2 Consider the infinitely repeated version of the symmetric two-player stage game in Figure PR13.2. The first number in a cell is player l's single-period payoff. Figure PR13.2 Player 2 y a 1,1 0,4 0,3 3,2 2,5 b 4,0 3,3 8,0 1,1 1,2 c 3,0 0,8 7,7 2,5 0,3 Player 1 d 2,3 1,1 5,2 6,6 1,2 e 5,2 2,1 3,0 2,1 0,0 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 d. (a) Derive the conditions whereby the following strategy profile is a subgame perfect Nash equilibrium: Player 1: In period 1, choose c. In period t(22): choose c if the outcome was (c,x) in period t-1; and choose d otherwise. Player 2: In period 1, choose x. In period t(2 2): choose x if the outcome was (c,x) in period t-1; and choose y otherwise.