Question:Recall the tit-for-tat strategy: cooperate in the first round, cooperate iff the other player cooperated in the last round. It is an equilibrium for both players to play tit-for-tat so long as ?>c/b.Argue that this equilibrium is not subgame perfect. That is, suppose the players somehow arrive at a subgame in which one player has defected in the last round, and argue that the other player would prefer to deviate by cooperating in this round.

3. Subgame Perfection in the Prisoners' Dilemma In this problem, subgame perfection will teach us an important lesson about about the dark side of reciprocity: that those who do not punish defections must, in equilibrium, be exploited, since otherwise, they will not have an incentive to follow through on their threat to punish defections. As a reminder, at each stage of the Repeated Prisoners' Dilemma, players the following normal form game: Cooperate Defect Cooperate (b - c, b - c) |( -c, b ) Defect ( b, - c) (0, 0) where b > c > 0. The game repeats with probability o E [0, 1].(a) Recall the tit-for-tat strategy: cooperate in the first round, cooperate iff the other player cooperated in the last round. It is an equilibrium for both players to play tit-for-tat so long as 6 > c/b. Argue that this equilibrium is not subgame perfect. That is, suppose the players somehow arrive at a subgame in which one player has defected in the last round, and argue that the other player would prefer to deviate by cooperating in this round