Econometrica: Jan 2005, Volume 73, Issue 1

The Expected Number of Nash Equilibria of a Normal Form Game

https://doi.org/10.1111/j.1468-0262.2005.00567.x
p. 141-174

Andrew McLennan

Fix 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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Supplemental Material

Supplement to "The Expected Number of Nash Equilibria of a Normal Form Game"

This supplement provides a detailed special case of the proof of Proposition 3.1 in "The Expected Number of Nash Equilibria of a Normal Form Game."

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