Consider the following game. The game has two players, and each player is asked a question. The players can answer a question honestly or they can lie. If both answer honestly, each receives a payoff of $100. If one player answers honestly and the other player lies, the liar gains at the expense of the honest player. In that event, the liar receives a payoff of $500 and the honest player gets nothing. If both lie, then each receives a payoff of $50.
(a) Construct the payoff matrix.
(b) What is the non-cooperative (Nash) equilibrium for this game? Explain how you have arrived at this answer.
(c) What is the optimum outcome? Is it likely to be reached? Explain.
(d) What is a "tit-for-tat" strategy? Why is it a rational strategy for the infinitely repeated prisoners' dilemma?