Econometrica: Jan 2005, Volume 73, Issue 1
The Expected Number of Nash Equilibria of a Normal Form Game
Andrew McLennanFix finite pure strategy sets , and let . In our model of a random game the agents' payoffs are statistically independent, with each agent's payoff uniformly distributed on the unit sphere in ℝ. For given nonempty we give a computationally implementable formula for the mean number of Nash equilibria in which each agent 's mixed strategy has support . The formula is the product of two expressions. The first is the expected number of totally mixed equilibria for the truncated game obtained by eliminating pure strategies outside the sets . The second may be construed as the “probability” that such an equilibrium remains an equilibrium when the strategies in the sets become available.
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