1 00:00:00,000 --> 00:00:04,259 Hi, we've been talking about the kernel blotter game. The kernel blotter game is a 2 00:00:04,259 --> 00:00:08,414 way to analyze competition, where it's along multiple fronts and the idea is to 3 00:00:08,414 --> 00:00:12,545 strategically mismatch your opponent. What I'm going to do this last lecture, I'm 4 00:00:12,545 --> 00:00:16,611 kind of blotto, is expand the discussion a little bit and talk about competition 5 00:00:16,611 --> 00:00:20,611 generally. So when you think about firms competing you think about sports teams 6 00:00:20,611 --> 00:00:24,608 competing we can think about individuals competing and what I'm going to do is 7 00:00:24,608 --> 00:00:28,503 think about some of the models we've discussed in these last couple lectures 8 00:00:28,503 --> 00:00:31,995 and see how they apply to our understanding of what happens in those 9 00:00:31,995 --> 00:00:35,840 competitive environments. Now as we do that I want to think of two different 10 00:00:35,840 --> 00:00:39,837 types of competition so one type of competition if you think of let's say some 11 00:00:39,837 --> 00:00:44,087 auto companies competing for market share you can have a position where each one is 12 00:00:44,087 --> 00:00:47,780 going to get a percentage in the market you know so GM may get 30 percent Toyota 13 00:00:47,780 --> 00:00:51,694 Ford maybe twenty% Toyota maybe get twenty percent Chrysler maybe get ten%. And so on 14 00:00:51,694 --> 00:00:56,289 right so there's more firms down here smaller firms so you can think about just 15 00:00:56,289 --> 00:01:00,429 competing for market share. You can also think about sports team. This is Siri A, 16 00:01:00,429 --> 00:01:04,313 you think about, here's different sports teams and they're gonna have win-loss 17 00:01:04,313 --> 00:01:08,346 records. So this team may go fourteen and six, this team may go seven and thirteen. 18 00:01:08,346 --> 00:01:12,380 Sorry about that [inaudible]. You know, each team's got a win-loss record and each 19 00:01:12,380 --> 00:01:15,965 is gonna play against each other. So we think about the data we got from 20 00:01:15,965 --> 00:01:19,998 competition, it could be one of two forms, it could be market share or it could be 21 00:01:19,998 --> 00:01:23,641 sort of win-losses against different teams. And what we wanna think about is, 22 00:01:23,641 --> 00:01:27,282 if we take our different models, can they help us make sense of that competition? 23 00:01:27,282 --> 00:01:30,968 And that by adjudicating between different models, can we figure out, maybe, what's 24 00:01:30,968 --> 00:01:34,336 really going on in these different environments? Does the auto market look 25 00:01:34,336 --> 00:01:38,842 differently than Soccer Competition between, like, a soccer league? So we've 26 00:01:38,842 --> 00:01:42,964 got a bunch of models. Let's just talk about four . We've got just a pure random 27 00:01:42,964 --> 00:01:46,981 model, performance is random. We've got our skill plus luck model. We've got a 28 00:01:46,981 --> 00:01:51,262 finite memory random [inaudible] model, and then we've got the Blotto model. These 29 00:01:51,262 --> 00:01:55,307 are all models that look at competition. So in the random model, it's just. You 30 00:01:55,307 --> 00:01:58,771 know, you just get a value, and it's random who wins. In the skill plus luck, 31 00:01:58,771 --> 00:02:02,283 there's a skill component, and a luck component. In the finite memory random 32 00:02:02,283 --> 00:02:05,981 luck, it's sort of random, but you've got this moving window. And then, finally, in 33 00:02:05,981 --> 00:02:09,773 Blotto, you've got some set of troops, and you're allocating them across fronts. So 34 00:02:09,773 --> 00:02:13,191 these are all different ways to think about competition, and they all say 35 00:02:13,191 --> 00:02:16,983 slightly different things. So what I wanna do in this lecture is just, just pretty 36 00:02:16,983 --> 00:02:20,775 quickly go through each one of them, and talk about the different things they say 37 00:02:20,775 --> 00:02:24,427 that we'd expect to see. And then we can think about which one of those fits a 38 00:02:24,427 --> 00:02:28,262 particular real world situation best. So let?s number the random model suppose 39 00:02:28,262 --> 00:02:32,309 performance really is random that it's like the efficient market I bought so 40 00:02:32,309 --> 00:02:36,510 suppose the case of who's a good stock broker really is random. Well, what should 41 00:02:36,510 --> 00:02:40,700 we expect? We should expect equal wins. We should expect no one to be better than 42 00:02:40,700 --> 00:02:44,733 anybody else. We should see a lot of regression to the mean. And we should see 43 00:02:44,733 --> 00:02:48,976 no time dependency. Somebody who's done well this period shouldn't necessarily do 44 00:02:48,976 --> 00:02:52,904 well next period. Now if we look at investment people, if we look at sort of, 45 00:02:52,904 --> 00:02:56,466 you know, mutual funds, it actually doesn't look unlike this. You know, 46 00:02:56,466 --> 00:03:00,709 there's not a lot of time dependency. Who won last year don't, doesn't necessarily 47 00:03:00,709 --> 00:03:04,899 determine who's gonna win this year. And this may not be a bad model of that. Now, 48 00:03:04,899 --> 00:03:08,880 if we contrast that with the skill plus luck, we'd expect to see unequal win. 49 00:03:08,880 --> 00:03:12,476 Wins. We'd expect to see some people who are consistent winners. So we'd expect 50 00:03:12,476 --> 00:03:16,026 sort of semi consistent rankings, with the higher ability people doing better, 51 00:03:16,026 --> 00:03:19,530 keeping in mind the paradox of skill of two people who are close in ability. 52 00:03:19,530 --> 00:03:23,423 They're gonna move bac k and forth in terms of who does better. But we'd expect 53 00:03:23,423 --> 00:03:27,218 to see semi consistency. And we wouldn't expect to see a huge amount of time 54 00:03:27,218 --> 00:03:31,411 dependency in the sense of like, how I did last period wouldn't have a big influence 55 00:03:31,411 --> 00:03:35,255 on what I do this period, you know, given that we know my skill level. So there 56 00:03:35,255 --> 00:03:38,999 wouldn't be any correlation in the error terms. And so you can look at some 57 00:03:38,999 --> 00:03:42,893 companies, you could argue that you know, if you look at industry market shares, 58 00:03:42,893 --> 00:03:47,037 that this may be a decent model. Or if you look at, you know, possibly some sports 59 00:03:47,037 --> 00:03:50,981 competition, this may be a decent model. But we'll see there's other models that 60 00:03:50,981 --> 00:03:54,623 might work as well. What about the finite memory random walk? Well, here, you're 61 00:03:54,623 --> 00:03:58,338 gonna have unequal wins, just like we had in the skill plus luck. And we're gonna 62 00:03:58,338 --> 00:04:02,192 have semi consistent rankings. 'Cause the fact that if you happen to get a bunch of 63 00:04:02,192 --> 00:04:06,047 good draws in a row, you're gonna continue to get those. You're gonna see a lot more 64 00:04:06,047 --> 00:04:09,716 time dependency; 'cause it's really gonna depend on what you did in the previous 65 00:04:09,716 --> 00:04:13,904 time. But where this is gonna differ from. The skill plus luck model, is you're gonna 66 00:04:13,904 --> 00:04:18,202 get movement from top to bottom. 'Cause in skill plus luck, remember, it's like A 67 00:04:18,202 --> 00:04:22,500 times luck plus one minus A times skill. And so if you've got high skill, you're 68 00:04:22,500 --> 00:04:26,580 always gonna stay pretty high. In the finite memory random walk, your values 69 00:04:26,580 --> 00:04:30,932 like XT plus XT minus one plus XT minus two and so on. Well, after you move ahead 70 00:04:30,932 --> 00:04:35,338 ten periods, your values are gonna be, all these values that made you good at this 71 00:04:35,338 --> 00:04:39,636 point in time will be gone. They'll have been chopped off the end of the random 72 00:04:39,636 --> 00:04:43,824 walk. So you're gonna see a lot more regression to the mean, and more movement 73 00:04:43,824 --> 00:04:47,874 from top to bottom in the finite. And whenever you ran a luck model then you 74 00:04:47,874 --> 00:04:51,605 would in the skill plus luck model. So again if you're looking at data within an 75 00:04:51,605 --> 00:04:55,101 industry or a [inaudible] and you want to think which one of these is it, this sort 76 00:04:55,101 --> 00:04:58,344 of statistical signature is going to be different than what you see from the 77 00:04:58,344 --> 00:05:02,122 [inaudible]. Okay, what about Blotto with equ al troops? [inaudible] equal troops, 78 00:05:02,122 --> 00:05:06,089 equal ability. Then the outcome's, this is gonna be hard to tell from random. It's 79 00:05:06,089 --> 00:05:10,105 gonna look a lot like random, but you're gonna see lots of maneuvering. Because of 80 00:05:10,105 --> 00:05:14,221 its Blotto, each period, everybody's gonna be trying to take a random action. And so 81 00:05:14,221 --> 00:05:18,088 therefore, you're gonna see all sorts of trade, all sorts of maneuvering, to try 82 00:05:18,088 --> 00:05:22,100 and position your troops [inaudible] over the troops of other people. But you're 83 00:05:22,100 --> 00:05:26,234 gonna see in the outcome itself any difference between Blotto and random. But 84 00:05:26,234 --> 00:05:30,744 you will be able to see it in terms of the actions that people take. What about when 85 00:05:30,744 --> 00:05:34,825 there's unequal troops? Well now it's gonna be more like the skill plus luck 86 00:05:34,825 --> 00:05:38,636 thing. Cuz if you've got more troops, you're gonna be more likely to win. 87 00:05:38,636 --> 00:05:42,180 However, because there's gonna be maneuvering, sometimes the lesser 88 00:05:42,180 --> 00:05:46,099 [inaudible] person would win. So statistically, it's gonna look a lot like 89 00:05:46,099 --> 00:05:49,739 skill luck, however, at the micro level. You're gonna see lots and lots of 90 00:05:49,739 --> 00:05:53,596 maneuvering. So if you look at something like American football, which has a salary 91 00:05:53,596 --> 00:05:57,500 cap, so you can only spend so much on your players. There are teams that have better 92 00:05:57,500 --> 00:06:01,264 management, and also just happen to have better players that they've signed into 93 00:06:01,264 --> 00:06:05,074 contracts. So the outcomes there may look a lot like the skill luck model. But you 94 00:06:05,074 --> 00:06:08,743 see tons and tons of maneuvering in professional football, which suggests that 95 00:06:08,743 --> 00:06:12,224 in fact, there may be a Blotto like character to it, Where you're trying to 96 00:06:12,224 --> 00:06:15,799 get players that match up well against the strengths and weaknesses of your 97 00:06:15,799 --> 00:06:19,320 opponents. So Blotto with unequal troops is going to lock, look somewhat like 98 00:06:19,320 --> 00:06:22,883 skill, we're going to see lots of unequal maneuvering. What if I add in limited 99 00:06:22,883 --> 00:06:26,579 movement? What I mean by that is that you can't just sort of reallocate your troops 100 00:06:26,579 --> 00:06:30,186 every period. You've actually gotta trade resources with someone else, which would 101 00:06:30,186 --> 00:06:33,704 be true in a football league, or it'd be true in a firm. We've gotta sort of get 102 00:06:33,704 --> 00:06:37,266 rid of employees and bring new employees. You can only move a little bit. Well if 103 00:06:37,266 --> 00:06:40,338 that's the ca se, if we go back to our example of sort of multi-player 104 00:06:40,338 --> 00:06:44,413 [inaudible], we should expect to see lots of cycles. We should expect to see where A 105 00:06:44,413 --> 00:06:48,809 beats B, B beats C, and C beats A. That's gonna be different than the skill-lock 106 00:06:48,809 --> 00:06:53,149 thing. So in the skill-lock model, we may have the case that, you know, one team 107 00:06:53,149 --> 00:06:57,432 wins 70%, one team wins 60, one team wins 50, one team wins 40, one team wins 30. 108 00:06:57,432 --> 00:07:01,997 Now we won't see a lot of cycles. We won't see consistently A beat B, B beat C, and 109 00:07:01,997 --> 00:07:05,999 then C beat A. If it's plotted with limited movement, you should be more 110 00:07:05,999 --> 00:07:10,415 likely to see that. But generally, how do we determine? How do we tell that it's a 111 00:07:10,415 --> 00:07:14,857 Blotto game, or whether it's a skill luck game? Well, one thing to think about this 112 00:07:14,857 --> 00:07:18,860 is in terms of dimensionality. If the players are making high dimensional 113 00:07:18,860 --> 00:07:23,137 strategic decisions, it's sort of more like Blotto. It's also the case that if 114 00:07:23,137 --> 00:07:27,524 it's definitely zero sum, then it's more like Blotto. You could have a skill luck 115 00:07:27,524 --> 00:07:32,572 game where we both get better. And so the things we're investing our resources in is 116 00:07:32,572 --> 00:07:37,549 just to improve our ability. That's more skill luck like, Whereas, in Blotto, it's 117 00:07:37,549 --> 00:07:42,464 all about strategically mismatching what we've got against you. And so you can 118 00:07:42,464 --> 00:07:47,189 think of high dimensional sports like football, may be more like Blotto. 100 119 00:07:47,189 --> 00:07:52,229 meter dash, marathon running, things like that, may be more skill luck. Tennis, more 120 00:07:52,229 --> 00:07:56,908 like Blotto, javelin throwing, more like skill luck. Let's take a particular case, 121 00:07:56,908 --> 00:08:00,759 let's take the presidential election United States. And think about. How do 122 00:08:00,759 --> 00:08:04,359 these different, what do these different models tell us and which one makes the 123 00:08:04,359 --> 00:08:08,005 most sense? So I could think that whoever wins the presidential election is just 124 00:08:08,005 --> 00:08:11,697 random because it just depends on random shocks to the economy and the winner is 125 00:08:11,697 --> 00:08:15,616 just gonna depend on these economic shocks and there is some evidence to support this 126 00:08:15,616 --> 00:08:19,490 but I think that it probably doesn't fully capture things. Now we could say that it's 127 00:08:19,490 --> 00:08:22,954 sort of luck and skill, that these candidates have skill, they got ability to 128 00:08:22,954 --> 00:08:26,600 communicate, they got past experience, and there's also these economic shocks and 129 00:08:26,600 --> 00:08:30,110 again, there's some evidence to support that better candidates do seem to win. 130 00:08:30,110 --> 00:08:34,332 [sound] You could also tell a random walk model. You could say, look, it's not just 131 00:08:34,332 --> 00:08:37,694 one random shot to economy, it's a whole bunch of random events. You know, it 132 00:08:37,694 --> 00:08:40,877 depends on what's happening in the world economy, it's what happening in 133 00:08:40,877 --> 00:08:44,584 international relations, what's happening domestically. What's happening? The social 134 00:08:44,584 --> 00:08:48,396 movements at the time. So a whole bunch of random events add up to determine the 135 00:08:48,396 --> 00:08:52,304 popular of the incumbent president, or the incumbent party, and that determines who 136 00:08:52,304 --> 00:08:55,926 wins. And again, that may not be a bad model. Finally with Blotto, if you think 137 00:08:55,926 --> 00:08:59,834 of it being, well there's only this sort of allocations of troops across fronts. In 138 00:08:59,834 --> 00:09:03,170 a presidential election, it's the electoral college game. And you gotta 139 00:09:03,170 --> 00:09:06,877 figure out, where do we allocate our troops? Now, that captures some of it, as 140 00:09:06,877 --> 00:09:10,969 well, right. But the thing is that you also think that we've got to have unequal 141 00:09:10,969 --> 00:09:14,854 troops; because whoever served got more skill or had to give shocks, is more 142 00:09:14,854 --> 00:09:19,169 likely to, needs fewer troops on some of those fronts. So what we see by having all 143 00:09:19,169 --> 00:09:23,500 these different models is we get many different lenses on what's going on in an 144 00:09:23,500 --> 00:09:27,343 election. Now is anyone of these right, no. Now [inaudible], when we say, oh, 145 00:09:27,343 --> 00:09:31,271 presidential elections, those things are just a pure luck skill. They're not. 146 00:09:31,271 --> 00:09:35,618 They're a combination of all these things, and by having multiple models to look at 147 00:09:35,618 --> 00:09:39,231 them, what we do is we have a lens, through which we will get a deeper 148 00:09:39,231 --> 00:09:43,132 understanding of what's going on. 'Cause where we wanna be, right, is you wanna be 149 00:09:43,132 --> 00:09:46,862 in a place when somebody confronts with something like, how does a presidential 150 00:09:46,862 --> 00:09:50,782 election unfold, that we've got a bunch of frameworks within which we can view that 151 00:09:50,782 --> 00:09:54,465 particular event, and say, here's what I learned from this framework. So you can 152 00:09:54,465 --> 00:09:58,101 say, there's a sense in which the winner of the presidential election is luck, 153 00:09:58,101 --> 00:10:01,927 because it comes down to economic shocks going their way. And at the other extent, 154 00:10:01,927 --> 00:10:05,563 we ca n also say, look, another way to think about these presidential elections, 155 00:10:05,563 --> 00:10:09,293 though, is it's this elaborate game of blotto. They're each trying to figure out 156 00:10:09,293 --> 00:10:13,118 where to allocate their resources, where to spend their time, where to spend their 157 00:10:13,118 --> 00:10:16,791 money, trying to convince voters, And except not only electoral college, but to 158 00:10:16,791 --> 00:10:20,827 win different factions of voters. Cuz you can also make a Blotto game playing out on 159 00:10:20,827 --> 00:10:24,574 factions of voters. What you get from those two lenses, and of course the other 160 00:10:24,574 --> 00:10:28,129 two lenses, is just a much richer understanding of the nature of political 161 00:10:28,129 --> 00:10:31,972 competition. It's gonna make you better able to predict what's gonna happen, also 162 00:10:31,972 --> 00:10:35,623 better understand what's going on and better able to think about how do you 163 00:10:35,623 --> 00:10:39,563 design institutions to pick a president. Again, which is one of the things we wanna 164 00:10:39,563 --> 00:10:41,933 do modeling for. Okay. Thank you.