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GameTheory2 - δ – if both players cooperate every period...

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Repeated Games In many real-world settings, players play the same game over and over again the simple constituent game that is played repeatedly is called the stage game Repeated play opens up the possibility of cooperation in equilibrium players can adopt trigger strategies cooperate as long as everyone else does
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Infinitely Repeated Games Recall the Prisoner’s Dilemma : Suppose both players follow a trigger strategy in the Prisoners’ Dilemma and each player’s discount rate is δ . F S F 1,1 3,0 S 0,3 2,2 if both players cooperate every period, the payoff over time
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Unformatted text preview: δ . – if both players cooperate every period, the payoff over time would be V eq = 2 + 2 δ + 2 δ 2 + … = 2/(1– δ ) – if a player deviates and then the other finks every period, that player’s payoff is V dev = 3 + 1 δ + 1 δ 2 + … = 3 + δ /(1– δ ) Infinitely Repeated Games • The trigger strategies form a perfect-subgame equilibrium if V eq ≥ V dev /(1 + 1 2/(1– δ ) ≥ 3 + δ /(1– δ ) δ ≥ 1/2...
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