Answer Happy

3.) Player 1 and Player 2 are going to play the following stage game an infinite number of times: Player 1 Cooperate Defect Cooperate 3,3 5,0 Player 2 Defect 0,5 2,2 The discount factor is 8 < 1. They agree that (i) Player 1 will play Defect in the odd-numbered periods and Cooperate in the even-numbered periods, and (ii) Player 2 will play Cooperate in the odd-numbered periods and Defect in the even-numbered periods. They adopt the following grim trigger strategy profile:

Player 1 will play Defect in period 1 and all subsequent odd-numbered periods. Player 1 will play Cooperate in an even-numbered period if Player 2 has played Cooperate in all odd-numbered periods up to that point in the game. Otherwise, Player 1 plays Defect. • Player 2 will play Defect in all even-numbered periods. ● Player 2 will play Cooperate in period 1. Player 2 will play Cooperate in any subsequent odd-numbered period if Player 1 has played Cooperate in all even-numbered periods up to that point in the game. Otherwise, Player 2 plays Defect. ● Characterize the range of values of 8 for which this strategy profile is a subgame perfect Nash equilibrium.