Question

Consider the infinitely repeated version of the symmetric two-player stage game in figure PR 13.2. The first number in a cell is player 1's single-period payoff. 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:

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 1's single-period payoff. Figure PR13.2 Player 2 a 1,10,4 0,3|3,22,5 b4,03,3 8,0 1,11,2 c 3,00,8 7,72,50,3 d2,31,15,26,6 1,2 e5,22,13,02,10,0 Player 1 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.

Answer 1

Solution

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