3. Consider our usual version of the Prisoner's Dilemma where I have listed only the payoffs for player 1. Consider the infinitely repeated version of this game, with a common discount factor (0,1). Recall that Tit-for-Tat, hereafter TFT, is the strategy in which the player plays C in period 1 and then, in period t+1, plays whatever the opponent played in period t. Assume that player 2 plays TFT. (a) Consider any continuation game in which the continuation path under mutual TFT is ((C,C),(C,C),). (Under mutual TFT, this holds initially and for any continuation game in which both players played C in the previous period.) Find the smallest such that for every , TFT yields a higher payoff for player 1 than the continuation strategy, Always D ( D in every period, regardless of history). 2 (b) Consider any continuation game in which the continuation path under mutual TFT is ((D,D),(D,D),). (Under mutual TFT, this holds for any continuation game in which both players played D in the previous period.) Find the largest such that for every , TFT yields a higher payoff for player 1 in this continuation game than the continuation strategy, Always C ( C in every period, regardless of history). (c) Conclude that there is no value of for which mutual play of TFT is a subgame perfect equilibrium of this repeated Prisoner's Dilemma. Remark 1. This question is essentially the same as one on the 20214011 Midterm 2. So you can just look up the solution to that (but the PD payoffs are different, so your calculation is slightly different). But see if you can do it on your own