consider a two

4. (15 points] Consider a two-period repeated game. The stage game is the following: (a) {3pts} )Find all purestrategy Nash equilibria if the stage game is played only once (b) (Spts) Now consider the two- period repeated game. Suppose the discount factor (5' = 1 for both players. Find a pair of subgame-perfect-equilibrium strategies in which player 1 plays B and player 2 plays R in the rst period. Explain why the pair of strategies is a subgame perfect equilibrium. Note that the game is not symmetric so you need to separately verify for each player: why player 1 wants to choose B in the rst period and whsr player 2 wants to cheese R in the rst period. (c) (time) Now assume that Player 1's discount factor equals 451 5 1 and Player 2 's discounter factor equals 62 5 1. Find the entire ranges of values of 61 and 62 so that the pair of strategies in Part (b) remain subgame perfect equilibrium