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The Prisoner's Dilemma as a Model of Cooperation

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神经经济学入门：大脑如何作出决定

国立高等经济大学

4.7（1,056 个评分） | 73K 名学生已注册

Economics, psychology, and neuroscience are converging today into a unified discipline of Neuroeconomics with the ultimate aim of creating a single, general theory of human decision-making. Neuroeconomics provides biologists, economists, psychologists and social scientists with a deeper understanding of how they make their own decisions and how others decide. Neuroscience, when allied with psychology and economics, creates powerful new models to explain why we make decisions. Neurobiological mechanisms of decision-making, decisions under risk, trust and cooperation will be central issues in this course. You will be provided with the most recent evidence from brain-imaging techniques (fMRI, TMS, etc.) and introduced to the explanatory models behind them. The course does not require any prior study of economics and neuroscience; however, it might require you to study novel interdisciplinary materials. The course provides an introduction to the methodology, assumptions, and main findings of Neuroeconomics. Our students have different backgrounds; therefore, I have adapted and simplified the course to allow all students to understand the interdisciplinary content. This course will help you to start your progress in the field of Neuroeconomics and to further develop your skills during other more advanced courses and trainings in the future. For some topics, the course will also provide supplementary videos to reveal the opinions of leading experts in the field. Each module provides optional reading material. The course structure is as follows: During each video, you will have to answer some relevant questions. Your answers will not affect your final grade. At the end of each module, you must complete a quiz consisting of 15 questions. To pass the course, you must reach a satisfactory standard in all the course modules by completing all graded quizzes and the final exam. In addition to watching video lectures and taking quizzes, you will receive an invitation to join our forum. We plan to join the discussions in the forum on a weekly basis. Welcome to Neuroeconomics World!

查看授课大纲

您将学习的技能

Neuroeconomics, Biology, Education, Neurobiology, Brain

审阅

4.7（1,056 个评分）

5 stars
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VM

Nov 16, 2017

Very interesting course and a very professional lecturer! Thank you for broadening my knowledge! However, I don't really see how we can apply this information to real life practices.

R

Jan 01, 2016

I really enjoyed this course. Therected were repetitions but I think that goes hand in hand with learning. The statistics were questionable but so is everything in Neuroscience :D

从本节课中

The Social Brain: Games in the Brain

Ancient Greek philosophers observed that we are fundamentally a social species. Indeed, the human brain has evolved to deal with complex social interactions. Day by day, we collectively analyze problems or situations and evaluate alternative courses of action within social groups. Game theory has proven useful in the investigation of the neural basis of social interactions and social decision-making. In particular, researchers have investigated what happens in the brains of subjects involved in games where each player can choose between cooperative and non-cooperative behaviors or between altruistic and selfish behaviors. Here we will apply game theory to studying the neural mechanism of decisions to cooperate or to defect. I will also introduce the mirror neurons mechanism of social interaction.

Game Theory as a Tool to Study Decisions in Groups17:23

The Prisoner's Dilemma as a Model of Cooperation13:36

教学方

Vasily Klucharev
Professor and Head of the Department of Psychology

脚本

[SOUND] To model, cooperative and

competitive behavior, we can

use the Prisoner's Dilemma game.

So this Prisoner's Dilemma game suggests,

that there are two suspects in a major crime.

And these two suspects, are held in different cells in the prison.

There is enough evidence, to convict each of these suspects in a minor offense.

But there is no enough evidence, to convict either of them of the major crime.

Unless one of them will fink.

And one of them, will actually tell and

give some information about the second suspect.

So, if both suspects stay quiet, both of them will be convicted for

the minor offense and

they will spend three months in jail, but if we, if one of them will fink.

And will give some information about the second suspect.

This guy will be freed and the second one will get 20 years in prison.

So, if both of them will fink, each will spend five years in prison.

So here each suspect faces a dilemma,

was to cooperate with another suspect or to deflect.

So we can actually represent this dilemma in a more formula way,

as a decision matrix.

So here, we see two suspects and

if both stay quite, they will spend three months in prison.

If both will fink, they will spend five years in prison.

If one will fink and another one will stay quiet, the first guy will be freed and

the second one, will spend 20 years in jail.

If the second one, will fink and the first one will stay quiet.

So we have as the opposite situation.

So here, we have an incentive to cooperate, and

also, we have an incentive to cheat.

And this is a dilemma, for two suspects.

So we can represent this, strategic game.

In the most horrible way.

So there are two suspects, two players.

There's a set of actions.

Each player can either cooperate or defect, so stay quiet or fink.

As there is a clear, set of preferences so, if there's a best outcome for

the suspect and the suspect finks and another suspect, is quiet and there

is a reverse situation, when our suspect stayed quiet and another one finks.

So, actually this situation models various, social situations,

and there is an incentive to cooperate, but also in a sense of the free right.

So prisoner dilemma, is a really great model that,

can help us to understand how the people make decisions in group.

So for example here, I illustrate another situation using the prisoner dilemma.

So here is your landlord and the customer.

A landlord and a student, for example.

Student would like to rent room.

If landlord provides a key and the customer pays, let's say $250 for

the room the landlord gets a profit, $250.

In case, if landlord gives a key, but

the customer, by some reason, doesn't pay back.

Actually, landlord can lose $250.

So in case, if the landlord doesn't give the key and

customer pays the money, the landlord can actually double the profit,

because he can collect the money and also get an extra $250 from another customer.

So, in case the landlord defects and the customer defects, nobody gets any money.

So prisoner dilemma nicely illustrates very social situations,

when we can cooperate or we can defect.

And we have some incentives to cooperate.

We also have some incentives to defect.

So, what is the optimal decision, in the prisoner dilemma?

You can apply a Nash equilibrium.

So, informally, a set of strategy is a Nash equilibrium,

if no player can do better by unilaterally changing his or her strategy.

So here is a prisoner dilemma.

Imagine that you're player one, so player two, for example, defects.

In this case, it is rational to also defect,

because otherwise you will lose $250.

Imagine now that the player two cooperates.

In this case, it is also rational.

To defect, because otherwise you would get twice less amount of money.

Since that pay of metrics is symmetrical,

actually there is only one decision, that represent a Nash equilibrium.

This is decision to defect.

So, present dilemma suggests.

There is only one rational solution for the dilemma, when both players defect.

Actually, it brings us a very sad conclusion.

It suggests that in the situation of the present dilemma, we always should defect.

So if we have a group of cooperators, if suddenly, due to a mutation,

for example, one defector, would appear in this group,

this defector, will outperform the rest of the group.

And with time, this group, will be overpopulated by defectors.

So, this metaphor of mm, prisoner dilemma suggests, that there is only one rational

solution for the prisoner dilemma, both players all players have to defect.

So, it doesn't bring us any space for cooperation.

And, actually, if we will come back to our world real life example.

Prisoner dilemma can be applied to a nuclear war situation.

And it was applied.

So the idea of the recent dilemma, was used in the Rand Corporation,

to model the decision, to bomb or not to bomb soviet union.

So actually, the great Game Serials like John Nash and John Neumann.

Were engaged into the analysis of the nuclear war, situation.

And actually, at that time, game theory,

suggested, to conduct a preemptive attack, the Soviet Union,

before Soviet Union would develop own nuclear bomb so here,

you see actual words of John Neumann, who suggested,

if you say why not the bombs in tomorrow I say why not today?

If you say today at five o'clock, I say why not at one o'clock?

And actually Bertrand Russell.

The famous mathematician of so

interesting there is a game theory suggests, that in the case of

the prisoner dilemma, you shouldn't cooperate, you should always defect.

But come on, we all understand that cooperation brings some benefits,

so, how can we find the place for cooperation using the game theory?

Actually, we can show that corporations can bring some benefits, but

to understand this, we have to introduce a new parameter omega,

the probability that the players will meet again.

This is so-called the shadow of the future parameter.

So if the, omega is low,

there is a very small chance that players will meet each other again.

And in this case, it doesn't make sense to cooperate.

But if omega is relatively large, it makes sense to cooperate,

because using various strategies, you can actually reinforce cooperative

behavior within the group and you can have a net benefit at the end.

So let's make a look to the details of this idea.

But first, let's try to understand the idea of the omega.

So, for example, why do you fink.

There is this interesting phenomena of a lame duck.

So, you know, that elected officials at the end of their tenure,

quite often are ignored by other politicians.

So why is a president of a big country,

at the end of his tenure is quite often ignored by other politicians?

So what do you fink?

Why is that happening?

So perhaps because the omega is very small.

So there is a very small chance that other politicians,

will meet this person again, during the political process.

That's why, they completely ignore this person as

they would never cooperate with him.

So, it is very rational, to not cooperate with the people.

You would never meet again, and it is more rational to cooperate with other people,

if there was a chance to meet these people again.

So, the game theory suggests, that if the game is played only once,

then each player, gets a higher payoff, from defecting than from cooperating,

but, if the game is played repeatedly, for example,

in the iterated prisoner dilemma game, there is a greater room for cooperation,

so people can re-enforce cooperation, by certain behavioral strategies.

So lets make a look to the strategies.

So Sir Robert Axelrod conducted the very famous competition.

So he compared different strategies, applied, for the, prisoner dilemma game.

So this competition showed the tit for tat strategy,

outperformed all other strategies, for the iterated prisoner dilemma game.

So what is a tit for tat strategy?

It's a very simple strategy.

Cooperate in the first trial and in the next trial,

repeat the behavior of the second player in the previous trial.

So, you should cooperate in the first trial and if another person, second

player, cooperates in the second trial, cooperates in the full ops trial also.

If another person defects.

Defect in the next trial, and so on.

So we can characterize the tit for tat strategy by four important points.

Be nice, so, cooperate in the first round.

Reciprocate.

Return defection for

defection, so if we, another person defect, also defect in the next round.

If person, a player, to cooperate.

Cooperate in the next trial.

Don't be envious.

Be fair with your partner.

And don't be too clever, because Robert Exler wrote competition shows that, very

simple strategy like tit for tat strategy, outperforms, more complex strategies.

So the tit for tat strategy is a, collectively stable strategy.

So if the group of cooperators, uses the tit-for-tat strategy.

This group, is resistant to the invasion, by their non-cooperators.

So, if they chance to meet another person,

again, is relatively high, if their omega is large.

So reciprocation of the cooperation and the reciprocation of the defection,

can stabilize the cooperative behavior of reasons of groups.

So many studies and models show that the group of cooperators,

can sustain cooperation within the group, using three important approaches.

So first of all, the group can use direct reciprocity.

So if, if, the defector defects cooperators should also defect,

in the next trials.

If the defector cooperates, cooperators should also cooperate in the next trial.

So this strategy is a tit-for-tat strategy,

can sustain cooperations in the group.

Additionally, cooperators should leave in groups.

The group of cooperators, can out perform the group of defectors.

And finally, it is important to punish defectors.

So you can punish those who defect, and

also you can punish those who do not punish those who defect.

So, with these different forms of punishment.

You can dramatically increase cooperation within the groups.

So let's try after the short break,

to understand, how this process are implemented in our brains.

[SOUND]

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