Consider the infinite repeated two-player game where at each stage the play- ers play the non-zero-sum game given by A В A (5,5) (0,7) B (7,0) | (2,2) (a) Consider the following strategies: SA: always play A. SB: always play B. • St: play A on the first stage, thereafter copy what the other player did in the preceding stage. Suppose that the total payoff involves a discount factor 8, and that both players are restricted to the pure strategies sA, 8B, and sr. Determine the set of d for which (sT, sT) is a Nash equilibrium. (b) Use the one stage deviation principle to determine whether the pair (ST, ST) is a subgame perfect Nash equilibrium for some range of val- ues of §.

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Consider the infinite repeated two-player game where at each stage the play-
ers play the non-zero-sum game given by
A
В
A (5, 5) (0,7)
В (7, 0) | (2, 2)
(a) Consider the following strategies:
SA: always play A.
SB: always play B.
• St: play A on the first stage, thereafter copy what the other player
did in the preceding stage.
Suppose that the total payoff involves a discount factor 8, and that both
players are restricted to the pure strategies SA, SB, and sT. Determine
the set of d for which (ST, ST) is a Nash equilibrium.
(b) Use the one stage deviation principle to determine whether the pair
(ST, ST) is a subgame perfect Nash equilibrium for some range of val-
ues of 8.
Transcribed Image Text:Consider the infinite repeated two-player game where at each stage the play- ers play the non-zero-sum game given by A В A (5, 5) (0,7) В (7, 0) | (2, 2) (a) Consider the following strategies: SA: always play A. SB: always play B. • St: play A on the first stage, thereafter copy what the other player did in the preceding stage. Suppose that the total payoff involves a discount factor 8, and that both players are restricted to the pure strategies SA, SB, and sT. Determine the set of d for which (ST, ST) is a Nash equilibrium. (b) Use the one stage deviation principle to determine whether the pair (ST, ST) is a subgame perfect Nash equilibrium for some range of val- ues of 8.
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