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EXERCISE 407.1 (Tit-for-tat as a subgame perfect equilibrium in the infinitely re- peated Prisoner's Dilemma) Consider the infinitely repeated Prisoner's Dilemma in which the payoffs of the component game are those given in Figure 407.1. Show that (tit-for-tat,tit-for-tat) is a subgame perfect equilibrium if and only if y - x = 1 and 8 = 1/x. (Use the fact that subgame perfect equilibria have the one-deviation property.) C D C D 0, y 1,1 y,0 Figure 407.1 The component game for the infinitely repeated Prisoner's Dilemma considered in Exer- cise 407.1.