MicroF04-II.1

Question from Past Microeconomics Qualifying Exam

Fall 2004 - Section II, Question one, George Mason University

Consider the following payoff matrix:

1. Find the two pure strategy Nash equilibria
2. Find the mixed strategy Nash equilibrium.

Answer

1. The two Pure Strategy Nash Equilibria in this game are (Peace, War) and (War, Peace). Given the other players decision no player would want to play differently in these situation.
2. The Mixed Strategy Nash Equilibrium can be calculated as follows:
   6σ + 1 (1 - σ) = 15σ
   5σ + 1 = 15σ
   σ = 0.1
   
   6φ + 1 (φ - 1) = 15φ
   φ = 0.1
   
   MSNE = (0.1, 0.1)

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