# solution11b - Econ 354K Game Theory Solutions to Problem...

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1 Econ 354K Game Theory Solutions to Problem Set No. 11b 1. Infinitely Repeated Chicken (a) Subgame perfect NE : Grim strategy: Play C in period 1 and in any period which has a history of everyone playing C. However, in any period in which someone has played S in the past, choose C with probability 3/(3+x) forever thereafter. First, note that playing the MS-NE forever after a deviation is subgame perfect in all the subgames reached after a deviation. Next consider the strategy at a “good” history in which everyone has played C in the past. If a player goes along, he gets 2 each period forever, so the go-along payoff is 2/(1- δ ) If a player deviates to S, he gets (2+x) this period, then starting next period (so discounted by δ ) he gets the payoff expected from the MS-NE (which is 6/(3+x) each period), forever, so the total payoff from deviating is: () 6 3 2 1 x x δ ⎛⎞ ⎜⎟ + ⎝⎠ ++ Thus deviating to S is NOT profitable if the payoff from deviating is not larger than the payoff from not deviating, or if 6 2 3 2

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## This note was uploaded on 06/09/2011 for the course ECON 354 taught by Professor Econ during the Spring '11 term at University of Texas at Austin.

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solution11b - Econ 354K Game Theory Solutions to Problem...

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