Consider an iterated prisoner's dilemma, with the following stage game. 3,3 0,4 D 4,0 1,1 5.4...

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Consider an iterated prisoner's dilemma, with the following stage game. 3,3 0,4 D 4,0 1,1 5.4 Consider a strategy called Limited Punishment. This strategy is defined as follows. If no player defected in the immediately prior round, play cooperate. If any player defected in the previous round, play defect in the current round no matter what, but also play cooperate in the following round no matter what (despite the defection). Consider the candidate equilibrium (Limited Punishment; Limited Punishment). Identify all possible states the game can take given those strategies, and draw trees for all states identifying which outcomes lead to which future states. 5.5 Determine under what conditions (Limited Punishment; Limited Punishment) is a Sub- game Perfect Nash Equilibrium of this game, while showing your work. A full answer must provide two things. First, the sequence of utility payoffs associated with equilibrium play, compared with the utility payoffs for deviation, for the necessary players and states. Second, a value of & above which the equilibrium holds. HINT: As you do the algebra to compare your payoff strings, you may find it useful to first stack the two equations on top of one another and cancel like terms before simplifying. Consider an iterated prisoner's dilemma, with the following stage game. 3,3 0,4 D 4,0 1,1 5.4 Consider a strategy called Limited Punishment. This strategy is defined as follows. If no player defected in the immediately prior round, play cooperate. If any player defected in the previous round, play defect in the current round no matter what, but also play cooperate in the following round no matter what (despite the defection). Consider the candidate equilibrium (Limited Punishment; Limited Punishment). Identify all possible states the game can take given those strategies, and draw trees for all states identifying which outcomes lead to which future states. 5.5 Determine under what conditions (Limited Punishment; Limited Punishment) is a Sub- game Perfect Nash Equilibrium of this game, while showing your work. A full answer must provide two things. First, the sequence of utility payoffs associated with equilibrium play, compared with the utility payoffs for deviation, for the necessary players and states. Second, a value of & above which the equilibrium holds. HINT: As you do the algebra to compare your payoff strings, you may find it useful to first stack the two equations on top of one another and cancel like terms before simplifying.

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Here are the possible states and state transition diagram given the strategies of Limited Punishment ... View the full answer