Consider a population consisting of two types, "cooperators" and "defectors." Each individual interacts with a randomly chosen member of the population. When two cooperators interact, each earns a payoff of 6. When two defectors interact, each gets a payoff of . When a cooperator and a defector interact, the former gets a payoff of 0 whereas the latter gets a payoff of 8.
a) Summarize the situation described above in the game matrix where two individuals, X and Y, decide whether to cooperate or to defect. What is a Nash equilibrium (equilibria) for this game?
b) Let c be the population share of Cooperators. What will be the equilibrium population share of each type? Illustrate your answers in a diagram with population share of cooperators on the horizontal axis and expected payoffs on the vertical axis.
Suppose that goggles are available, at the cost of 1 per pair, which enables the wearer to identify each person's type ,with certainty.
c) What will be the equilibrium population share of cooperators in this case?