Consider the following Prisoner's Dilemma game:

Suspect C,C - 3,3

C,D - 0,5

D,C - 5,0

D,D - 1,1

where C corresponds to Cooperate while D corresponds to Defect. The first entry of each cell is the payoff of Suspect 1 while the second entry is the payoff of Suspect 2.

The set of feasible payoff profiles of a strategic game is the set of all weighted averages of payoff profiles in the game.

Draw a diagram showing the set of feasible payoff pairs for the above Prisoner's Dilemma game. In this diagram indicate the payoff combinations which can be sustained as equilibrium payoffs in the repeated Prisoner's Dilemma game.

Suppose that the above strategic game is repeated infinitely. Suppose that the common discount factor is 0 < < 1. Suppose that both suspects adopt the following resolution:

a. Choose C in period t=1.

b. Choose C in period t1 if the other suspect played C in period t-1.

c. Choose D in period t1 if the other suspect played D in period t-1.

Find the range of values for the discount factor for which the strategy pair in which each suspect uses the above strategy is a Nash equilibrium.