game theory

1. (30 points) The matrix given below is the stage game of an infinitely repeated game. Recall that a player's payoff in an infinitely repeated game is his/her average payoff received across all of the stages. player 2 X Y player 1 A 6,0 1, 1 B 3, 3 0, 7 (a) (15 points) What is the lowest sum of payoffs that is consistent with a subgame perfect Nash equilibrium of the infinitely repeated game? (By sum of payoffs, I mean the sum of player I's average payoff and player 2's average payoff. ) Find a subgame perfect Nash equilibrium that yields this payoff, and specify the strategy profile completely. (b) (15 points) What is the highest sum of payoffs that is consistent with a subgame perfect Nash equilibrium of the infinitely repeated game? Find a subgame perfect Nash equilibrium that yields this payoff, and specify the strategy profile completely