Assume that there is a large population in which each member's behavior is hardwired into them, so that each player is either a defector or a tit-for-tat player. (As described in the textbook, in multiple rounds of a prisoner's dilemma, a tit-for-tat player cooperates on the first play. In subsequent rounds she does whatever her opponent did on the preceding play).

Let the population proportion of defectors bepand the proportion of tit-for-tat player be (1 -p). Each member of the population plays sets of dilemmas n times (wheren?2), matched against a new, randomly chosen opponent for each new set. The payoff to each player in one whole set (ofnplayers) is the sum of her payoffs in thenplays.

(e) If evolution leads to a gradual increase in the proportion of the fitter type in the population, what are the possible eventual equilibrium outcomes of this process for the population described in this exercise? (That is, what are the possible equilibria, and which are evolutionary stable?) Use a diagram with the fitness graphs to illustrate your answer).

(f) In what sense does more repetition (larger values ofn) facilitate the evolution of cooperation?

Player 2 T D T 4. 4 1, 5 Player 1 D 5, 1 2, 2