We live in a complex world with diverse people, firms, and governments whose behaviors aggregate to produce novel, unexpected phenomena. We see political uprisings, market crashes, and a never ending array of social trends. How do we make sense of it? Models. Evidence shows that people who think with models consistently outperform those who don't. And, moreover people who think with lots of models outperform people who use only one. Why do models make us better thinkers? Models help us to better organize information - to make sense of that fire hose or hairball of data (choose your metaphor) available on the Internet. Models improve our abilities to make accurate forecasts. They help us make better decisions and adopt more effective strategies. They even can improve our ability to design institutions and procedures. In this class, I present a starter kit of models: I start with models of tipping points. I move on to cover models explain the wisdom of crowds, models that show why some countries are rich and some are poor, and models that help unpack the strategic decisions of firm and politicians. The models covered in this class provide a foundation for future social science classes, whether they be in economics, political science, business, or sociology. Mastering this material will give you a huge leg up in advanced courses. They also help you in life. Here's how the course will work. For each model, I present a short, easily digestible overview lecture. Then, I'll dig deeper. I'll go into the technical details of the model. Those technical lectures won't require calculus but be prepared for some algebra. For all the lectures, I'll offer some questions and we'll have quizzes and even a final exam. If you decide to do the deep dive, and take all the quizzes and the exam, you'll receive a Course Certificate. If you just decide to follow along for the introductory lectures to gain some exposure that's fine too. It's all free. And it's all here to help make you a better thinker!
Applications of Colonel Blotto
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Из курса от партнера University of Michigan
Model Thinking
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Randomness and Random Walks & Colonel Blotto
In this section, we first discuss randomness and its various sources. We then discuss how performance can depend on skill and luck, where luck is modeled as randomness. We then learn a basic random walk model, which we apply to the Efficient Market Hypothesis, the ideas that market prices contain all relevant information so that what's left is randomness. We conclude by discussing finite memory random walk model that can be used to model competition. The reading for this section is a paper on distinguishing skill from luck by Michael Mauboussin.
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Scott E. PageProfessor of Complex Systems, Political Science, and Economics
Center for the Study of Complex Systems
Hi. [sound]. Talking about the Colonel Balotto gain. What I want to do in this
very brief lecture is talk about its wider applicability. So one of the reasons we
construct models is that they're often incredibly fertile. So we can take a model
that we used for one reason and apply it in other settings. So we saw some extreme
examples of this with the Markov process, right. [inaudible] Markov process fit to a
reason, and we could use it for figuring out whether drug protocols work, and we
can even use it to figure out who wrote a particular book. Here we're going to use a
more direct application. So we've got this [inaudible], which is troops and fronts.
So it has military origins. What we're going to see is that same model can be
used in other contexts to help us understand other forms, Terms of
competition. So, just what I'm going to do in this lecture, is go through some
examples, where in my opinion anyway, Blotto applies. So again let's remind
ourselves what blotto is we got two players each one has some set of troops
that they have to allocate across some fronts [sound] their action is just how do
I allocate my troops across those fronts and then we determine the winner by
looking front by front to see who had the most troops whoever had the most troops
wins the game very straight forward so its clear that, that works for a military
battle where each one of us is lining up our troops along these fronts and whoever
has the most troops if you have more troops here you win so it's clear that it
works in a military setting. But does it apply elsewhere? What I'm gonna convince
you is yes. So here's the first example, The US electoral college. So, to be
President of the United States, you don't have to win the most votes. What you have
to do is win the most states. What you can think of is you can think of each state as
a front. So you've got Colorado's a front, Michigan's a front, Florida's a front,
increasingly Ohio's a front. So what you have to do, if you're running from
president, where do I allocate my quot e unquote troops. Now what are troops here?
Troops are money. So each candidate has some set of money that they can use for.
Hiring volunteers, running television radio ads, running rallies, They've also
got troops, can also be their personal time. Where do they spend time? So if you
think about political candidates spend time, there's some States like recently
California, even though it's got the most votes, hasn't been in play for the
Republican candidate. And so therefore, since the Republicans know the Democrats
are gonna win, neither candidate even campaigns there. So they don't put any
troops there. So you can think of the Electoral College game as just one big
game of Blotto, where each person's trying to decide where to allocate troops. So you
have some elections, like the contested election between Bush and Gore, where, at
the last minute, George Bush went and put a whole bunch of troops in Tennessee,
which was Gore's home state. Gore hadn't put many troops in Tennessee, 'cause he
thought for sure he'd win it. And it turns out that then Bush then won Tennessee,
costing Gore the election. So this Electoral College game is a lot like a
game of Blotto. And how do you win? Well. You have more troops, more money, more
resources and you strategically out think the other person, figuring out where
should I allocate my troops, just so I can edge out the other person in that
campaign. Terrorism is another example. You think of terrorism there's a whole
bunch of places where a terrorist organization could attack. So what? The
government has to do is, the government has to then somehow put constraints on
them, put troops, resources in places to prevent terrorist activities from taking
place. So you could think of all these possible fronts. Airports, train stations,
bus stations, stadiums, financial service systems, water systems, all sorts of
things. All sorts of, whole set of fronts, and they've gotta decide, the government
does, how do we allocate our resources so we can stop the terrorist? Now here, it's
slight ly different maybe than Blotto, in the sense that the terrorist might not
need to win every front. They might only need to win one front. Now you think well
that's gonna be easy. Well it may not be easy because the fact is the government
has a lot more resources then the terrorist group has. In fact if the
government knows exactly how many resources the terrorist group has, they
can put exactly enough resources on each front to prevent them from being
successful. Let's take something else. Let's take trials. Suppose you've got two
lawyers going at each other. Would Blotto work there? Well, it's not actually a very
bad approximation. So who are the players? The players are, the, you know, the
prosecution and the defense, the two lawyers. And then you think, what are the
fronts? Well, the fronts could be lines of defense or lines of prosecution. So you've
gotta sit there and think, well, okay, these are the ways this case could get
played out. Now, in preparing for this case, the lawyers have to decide, how much
time do I spend on each of those lines of defense? And the point is, if I don't
spend much time on one of them, and my opponent does, I could lose that.
Argument, and whoever wins the most arguments, may win the case. Now again,
it's not a perfect match, but its close. So you think about, boy, my lawyer really
outsmarted the other lawyer. Well did she or did she just happen to have put her
troops on the right fronts, given where the other lawyer had put his troops, Even
hiring. It's interesting, when I talk to you about hiring; I often find that hiring
looks a lot like blood. Because what happens? You get a bunch of employees and
you're trying to decide, who do we hire? Let's suppose that we just got two
applicants, and you look at their resumes. And you see, okay, they've got education,
they've got work experience, they've got, maybe, some set of skills, maybe they've
got interviewing skills, you know, they got technical skills, interviewing skills.
And when you do this for each person you can write down a number for their
education level, their work experience, their strategic skills, their technical
skills, their interviewing skills, whatever. And then you compare them one by
one. It becomes almost like a game. Blotto for this position, You decide what the
fronts are, which are the skills you want the person to have for the job and then
you compare people one by one. So it's like a game of Blotto. And the winner
isn't necessarily someone who's better, who has more ability. It could be the
person who happens to have the right troops, so to speak, the right abilities
relative to the other person. [sound] Finally sports. Think of sports. Think of
two people playing tennis or, you know, people wrestling or boxing or something
like that. You can think of there being many fronts, or many dimensions, on which
the game is played. So let's take tennis. There's serving, there's return of serve.
There's volley, there's net play, ground strokes, all sorts of stuff. Each one of
those is like a front. You can think of a player's ability as being their skills on
each of those fronts. Now if I dominate you, if my return of serve is really good
and your serve is weak that means I'm gonna win on that front. And whoever wins
on the most fronts may be likely to win the match. This could explain why some
players have. [inaudible] against others. Like so maybe a can be b and b can be c
but then c in turn can be a, because of the fact that it isn't just, person of
higher ability. In fact it's the case that you see cycles because of the fact that it
really is a game of Balotto. So what have we learned? We've learned that Blotto,
which was developed for warfare for putting troops on fronts, applies to a
whole bunch of different stuff. It applies for the Electoral College, to terrorism,
to trials, to sports, even hiring decisions. And we can get insights from
Blotto to all those different environments. We've already seen from
Blotto that any position can be beaten by somebody else. We've also seen that you
don't need all your troops to win. What we're gonna do in the next lecture is see
how much of an advantage it is to really have more troops. And what you should do.
So, if you're at a disadvantage, if you don't have all those troops. Okay. Thanks.
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