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With regard to the above matrix, each prisoner is looking to minimize his prison time. Since the criminal 1 and/or player 1 does not know whether his partner in crime has confessed or not, first he assumes that he has not. If prisoner 1 does not confess either then both will go to the prison for 1 year. this is good for them. But, if prisoner 1 confesses, he will go free, while his partner goes to prison. Now consider the other possibility that Prisoner 2 confesses. In this situation if prisoner 1 does not confess, he will go to prison for 10 years. But if he does confess, he will be in prisonfor 5 years. In this case it is obviously better to confess. According to the matrix, it is obvious that the best payoff for the both prisoners is when neither confesses. But game theory says that it is better for both to confess, since this situation is a non-cooperative form, so the player cannot rely on the other player.As is understood from the results of the game, players in the game should choose a decision to find the best outcome according to the opponent’s decision while this decision may not lead to the best outcome of the system. In general, it must be said that the Nash equilibrium point is not necessarily coincide with the Pareto optimal point.
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