 incentive structures and information structures so that we induce people to 150 00:10:42,576 --> 00:10:46,207 take the right actions. We can't see what they're going to do, so what we'd like 151 00:10:46,207 --> 00:10:49,930 them to do is somehow incentives so we know they're going to take the actions we 152 00:10:49,930 --> 00:10:53,585 want. Second thing we can use mechanisms to overcome is hidden information, Ju st 153 00:10:53,589 --> 00:10:57,158 like we saw in this public project case, or in the auction case. We don't know 154 00:10:57,158 --> 00:11:00,912 people's values, so what we'd like to do is we'd like to create a mechanism where 155 00:11:00,912 --> 00:11:04,665 people truthfully reveal their values, and where we get outcomes that are desired 156 00:11:04,665 --> 00:11:08,419 outcomes. So in the case of an auction, we sell it to the person who values it the 157 00:11:08,419 --> 00:11:12,173 most. And in the case of a public project, we undertake the public project if it's 158 00:11:12,173 --> 00:11:15,946 worth doing. All right, so that's mechanism design and it's really 159 00:11:15,946 --> 00:11:20,739 interesting, it's a way to use models to try and design institutions so they're 160 00:11:20,739 --> 00:11:24,547 more efficient. Now one thing we saw now, and I wanna be very careful, is most 161 00:11:24,547 --> 00:11:28,206 mechanism design assumes people are rational, but we talk about auctions, some 162 00:11:28,206 --> 00:11:31,626 [inaudible] we saw that, if we don't assume people rational, we maybe get 163 00:11:31,626 --> 00:11:35,427 slightly different implications of what we should do. So, for example, we have the 164 00:11:35,427 --> 00:11:39,085 revenue equivalents theorem that said, it doesn't matter what auction you use, 165 00:11:39,085 --> 00:11:42,696 you're gonna get the same outcome in each case. But, we saw that if we have a 166 00:11:42,696 --> 00:11:46,591 different model of human behavior, some auction mechanisms might be preferred over 167 00:11:46,591 --> 00:11:50,534 others. So, depending on how sophisticated people are, we might wanna use a different 168 00:11:50,534 --> 00:11:54,614 auction mechanism. The same goes for these public project mechanisms. We can think 169 00:11:54,614 --> 00:11:58,656 about mechanism design but then we can start around as a benchmark but setting 170 00:11:58,656 --> 00:12:02,699 some rational actors or something. If anybody can fully figure this out what we 171 00:12:02,699 --> 00:12:06,793 can get then you can use your judgment and say lets now try for more some more 172 00:12:06,793 --> 00:12:10,989 realistic models on how people behave and how these same mechanisms hold up. Again 173 00:12:10,989 --> 00:12:14,981 having model O is going to be really useful here because it actually helps to 174 00:12:14,981 --> 00:12:18,921 think through all the implications and decisions you are making when you are 175 00:12:18,921 --> 00:12:21,276 design those institutions. All right. Thank you.