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Unformatted text preview: ECON 212 Game Theory Prof. Andrew Postlewaite Fall 2010 University of Pennsylvania Suggested Solution for Problem Set 4 1. a. There are essentially two states: G in which ( B,B ) is expected to be played and B in which ( C,C ) is expected. Let V i ,i = G,B be the expected payoff in a repeated game each player expects from the prescribed strategy in state i (Note that both players get the same expected payoff according to the strategy profile). Then V G = (1- δ )4 + δV G = 4 V B = (1- δ )(- 1) + δV G = 5 δ- 1 . For the given strategy profile to be a SPNE, no player should have an incentive to deviate. The strategy profile is incentive compatible in state G iff V G ≥ (1- δ )5 + δV B ( deviation to A ) V G ≥ (1- δ )1 + δV B ( deviation to C ) Solving these inequalities, we end up with δ ≥ 1 5 . The strategy profile is incentive compatible in state B iff V B ≥ (1- δ )0 + δV B ( deviation to either A or B ) ⇔ δ ≥ 1 5 We conclude that the strategy profile is a SPNE if δ ≥ 1 5 . b. ( A,A ) is the unique strategy-game NE. Since this is a finitely repeated game, always playing ( A,A ) is the unique SPNE. c. Consider the following strategy profile: each player plays A in the first stage. If ( A,A ) was played in the first stage, then play A . Otherwise, play C . Ob- viously, this is not a SPNE because ( C,C ) is not a stage-game NE. Incentive compatibility in both periods are immediate.compatibility in both periods are immediate....
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This note was uploaded on 02/29/2012 for the course GG 101 taught by Professor Gg during the Spring '12 term at UPenn.
- Spring '12