Name: 5.納什均衡：不良時尚與銀行擠兌事件 (5. Nash equilibrium: bad fashion and bank runs)
Uploaded: 2021-01-14T06:08:09.000Z
Duration: 1 h 9 min 14 s
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Professor Ben Polak: Okay, so last time we came

過去簡單式

across a new idea, although it wasn't very new for

a lot of you, and that was the idea of Nash

discuss Nash Equilibrium, see how we find that

And then in the second half of the day I want to look at an

application where we actually have some fun and play a game.

At least I hope it's fun. But let's start by putting down

a formal definition. We only used a rather informal

A strategy profile--remember a profile is one strategy for each

S_M* if there are M players playing the game--so

this profile is a Nash Equilibrium (and I'm just going

to write NE in this class for Nash Equilibrium from now on)

player i, her choice--so her choice here is S_i*,

i is part of that profile is a best response to the other

players' choices. Of course, the other players'

playing a best response to everyone else.

Now, this is by far the most commonly used solution concept

interviewing for McKenzie or something, you're going to find

that they're going to expect you to know what this is.

So one reason for knowing what it is, is because it's in the

textbooks, it's going to be used in lots of applications,

it's going to be used in your McKenzie interview.

That's not a very good reason and I certainly don't want you

to jump to the conclusion that now we've got to Nash

Equilibrium everything we've done up to know is in some sense

It's not always going to be the case that people always play a

when we played the numbers game, the game when you chose a

week or last time, that the equilibrium in that

but when we actually played the game, the average was much

higher than that: the average was about 13.

It is true that when we played it repeatedly,

but the play of the game when we played it just one shot first

time, wasn't a Nash Equilibrium. So we shouldn't form the

mistake of thinking people always play Nash Equilibrium or

people, "if they're rational," play Nash Equilibrium.

Nevertheless, there are some good reasons for

thinking about Nash Equilibrium other than the fact it's used by

other people, and let's talk about those a

motivations here--the first motivation we already discussed

audience mentioned it, and it's the idea of "no

It says, suppose we're looking at a Nash Equilibrium.

If we hold the strategies of everyone else fixed,

no individual i has an incentive to deviate,

to move away. Alright, I'll say it again.

Holding everyone else's actions fixed, no individual has any

incentive to move away. Let me be a little more careful

So no individual can do strictly better by moving away.

No individual can do strictly better by deviating,

So why I call that "no regret"? It means, having played the

game, suppose you did in fact play a Nash Equilibrium and then

and now you know what everyone else has done and you say,

"Do I regret my actions?" And the answer is,

"No, I don't regret my actions because I did the best I could

given what they did." So that seems like a fairly

important sort of central idea for why we should care about

and we'll see others arise in the course of today.

A second idea is that a Nash Equilibrium can be thought of as

self-fulfilling beliefs. So, in the last week or so

we've talked a fair amount about beliefs.

If I believe the goal keeper's going to dive this way I should

shoot that way and so on. But of course we didn't talk

about any beliefs in particular. These beliefs,

if I believe that--if everyone in the game believes that

everyone else is going to play their part of a particular Nash

play their part of that Nash Equilibrium.

believes that everyone else is playing their part of this

particular Nash Equilibrium that that's so fulfilling and people

actually will play that way? Why is that the case?

Student: Because your Nash Equilibrium matches the

best response against both. Professor Ben Polak:

Exactly, so it's really--it's almost a repeat of the first

going to play their particular--if I think players 2