Please answer the question according to the picture.

Consider the infinitely repeated Prisoner's Dilemma we studied in class. The players have the same discount factor ? ? (0, 1)

and the stage game is given by

C D

C 2, 2 0, 3

D 3, 0 1, 1

Define the Tit-for-Tat strategy of player i as si1 = C, jQuery224027582385474312565_1621672414254 ? (?1, ?2,..., ???1) = ???1

? for ? ? ? and all ? > 1. In words, according to

this strategy, a player ? starts with ? and then chooses the action another player chose in the previous round.

(a) [1pt] For which ? does a pair of Tit-for-Tat strategies constitute a subgame perfect Nash equilibrium of the infinitely repeated game?

(b) [1pt] For which ? does a pair of Tit-for-Tat strategies constitute a Nash equilibrium of the infinitely repeated game? d1=d2=0

Note that this is a question about NE of the normal form representation of the repeated game, not the stage game.

Hint: What is a best response to the Tit-for-Tat strategy of the opponent in the the normal form representation of the repeated game?

1. Consider the infinitely repeated Prisoner's Dilemma we studied in class. The players have the same discount factor S e (0, 1) and the stage game is given by C D C 2,2 0,3 D 3,0 1, 1 Define the Tit-for-Tat strategy of player i as s, = C. s(al, a,.... at-1) = al for j # i and all t > 1. In words, according to this strategy, a player i starts with C and then chooses the action another player chose in the previous round. (a) [1pt] For which & does a pair of Tit-for-Tat strategies constitute a subgame perfect Nash equilibrium of the infinitely repeated game? (b) [ipt] For which & does a pair of Tit-for-Tat strategies constitute a Nash equilibrium of the infinitely repeated game? Note that this is a question about NE of the normal form representation of the repeated game, not the stage game. Hint: What is a best response to the Tit-for-Tat strategy of the opponent in the the normal form representation of the repeated game