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The Prisoners' Dilemma

You and your friend have been arrested by the police and placed in separate rooms to be interrogated. Both of you are told that if one testifies against the other and the other does not testify, the former will go free and the latter will get five years of jail time. However, if both of you testify against the other, both of you receive three years in jail. If neither of you testify, the police do not have enough evidence to convict and you both go free. (Example adapted from Harrington's Games, Strategies, and Decision Making).

The Payoff matrix looks something like this:
C = Cooperate
T = Testify

     C         T
C  (0,0)   (-5,0)
T  (0,-5)  (-3,-3)

This is what is known as the Prisoners' Dilemma.

A Nash Equilibrium is the optimal strategy for each player given that each player is rational and trying to maximize their payoffs (e.g. less jail time). In the Prisoners' Dilemma, the Nash Equilibrium is {testify, testify}, which results in both players receiving jail time. 

What makes the Prisoners' Dilemma a fascinating case is that the optimal strategy for each player, testify, results in an outcome that is both Pareto and Welfare dominated. The best (i.e. most rational) strategy for each player results in a suboptimal outcome for both players.

There is no solution to the Prisoners' Dilemma. Additionally, the dilemma arises no matter how many times the game is iterated. One may only 'solve' the Prisoners' Dilemma by changing the parameters of the game.

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