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Unformatted text preview: 1 ANSWER KEY (Problem Set 4) Problem 1 : (a) (L, L) every period is the only SPE. Proof: Consider any period t and suppose that in all periods t+1, t+2, …, T, both players choose L regardless of prior play. Then L is dominant for each player, so (L, L) played in period t. Repeating the argument we see that (L, L) will be played each period 1, 2, 3, …, t as well. To complete the proof, note that in period T, L is dominant for each player, so the argument above (setting t = T – 1) implies (L, L) is played every period. (b) Yes. At each decision node, L is optimal for each player given the strategies of their opponents. (c) Player 1: π c = 10, π d = 11, π p = 1. π c /(1  δ ) ≥ π d + δ π p /(1  δ ) So δ ≥ 1/10 Player 2: π c = 10, π d = 15, π p = 1. π c /(1  δ ) ≥ π d + δ π p /(1  δ ) So δ ≥ 5/14 Thus we need δ ≥ 5/14 for each player to obtain a payoff of 10 each period. 5/14 for each player to obtain a payoff of 10 each period....
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 Spring '08
 PHILIPHAILE
 Game Theory, Period, Periodic function, SPE

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