Gametheory
(Taget direkte fra den store lærebog)
Prisoners dilemma
The story behind this game is as follows: Two individuals are arrested for allegedly engaging in a serious crime and are held is separate cells. The district attorney tries to extract a confession from each prisoner. Each is privately told that if he is the only to confess, then he will be rewarded with a light sentence of 1 year while the recalcitrant prisoner will go to jail for 10 years. However, if he is the only one not confesses, and then he will serve the 10 years. However, if both confess, they will both be shown the mercy: they will each get 5 years. Finally, if neither confess, it will be possible to convict both of a lesser crime that carries a sentence of 2 years. Each player wishes to minimize the time he spends in jail. What will the outcome of the game be?
| |Prisoner 2 |
| |Don’t confess |confess |
|Prisoner 1 |Don’t confess |-2,-2 |-10,-1 |
| |confess |-1,-10 |-5, -5 |
There is only one plausible answer: “confess”, “confess”. To see why, note that playing “confess” is each player’s best strategy regardless of what the other player does. This type of strategy is known as a strictly dominant strategy. In words, a strategy is a strictly dominant strategy for player i if it maximizes uniquely player i’s payoff for any strategy that player i’s rivals might play.
The striking aspect of the “confess”, “confess” outcome in the Prisoners Dilemma is that although it is the one we expect to arise, it is not the best outcome for the players jointly; both players would prefer that neither of them confess. For this reason, the Prisoners dilemma is the paradigmatic example of self-interested, rational behaviour not leading to a socially optimal result.
In a Nash equilibrium, each player’s
Prisoners dilemma
The story behind this game is as follows: Two individuals are arrested for allegedly engaging in a serious crime and are held is separate cells. The district attorney tries to extract a confession from each prisoner. Each is privately told that if he is the only to confess, then he will be rewarded with a light sentence of 1 year while the recalcitrant prisoner will go to jail for 10 years. However, if he is the only one not confesses, and then he will serve the 10 years. However, if both confess, they will both be shown the mercy: they will each get 5 years. Finally, if neither confess, it will be possible to convict both of a lesser crime that carries a sentence of 2 years. Each player wishes to minimize the time he spends in jail. What will the outcome of the game be?
| |Prisoner 2 |
| |Don’t confess |confess |
|Prisoner 1 |Don’t confess |-2,-2 |-10,-1 |
| |confess |-1,-10 |-5, -5 |
There is only one plausible answer: “confess”, “confess”. To see why, note that playing “confess” is each player’s best strategy regardless of what the other player does. This type of strategy is known as a strictly dominant strategy. In words, a strategy is a strictly dominant strategy for player i if it maximizes uniquely player i’s payoff for any strategy that player i’s rivals might play.
The striking aspect of the “confess”, “confess” outcome in the Prisoners Dilemma is that although it is the one we expect to arise, it is not the best outcome for the players jointly; both players would prefer that neither of them confess. For this reason, the Prisoners dilemma is the paradigmatic example of self-interested, rational behaviour not leading to a socially optimal result.
In a Nash equilibrium, each player’s