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Question 6. Consider the following single-play version of a Prisoner's Dilemma game Player 2 T D T 4, 4 1 5 Player 1 D 5, 1 2, 2 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 be p and the proportion of tit-for-tat player be (1 - p). Each member of the population plays sets of dilemmas n times (where n 22), matched against a new, randomly chosen opponent for each new set. The payoff to each player in one whole set (of n players) is the sum of her payoffs in the n plays. (b) Find the fitness (average payoff in one set against a randomly chosen opponent) for a defector. (c) Find the fitness for a tit-for-tat player. (d) Use the answers in part (b) and part (c) to show that, when p > (n - 3/2)/ (n - 1), the defector type has greater fitness and that, when p