Question

<p>Suppose two people are playing a game (Bill and Amanda). Each player has two possible actions: Left; and<br />Right. The payos are reported in the table below; the rst number is Amanda's payo and the second is<br />Bill's.<br />Bill<br />Left Right<br />Amanda Left 6,6 11,2<br />Right 2,11 9,9<br />a) What is the pure strategy Nash equilibrium of this game?<br /><br />Now suppose this game is played twice, once today and once tomorrow (repeated prisoners' dilemma).Further, suppose that because of discounting, a payoff tomorrow of X, is only worth (.9)X today.<br />b) What is Amanda's payoff when both players play the Nash equilibrium on both days?<br /><br />Suppose Bill makes the following credible claim "I will play "Right" on each day. However, if on the first day I play "Right" and Amanda plays "Left," I will play "Left" for the rest of time."<br />c) What is Amanda's payoff if she plays "Right" on both days.<br />d) What is Amanda's payoff if she plays "Left" on the first day and plays "Right" on the second day?<br />e) What is Amanda's optimal strategy?</p>