Name: ゲーム理論。意思決定の科学 (Game Theory: The Science of Decision-Making)
Uploaded: 2021-01-14T06:35:19.000Z
Duration: 9 min 50 s
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When you’re hanging out with your friends, you probably don’t think too hard about

the math behind the decisions you’re making.

But there’s a whole field of math — and science — that applies to social interactions.

Game theory was pioneered in the 1950s by mathematician John Nash, the guy from that

Russell Crowe played in A Beautiful Mind.

But game theory isn’t about games the way we normally think about them.

Instead, a game is any interaction between multiple people in which each person’s payoff

is affected by the decisions made by others.

So, sure, that could apply to a game of poker.

But it could also apply to practically any situation where people get together and get

Like, did you interact with anyone today?

Well, you can probably analyze the decisions you made using game theory.

Game theory is incredibly wide-ranging, and it’s used all the time by economists, political

scientists, biologists, military tacticians, and psychologists, to name just a few.

Game theory has two main branches: cooperative, and noncooperative, or competitive, game theory.

Noncooperative game theory covers competitive social interactions, where there will be some

Probably the most famous thought experiment in competitive game theory is the Prisoner’s

The prisoner’s dilemma describes a game — a social interaction — that involves

Wanda and Fred were arrested fleeing from the scene of a crime, and based on the evidence

the police have already collected, they’re going to have to spend two years in jail.

So he offers them both a deal: if you confess to the crime, and your partner does not, you’ll

Your partner, though, will serve ten years in jail.

If you both confess, and dish up loads of dirt about each other, then you will both

But if neither of you confess, you’ll both spend only two years in jail.

They don’t know what their partner is going to do.

They have to make their decisions independently.

Now, Wanda and Fred they- they’ve had some wild times stealing diamonds or whatever,

but they don’t have any special loyalty to each other.

They’re not brother and sister; they’re hardened criminals.

Fred has no reason to think Wanda won’t stab him in the back, and vice versa.

Competitive game theory arranges their choices and their potential consequences into a grid

If both Wanda and Fred choose not to confess, they’ll both serve two years.

In theory, this is the best overall outcome.

Combined, they would spend as little time in prison as possible.

But … that immunity sounds pretty good.

If one of them chooses to confess, and the other one doesn’t, the snitch gets to walk.

That’s the problem: Wanda and Fred have no reason to trust each other.

Wanda might consider not confessing, because if Fred doesn’t confess either, they both

If they could really trust each other, that would be their best bet.

But Wanda can’t be sure that Fred won’t snitch.

If he does decide to confess, and she keeps silent, she’s risking ten years in jail

Compared to that, the five years they’d get for both turning on each other doesn’t

And that is game theory’s solution: they should both confess and rat each other out.

So, right now you’re thinking, “Wow, game theory is a jerk.”

That square in the grid where they both confess is the only outcome that’s reached what’s

This is a key concept in competitive game theory.

A player in a game has found Nash Equilibrium when they make the choice that leaves them

better off no matter what their opponents decide to do.

If Wanda confesses, and Fred does not confess … she’s better off.

By confessing, she went from serving two years in prison to serving none.

If Fred does confess...she’s still better off.

If she’d kept her mouth shut, she’d be spending ten years in prison.

Sure, if she decides not to confess, and Fred keeps his pinky promise too, they both get

Because Wanda can’t trust Fred- she doesn’t know what he’s going to do.

This is not a cooperative game: all of the players stand to gain from stabbing each other

The Prisoner’s Dilemma is just one example of a competitive game, but the basic idea

behind its solution applies to all kinds of situations.

Generally, when you’re competing with others, it makes sense to choose the course of action

that benefits you the most no matter what everyone else decides to do.

Then there are cooperative games, where every player has agreed to work together toward

This could be anything from a group of friends deciding how to split up the cost to pay the

bill at a restaurant, to a coalition of nations deciding how to divvy up the burden of stopping

In game theory, a coalition is what you call a group of players in a cooperative game.

When it comes to cooperative games, game theory’s main question is how much each player should

contribute to the coalition, and how much they should benefit from it.

In other words, it tries to determine what’s fair.

Where competitive game theory has the Nash Equilibrium, cooperative game theory has what’s

The Shapley Value is a method of dividing up gains or costs among players according

to the value of their individual contributions.

Number one: the contribution of each player is determined by what is gained or lost by

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ゲーム理論。意思決定の科学 (Game Theory: The Science of Decision-Making)

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