Prelim_1_Solutions

# Prelim_1_Solutions - Kaushik Basu Spring 2008 Econ 367...

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Kaushik Basu Spring 2008 Econ 367. Game-Theoretic Methods Prelim Exam 1 Solutions [1 hour. Total 15 points] 1. Consider the two-player game described below, in which each player chooses between A and B A B A 5, 5 0, 6 B 6, 0 0, 0 (a) Locate all the pure strategy Nash equilibria of this game. Answer: (A,B), (B,A) and (B,B). (b) Is there a mixed strategy Nash equilibrium in which both players mix both strategies (that is, attaches a positive probability to each strategy)? Briefly explain your answer. Answer: No. Each player is willing to mix his/her two strategies (that is, to attach a positive probability to each strategy) only when the other player plays the pure strategy B. Hence there does not exist any Nash equilibrium in which both players mix both strategies. (c) If players iteratedly eliminate their (weakly) dominated strategies, which are the strategies that will survive all such elimination? Answer: (B,B) (d) Treating the above game as an evolutionary game, locate all evolutionarily stable strategies. Answer: Strategy B is immune to A and thus it is the Evolutionarily Stable Strategy. [1 + 2 + 1 + 1 points] 2. There is a circular city as shown below in which people live uniformly spread all along the rim. Let the circumference be 1 mile. Think of the rim as a circular road, one mile long, along which people live.

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Two vendors A and B have to each choose a location on the rim. Each vendor’s aim is to maximize her customers. Citizens travel along the rim (either direction)
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Prelim_1_Solutions - Kaushik Basu Spring 2008 Econ 367...

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