Consider the follwing

5. (24 points) Consider the following strategy in an infinitely repeated game with both players having a discount rate of o. The strategy (s) is as follows. . (i) Play a in the first round and if no one has deviated in the previous round. . (ii) If anyone deviates from (i), play c once then return to (i). . (iii) If anyone deviates from (ii), play d once then return to (ii). . (iv) If anyone deviates from (iii), repeat (iii). a b C d a 2,2 1,3 1,1 -3,-3 b 3, 1 -1,-1 0,0 -3,-3 C 1,1 0,0 0,0 -3,-3 d -3,-3 -3,-3 -3,-3 -1,-1 (a) What will be the sum of discounted payoffs for a player if he deviates just once from the strategy s by playing b in the first round while the other player follows the strategy s and then he returns to playing the strategy s? (b) What is the best one-shot deviation a player can make in stage (ii) of strategy s? What will the player's sum of discounted payoffs be in that case? (c) Find the range of o for which (s,s) is a subgame perfect equilibrium. (d) For which values of o is the strategy (s,s) a Nash equilibrium? Ex- plicitly state the most profitable deviation a player can make with the other player playing s