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One of the most famous and most thoroughly studied examples of game theory is the Prisoners Dilemma In this situation the police have caught two people and charged them with a crime The police separate the prisoners into different rooms and give them the option of confessing The police tell the two prisoners that they have enough evidence of the crime to send them to jail for X amount of years However if one prisoner confesses fully to the crime and testifies against the other but the other doesnt then the prisoner who confessed will get get a much lighter sentence than X and the prisoner who did not confess will get a heavier sentence than X However if both of the prisoners confess and testify against the other then the police have enough evidence to convict both prisoners for a slightly heavier sentence than X Since neither of these prisoners knows what the other one is saying we can use a decision tree to determine the dominant strategy for these people see figure A on attached sheet In this dilemma the dominant game strategy for the prisoners is to confess Although the strategy for these games seems very predictable there is a paradox that arises The police are also a player in this game The police have evidence to put these criminals away for only X years but if the prisoners confess then they have enough evidence to put them away for slightly more than X years In this situation the police want to do all they can in their power to make these criminals confess to the crime The actions by the authorities have to be included in the outcome of the game The way the authorities can change the outcome of the game is to penalize the prisoners if they do not do what the authorities want Therefore the only two actions that the authority can perform are to penalize or not
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