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.Log In To View Full Content