Consider a Prisoners' Dilemma game involving two players, N = {1,2), each of whom may choose either to co-operate (C) or to defect (D). The payoffs in this game are illustrated in the below table. Player 1 receives the first listed payoff in each cell while player 2 receives the second listed payoff in each cell. 2 с 3,3 4,0 D 0,4 1,1 a. Solve for the pure strategy Nash equilibrium of this static game. Are the

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Consider a Prisoners' Dilemma game involving two players, N = {1,2}, each of whom
may choose either to co-operate (C) or to defect (D). The payoffs this game are
illustrated in the below table. Player 1 receives the first listed payoff in each cell while
player 2 receives the second listed payoff in each cell.
2
с
3,3
4,0
D
0,4
1, 1
a. Solve for the pure strategy Nash equilibrium of this static game. Are the
players able to co-operate with one another? Explain why or why not.
Suppose now that the above game is repeated infinitely many times and let 8 > 0
denote the common discount factor between periods. Suppose that the two players
make the following agreement:
"Play C in every period. If D is ever played, play D in every period thereafter."
b. Explain how the one-deviation principle can be used to check whether the
above agreement represents a subgame perfect Nash equilibrium of the
infinitely repeated game.
c. Use the method described in part b. of this question to calculate the values of
the discount factor & for which the above agreement is indeed a subgame
perfect Nash equilibrium of the infinitely repeated game.
Transcribed Image Text:Consider a Prisoners' Dilemma game involving two players, N = {1,2}, each of whom may choose either to co-operate (C) or to defect (D). The payoffs this game are illustrated in the below table. Player 1 receives the first listed payoff in each cell while player 2 receives the second listed payoff in each cell. 2 с 3,3 4,0 D 0,4 1, 1 a. Solve for the pure strategy Nash equilibrium of this static game. Are the players able to co-operate with one another? Explain why or why not. Suppose now that the above game is repeated infinitely many times and let 8 > 0 denote the common discount factor between periods. Suppose that the two players make the following agreement: "Play C in every period. If D is ever played, play D in every period thereafter." b. Explain how the one-deviation principle can be used to check whether the above agreement represents a subgame perfect Nash equilibrium of the infinitely repeated game. c. Use the method described in part b. of this question to calculate the values of the discount factor & for which the above agreement is indeed a subgame perfect Nash equilibrium of the infinitely repeated game.
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