Hi, we've been talking about the kernel blotter game. The kernel blotter game is a

way to analyze competition, where it's along multiple fronts and the idea is to

strategically mismatch your opponent. What I'm going to do this last lecture, I'm

kind of blotto, is expand the discussion a little bit and talk about competition

generally. So when you think about firms competing you think about sports teams

competing we can think about individuals competing and what I'm going to do is

think about some of the models we've discussed in these last couple lectures

and see how they apply to our understanding of what happens in those

competitive environments. Now as we do that I want to think of two different

types of competition so one type of competition if you think of let's say some

auto companies competing for market share you can have a position where each one is

going to get a percentage in the market you know so GM may get 30 percent Toyota

Ford maybe twenty% Toyota maybe get twenty percent Chrysler maybe get ten%. And so on

right so there's more firms down here smaller firms so you can think about just

competing for market share. You can also think about sports team. This is Siri A,

you think about, here's different sports teams and they're gonna have win-loss

records. So this team may go fourteen and six, this team may go seven and thirteen.

Sorry about that [inaudible]. You know, each team's got a win-loss record and each

is gonna play against each other. So we think about the data we got from

competition, it could be one of two forms, it could be market share or it could be

sort of win-losses against different teams. And what we wanna think about is,

if we take our different models, can they help us make sense of that competition?

And that by adjudicating between different models, can we figure out, maybe, what's

really going on in these different environments? Does the auto market look

differently than Soccer Competition between, like, a soccer league? So we've

got a bunch of models. Let's just talk about four . We've got just a pure random

model, performance is random. We've got our skill plus luck model. We've got a

finite memory random [inaudible] model, and then we've got the Blotto model. These

are all models that look at competition. So in the random model, it's just. You

know, you just get a value, and it's random who wins. In the skill plus luck,

there's a skill component, and a luck component. In the finite memory random

luck, it's sort of random, but you've got this moving window. And then, finally, in

Blotto, you've got some set of troops, and you're allocating them across fronts. So

these are all different ways to think about competition, and they all say

slightly different things. So what I wanna do in this lecture is just, just pretty

quickly go through each one of them, and talk about the different things they say

that we'd expect to see. And then we can think about which one of those fits a

particular real world situation best. So let?s number the random model suppose

performance really is random that it's like the efficient market I bought so

suppose the case of who's a good stock broker really is random. Well, what should

we expect? We should expect equal wins. We should expect no one to be better than

anybody else. We should see a lot of regression to the mean. And we should see

no time dependency. Somebody who's done well this period shouldn't necessarily do

well next period. Now if we look at investment people, if we look at sort of,

you know, mutual funds, it actually doesn't look unlike this. You know,

there's not a lot of time dependency. Who won last year don't, doesn't necessarily

determine who's gonna win this year. And this may not be a bad model of that. Now,

if we contrast that with the skill plus luck, we'd expect to see unequal win.

Wins. We'd expect to see some people who are consistent winners. So we'd expect

sort of semi consistent rankings, with the higher ability people doing better,

keeping in mind the paradox of skill of two people who are close in ability.

They're gonna move bac k and forth in terms of who does better. But we'd expect

to see semi consistency. And we wouldn't expect to see a huge amount of time

dependency in the sense of like, how I did last period wouldn't have a big influence

on what I do this period, you know, given that we know my skill level. So there

wouldn't be any correlation in the error terms. And so you can look at some

companies, you could argue that you know, if you look at industry market shares,

that this may be a decent model. Or if you look at, you know, possibly some sports

competition, this may be a decent model. But we'll see there's other models that

might work as well. What about the finite memory random walk? Well, here, you're

gonna have unequal wins, just like we had in the skill plus luck. And we're gonna

have semi consistent rankings. 'Cause the fact that if you happen to get a bunch of

good draws in a row, you're gonna continue to get those. You're gonna see a lot more

time dependency; 'cause it's really gonna depend on what you did in the previous

time. But where this is gonna differ from. The skill plus luck model, is you're gonna

get movement from top to bottom. 'Cause in skill plus luck, remember, it's like A

times luck plus one minus A times skill. And so if you've got high skill, you're

always gonna stay pretty high. In the finite memory random walk, your values

like XT plus XT minus one plus XT minus two and so on. Well, after you move ahead

ten periods, your values are gonna be, all these values that made you good at this

point in time will be gone. They'll have been chopped off the end of the random

walk. So you're gonna see a lot more regression to the mean, and more movement

from top to bottom in the finite. And whenever you ran a luck model then you

would in the skill plus luck model. So again if you're looking at data within an

industry or a [inaudible] and you want to think which one of these is it, this sort

of statistical signature is going to be different than what you see from the

[inaudible]. Okay, what about Blotto with equ al troops? [inaudible] equal troops,

equal ability. Then the outcome's, this is gonna be hard to tell from random. It's

gonna look a lot like random, but you're gonna see lots of maneuvering. Because of

its Blotto, each period, everybody's gonna be trying to take a random action. And so

therefore, you're gonna see all sorts of trade, all sorts of maneuvering, to try

and position your troops [inaudible] over the troops of other people. But you're

gonna see in the outcome itself any difference between Blotto and random. But

you will be able to see it in terms of the actions that people take. What about when

there's unequal troops? Well now it's gonna be more like the skill plus luck

thing. Cuz if you've got more troops, you're gonna be more likely to win.

However, because there's gonna be maneuvering, sometimes the lesser

[inaudible] person would win. So statistically, it's gonna look a lot like

skill luck, however, at the micro level. You're gonna see lots and lots of

maneuvering. So if you look at something like American football, which has a salary

cap, so you can only spend so much on your players. There are teams that have better

management, and also just happen to have better players that they've signed into

contracts. So the outcomes there may look a lot like the skill luck model. But you

see tons and tons of maneuvering in professional football, which suggests that

in fact, there may be a Blotto like character to it, Where you're trying to

get players that match up well against the strengths and weaknesses of your

opponents. So Blotto with unequal troops is going to lock, look somewhat like

skill, we're going to see lots of unequal maneuvering. What if I add in limited

movement? What I mean by that is that you can't just sort of reallocate your troops

every period. You've actually gotta trade resources with someone else, which would

be true in a football league, or it'd be true in a firm. We've gotta sort of get

rid of employees and bring new employees. You can only move a little bit. Well if

that's the ca se, if we go back to our example of sort of multi-player

[inaudible], we should expect to see lots of cycles. We should expect to see where A

beats B, B beats C, and C beats A. That's gonna be different than the skill-lock

thing. So in the skill-lock model, we may have the case that, you know, one team

wins 70%, one team wins 60, one team wins 50, one team wins 40, one team wins 30.

Now we won't see a lot of cycles. We won't see consistently A beat B, B beat C, and

then C beat A. If it's plotted with limited movement, you should be more

likely to see that. But generally, how do we determine? How do we tell that it's a

Blotto game, or whether it's a skill luck game? Well, one thing to think about this

is in terms of dimensionality. If the players are making high dimensional

strategic decisions, it's sort of more like Blotto. It's also the case that if

it's definitely zero sum, then it's more like Blotto. You could have a skill luck

game where we both get better. And so the things we're investing our resources in is

just to improve our ability. That's more skill luck like, Whereas, in Blotto, it's

all about strategically mismatching what we've got against you. And so you can

think of high dimensional sports like football, may be more like Blotto. 100

meter dash, marathon running, things like that, may be more skill luck. Tennis, more

like Blotto, javelin throwing, more like skill luck. Let's take a particular case,

let's take the presidential election United States. And think about. How do

these different, what do these different models tell us and which one makes the

most sense? So I could think that whoever wins the presidential election is just

random because it just depends on random shocks to the economy and the winner is

just gonna depend on these economic shocks and there is some evidence to support this

but I think that it probably doesn't fully capture things. Now we could say that it's

sort of luck and skill, that these candidates have skill, they got ability to

communicate, they got past experience, and there's also these economic shocks and

again, there's some evidence to support that better candidates do seem to win.

[sound] You could also tell a random walk model. You could say, look, it's not just

one random shot to economy, it's a whole bunch of random events. You know, it

depends on what's happening in the world economy, it's what happening in

international relations, what's happening domestically. What's happening? The social

movements at the time. So a whole bunch of random events add up to determine the

popular of the incumbent president, or the incumbent party, and that determines who

wins. And again, that may not be a bad model. Finally with Blotto, if you think

of it being, well there's only this sort of allocations of troops across fronts. In

a presidential election, it's the electoral college game. And you gotta

figure out, where do we allocate our troops? Now, that captures some of it, as

well, right. But the thing is that you also think that we've got to have unequal

troops; because whoever served got more skill or had to give shocks, is more

likely to, needs fewer troops on some of those fronts. So what we see by having all

these different models is we get many different lenses on what's going on in an

election. Now is anyone of these right, no. Now [inaudible], when we say, oh,

presidential elections, those things are just a pure luck skill. They're not.

They're a combination of all these things, and by having multiple models to look at

them, what we do is we have a lens, through which we will get a deeper

understanding of what's going on. 'Cause where we wanna be, right, is you wanna be

in a place when somebody confronts with something like, how does a presidential

election unfold, that we've got a bunch of frameworks within which we can view that

particular event, and say, here's what I learned from this framework. So you can

say, there's a sense in which the winner of the presidential election is luck,

because it comes down to economic shocks going their way. And at the other extent,

we ca n also say, look, another way to think about these presidential elections,

though, is it's this elaborate game of blotto. They're each trying to figure out

where to allocate their resources, where to spend their time, where to spend their

money, trying to convince voters, And except not only electoral college, but to

win different factions of voters. Cuz you can also make a Blotto game playing out on

factions of voters. What you get from those two lenses, and of course the other

two lenses, is just a much richer understanding of the nature of political

competition. It's gonna make you better able to predict what's gonna happen, also

better understand what's going on and better able to think about how do you

design institutions to pick a president. Again, which is one of the things we wanna

do modeling for. Okay. Thank you.

Blotto and Competition

Model Thinking

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