Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9551711 | Games and Economic Behavior | 2005 | 32 Pages |
Abstract
The formula given by McLennan [The mean number of real roots of a multihomogeneous system of polynomial equations, Amer. J. Math. 124 (2002) 49-73] is applied to the mean number of Nash equilibria of random two-player normal form games in which the two players have M and N pure strategies respectively. Holding M fixed while Nââ, the expected number of Nash equilibria is approximately (ÏlogN/2)Mâ1/M. Letting M=Nââ, the expected number of Nash equilibria is exp(NM+O(logN)), where Mâ0.281644 is a constant, and almost all equilibria have each player assigning positive probability to approximately 31.5915 percent of her pure strategies.
Keywords
Related Topics
Social Sciences and Humanities
Economics, Econometrics and Finance
Economics and Econometrics
Authors
Andrew McLennan, Johannes Berg,