Consider a population in which there are two phenotypes: natural-born cooperators (who do not confess under questioning) and natural-born defectors (who confess readily). If two members of this...

Consider a population in which there are two phenotypes: natural-born cooperators (who do not confess under questioning) and natural-born defectors (who confess readily). If two members of this population are drawn at random, their payoffs in a single play are the same as those of the husband–wife prisoners’ dilemma game of Chapter 4, reproduced below. In repeated interactions there are two strategies available in the population, as there were in the restaurant-dilemma game of Section 12.2. The two strategies are A (always confess) and T (play tit-for-tat, starting with not confessing).

(a) Suppose that a pair of players plays this dilemma twice in succession. Draw the payoff table for the twice-repeated dilemma.

(b) Find all of the ESSs in this game.

(c) Now add a third possible strategy, N, which never confesses. Draw the payoff table for the twice-repeated dilemma with three possible strategies and find all of the ESSs of this new version of the game.