Pset2.pdf - Problem Set 2 Economics 2020b HBS 4011 HKS...

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Problem Set 2 Economics 2020b / HBS 4011 / HKS API-112 4 th February 2015 1. Pollution Game Consider the three-player pollution game discussed in class (and reproduced below). Payoffs are written as (PI, PII, PIII). (a) Verify that there are four pure strategy Nash equilibria. (b) Verify that there are three mixed strategy Nash equilibria where one firm cleans for sure and the other two firms clean with probability 2/3. (c) Verify that there are two symmetric mixed strategy Nash equilibria (where all players use the same probabilities in their mixed strategy). (d) Verify that the 9 equilibria listed above constitute the full set of Nash equilibria. 2. Extreme Battle of the Sexes Consider the symmetric Battle of the Sexes game shown below. Football Concert Football 1 , a 0 , 0 Concert 0 , 0 a , 1 (a) How does the mixed strategy equilibrium vary with a ? (b) What happens to the probability of the outcome (0,0) as a goes to infinity? (c) What happens to the probability of the outcome (0,0) as a goes to zero?

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