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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.