October 03, 2006

DON'T HATE THE GAME (THEORY) 2: THE PRISONER'S DILEMMA


Caption: These prisoners have lots of dilemmas.

This is the second post in a series about how one aspect of game theory can shed very practical light on many kinds of human (yes, and animal) interactions.

The series is inspired by the insights of Robert Axelrod's The Evolution of Cooperation.

One scenario often used to study situations in which one party doesn't know how another will react is the Prisoner's Dilemma. Axelrod describes it thus:

The story is that of two accomplices to a crime are arrested and questioned separately. Either can defect against the other by confessing and hoping for a lighter sentence. But if both confess, their confessions are not as valuable. On the other hand, if both cooperate with each other by refusing to confess, the district attorney can only convict them on a minor charge. Assuming that neither player has moral qualms about, or fear of, squealing, the payoffs can form a Prisoner's Dilemma.


This game is interesting because it is a common situation in real life in this respect: both players can mutually benefit each other or one can take advantage of the other or neither can cooperate.

It sort of corresponds to win/win, win/lose, or lose/lose.

This game is different from chess or, say, jiu jitsu, where there's nearly always a winner and a loser. In those games, you can always expect your opponent to try to do the most harm possible, either by putting you in checkmate or doing unspeakable things to your arms, legs or carotid arteries.

With the Prisoner's Dilemma, the other player might be nasty or nice and you have no idea which one it will be.

Here's the scoring system for the Prisoner's dilemma:

*If both parties cooperate (win/win), they get a reward of 3 points (R).

*If both parties defect (lose/lose), they get 1 point as a punishment for defection (P).

*If one party defects and the other cooperates, the first gets 5 points--this is the temptation to defect (T). The other party who cooperated and got stung gets the sucker's payoff of 0 (S).

Payoffs in order are thus: T=5, R=3, P=1, S=0.

This means the highest reward (T) goes to someone who takes advantage of someone else and the lowest (S) goes to the one who is exploited. But both can do pretty well by cooperating (R) and less well while defecting (P).

So what strategy works best? That is the subject of the next post.

But here's a hint: it depends on how many times you play the game with the same person.

GOAT ROPE ADVISORY LEVEL: ELEVATED

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