Consider the repeated play of a prisoner's dilemma game, whose payoffs are given in the following payoff matrix:
P1/P2
C
D
C
(3, 3)
(0, 5)
D
(5, 0)
(2, 2)
a) Suppose the game is played only three times. Then, how many subgames (including the entire game) do we have? and what is a sub-game Perfect Nash Equilibrium?
b) Suppose the game is played indefinitely and players discount future payoffs with a common discount factor δ. Find the range of a discount factor which can sustain cooperation, i.e., repeated play of (C, C), by employing the trigger strategies.