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What is game theory?

Game theory is the study of mathematical models of conflict and cooperation between intelligent rational decision-makers. Games are used to heuristically (test methods in a controlled environment) expose possible problems in economics, sociology, law and general philosophy. It is part of Logic.

Prisoners’ dilemma

Prisoners’ dilemma is perhaps the most well known game and it applies to many economic and sociological problems in many situations.

As it is a game, you have to act rationally – choose the move that is logically the best possible move.

Here is the situation.

Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge. They hope to get both sentenced to a year in prison on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to: betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The offer is:

[list]
[*]If A and B each betray the other, each of them serves 2 years in prison
[*]If A betrays B but B remains silent, A will be set free and B will serve 3 years in prison (and vice versa)
[*]If A and B both remain silent, both of them will only serve 1 year in prison (on the lesser charge)
[/list]
[table=95][tr][td]Prisoners dilemma[/td][td]Silent A[/td][td]Betray A[/td][/tr][tr][td]Silent B[/td][td]-1 A -1 B[/td][td]0 A -3 B[/td][/tr][tr][td]Betray B[/td][td]-3 A 0 B[/td][td]-2 A -2 B[/td][/tr][/table]

Interpretation

If you (A) decide to stay silent and B stays silent, you only serve one year in prison each, so the game ties at -1 each.

If A betrays B and B betrays A, A is set free and B serves 3 years, so the game is 0 for A and -3 for B. Reverse this for B betrays A, A remains silent.

If you betray each other, you both serve 2 years, but the game score is -2 for A and B.

The paradox

It is implied that the prisoners will have no opportunity to reward or punish their partner other than the prison sentences they get, and that their decision will not affect their reputation in the future. Because betraying a partner offers a greater reward than cooperating with them, all purely rational self-interested prisoners would betray the other, and so the only possible outcome for two purely rational prisoners is for them to betray each other. The interesting part of this result is that pursuing individual reward logically leads both of the prisoners to betray, when they would get a better reward if they both kept silent.

So betrayal becomes the most rational choice, even though remaining silent for both players is the best possible equilibrium for both players. Given the options, betrayal will leave the least damage for both players when the game is played a number of times.

There are many other ways to play the game, tit-for-tat, which is when each player returns the previous players move, eventually one player will betray on the last round, but over all both players score higher in the game. There are differences in the outcomes when the game is extended in the number of rounds. If there aren’t many rounds, betrayal becomes more likely to happen, but if you have a game with 20 or 50 rounds, or even infinite rounds, silence becomes more likely.

It’s an interesting game because it brings into question the concept of purpose and ends in real life situations, professional criminals are well aware of how this game works and so pre-define the rules of their game to remain silent no matter what. Individual self interest and collective action problems are all played out and exposed as paradoxical in this dilemma.

[Socrates]

This video is very helpful too:

[video=youtube]https://www.youtube.com/watch?v=DanTKx1FLY8[/video]

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