4. Consider the following modification of the iterated Prisoner’s Dilemma problem. Instead of punishments, years in jail, suppose the problem is phrased in terms of rewards. If both cooperate, they each get 3 points. If both defect, they each get 1 point. If one cooperates and the other defects, the defector gets 5 points and the cooperator 0 points. Suppose the player to be advised wishes to maximize expected points. [By problem 3, this change does not affect the fact that defection is the optimal strategy in a single iteration situation.]

Now suppose that the player we advise is to play a five-iteration Prisoner’s Dilemma as specified in the above paragraph against each of 10 players. He will then choose one of these 10 players to play a 100-iteration Prisoner’s Dilemma with. How would you advise our player to play in the first phase, which player should he choose for the 100-iteration game, and how should he play in the 100-iteration second phase?

Explain your reasoning.