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.