1:08

So this is the equilibrium prediction based on Nash equilibrium.

Actually in this game, black player is stronger than red player, and

more precisely, the winning rate of black player is 0.6,

and the winning rate of led, red player is 0.4, okay?

So now I'd like to ask you to think about the accuracy of

this game theoretic prediction, so those are the theory number, and

on the other hand I have real data winning rate calculated from the play

of the game in the first week, and I'm going to give you

three possibilities about the difference between the actual data and

the equilibrium prediction, number one, number two, and the number three.

And you should, you should think which one fits to

your expectation about the accuracy of this game's theoretic prediction,

so the first possibility so let's talk about red player.

The winning rate of red player should be 0.4 according to

game theoretic prediction, okay, so

the possibility number one says game theoretic prediction works so-so.

So the actual data actual winning de,

winning rate in the data is, is in the range of say 0.3 and

0.5, okay, so that's possibility number one.

Possibility number two the game theoretic prediction works reasonably well,

so the actual winning rate of red player is in the range of 0.35 and 0.45.

Okay, the last possibility, number three says that the game

theoretic prediction works reas, amazingly well,

so the actual winning rate of red player is in the range of 0.39 and 0.4.

Okay, number one, number two, number three, so please think which one

fits to your expectation about the accuracy of game theoretic prediction.

4:53

And my hunch is the following.

In the video game instruction card number one was phrased as ace, and usually,

ace is a pretty strong card in many card games, so maybe you are inclined to play

this strong card, ace, but otherwise the prediction worked pretty well.

And also by using this experiment o, of the card game,

I'm going to address the three concerns about game theory or

about predicting people's behavior by mathematical formula, okay.

So in the first week I explained that there are three valid, or

natural concerns about predicting people's behavior by using mathematical formula and

I use this game to address those concerns at the end of this lecture.

5:50

Okay, so this game was first invented by Barry O'Neill,

he is a professor at the UCLA now, and he discovered that

he ran lab experiments and he discovered that people's behavior

in this card game is amazingly close to Nash equilibrium prediction, right?

The result was in was reported in one of the leading science journals Proceedings

of the National Academy of Sciences in 1987, and I also have conducted

a series of experiments in my game theory class in the University of Tokyo.

So I have a large number of datasets, so

let's let me explain what I have found in those experiments, okay?

6:42

So this is my dataset.

I know the result of Barry O'Neill's original experiment in 1987, and

in the past ten years, I have been conducting this card game

with my undergraduate students in my game theory class at the University of Tokyo,

and I also had a few occasions which I, I let high

school students play this game, 'kay, so this is my dataset, and

let me show you what I have found, okay, about the winning red.

Okay, so equilibrium says that winning rate for red is 0.4, and

black's winning rate is 0.6.

In the original lab experiment by Barry O'Neill, 'kay,

the result is very close to the Nash equilibrium, 'kay, so I was surprised

when I first read his paper but I thought that he was just lucky, 'kay?

I thought he just got this almost perfect fit by chance,

so just to see if this experimental result can be reproduced I I

conducted studies of followup experiments in my game theory classes.

Okay so the first card game was conducted in 2004 in my class, and again,

the outcome was amazingly close to the Nash equilibrium prediction, and

I ran similar experiments again and again and every time, you know, the outcome

was amazingly close to Nash equilibrium prediction in terms of winning rates.

8:30

What about the distribution of cards?

Okay, equilibrium says that king should be played with a large probability,

probability 0.4, and each number card should be played with probability 0.2.

That's the equilibrium prediction.

In the original experiment by Barry O'Neill,

also the outcome was very close to Nash equilibrium prediction, okay?

And in my first experiment also, the outcome was very close, and

second, it was also close, and as you can see in all those experiments,

the outcome was amazingly close to the equilibrium prediction, okay.

Surprisingly, people's behavior is closely predicted by Nash

equilibrium, okay, so with those results in mind, let me address

three concerns about predicting people's behavior by mathematical formula.

Okay, so mathematical formula has been proven to be useful to predict natural

phenomenon like a falling ball, but now game theory is trying to apply

mathematical formula to predict people's behavior, and there are a few common and

valid concerns about predicting people's behavior by a mathematical model, okay?

So I explained those concerns in the first week, and there were three concerns.

The concern number one, well, people have free will, 'kay?

The falling ball doesn't have any,

you know, free will so it evades the mathematical law of motion,

okay, Newton's law and every time, it follows Newton's law but

human being have free will and we can do anything, right?

So if game theory says that this is, this is your behavior, this is your

this is the equilibrium prediction, we can always deviate because we have free will.

So concern number one about using mathematics to

predict the people's behavior says that we have free will, and

free will defeats any attempt to predict human behavior by a mathematical model or

a mathematical formula, well and second concern,

okay the subject of game theory of humans, okay?

And humans take certain behavior because they have some intentions, so

ultimately, you can use, always ask why did you do that,

okay, and then you can find out the reason.

So concern number two says that in mathematical formulation is useless, or

we don't need any mathematical model.

We can just collect facts, and we can just conduct interviews to find out what was

happening, and indeed, this was the the way we conducted

social science research before the invention of game theory.

We just used our intuition to explain how people behave, and

all you need is fact-finding, what happened, and

all we need is interview, why did you do that, so this was the second concern.

We don't need any mathematical model in social sciences, and

the third concern says I've never heard that game theory works, 'kay?

So I'm going to address all those valid concerns about game theory by means of

this card game.

12:13

Okay, concern number one,

free will defeats any attempt to predict human behavior by mathematical formula.

Well, it works pretty well in the card game, 'kay?

So even if people have free will,

they are attracted to the behavior that is best for them, okay?

So in this card game, given that other players are choosing an equilibrium

strategy, it's best for you to follow this equilibrium, so you are naturally

attracted to the behavior that is best for you even if you have a free will, okay.

13:01

Okay, so this is a result of a card game, and the data shows that people's behavior

is amazingly close to Nash equilibrium prediction but ask yourself

the following question, why did you choose your card in a subtle way, this way?

King was large probability and small probability for one, two, and three.

Well, I guess lots of you have hard time in articulating why you did it,

okay, so you used your instinct or intuition to play this game and

outcome was amazingly close to Nash equilibrium, okay.

So game theory can uncover the mech,

mechanism operating behind your instinctive behavior, so

sometimes you take some action out of intuition or out of some reason, but

oftentimes, you, you have hard time in articulating why you did it,

14:13

tool to find out that mechanism operating behind people's behavior, okay?

So just asking people how, why you do this?

In this particular card game, this kind of research program doesn't really work,

okay, so maybe you can find out that the distribution is uncertain, you know,

the distribution of the card is this way but

by just conducting interview with each

individual you can never find out why people just does this distribution.

15:00

the following except the mathematician Stan Ulam was teasing Paul Samuelson,

long-time ago back in 1930s, okay.

Stan Ulam was saying that social science is a fake sciences.

Natural sciences are the true sciences, 'kay, and

he teased Paul Samuelson, an economist, by posing the following question, 'kay?

Ulam challenged, okay, name me one proposition in

all of the social sciences which is both true and non-trivial.

Social sciences say that such and such thing should be true but

almost all of them are trivial, okay,

and there is no proposition in social science which is true and non-trivial.

That was true back in 1930s, but now with game theory we have many such examples.

This card game is one of those examples.