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.

(a) Show in a two-by-two table the payoffs to a player of each type when, in one set of plays, each player meets an opponent of each of the two types.

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