1. Consider an infinitely repeated version of the symmetric two-player stage game in the figure below. Player2 Left Right Player 1 Up 4, 4 8,2 Down 2,8 6,6 Assume that past actions are common knowledge. Each player's payoff is the present value of the stream of single-period payoffs, where the discount factor is 6. a. What is the Nash equilibrium of the stage game? b. Find an outcome that yields higher payoffs to both players than the Nash equilibrium. C. Define a grim trigger strategy aimed at sustaining the mutually beneficial outcome as a subgame perfect Nash equilibrium. d. Derive the condition on the discount factor that ensures that the grim-trigger strategy profile you defined is a subgame perfect Nash equilibrium