Game Theory Notes

The police lack sufficient evidence to convict the

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Unformatted text preview: ailable to each player  ­The payoff received by each player for each combination of strategies that could be chosen by the players The Prisoner's Dilemma Two suspects are arrested and charged with a crime. The police lack sufficient evidence to convict the suspects, unless at least one of them confesses. The police hold the suspects in separate cells and explain the consequences of the actions they may take. If neither confesses then both will be convicted for minor offences and sentenced to one month in jail. If both confess then both will be sentenced to jail for six months. Finally, if one confesses but the other does not, then the confessor is immediately released and the other is sentenced to nine months  ­ six for the crime and three more for obstructing justice. The normal form representation of a two player game specifics the player's strategy spaces S1; S2; and their payoff functions u1; u2: We denote this game by G = fS1; S2; u1; u2g This definition easily extends more generally, to n ­player games. If strategy s1 strongly dominates strategy s2 for player one, then that means that it is better for player one to use s1 rather than s2 irrespective of what player two plays. If strategy s1 weakly dominates strategy s2 for player one, then that means that player one can never lose by playing s1 rather than s2....
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This document was uploaded on 03/10/2014 for the course AECO 1330A at Sciences Po.

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