Consider the following prisoner’s dilemma game (the bigger the number the better):

1. Assume that the game is repeated infinitely. What is player 1’s payoff if they will cooperate for the entirety of the game?

2. Assume that the game is repeated infinitely and that both players decide to cooperate. Consider a grim strategy where if player 1 defects, they will obtain a payoff of 12 at the period when they defected and then receive a payoff of 4 in subsequent periods. What is player 1’s payoff for this grim strategy?

3. Assume that the game is repeated infinitely and that both players decide to cooperate. Consider a limited punishment strategy where if player 1 defects, they will obtain a payoff of 12 at the period when they defected and then receive a payoff of 4 in four subsequent periods only, thereafter they receive a payoff of 8 for the rest the game. What is player 1’s payoff for this limited punishment strategy?

4. Suppose player 1 has ???? = ????. ????????. Would player 1 defect? Would they cooperate? Explain.
 

Player 1 Cooperate Defect Player 2 Cooperate 8,8 12,2 Defect 2,12 4,4