Name
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 N→∞, the expected number of Nash equilibria is approximately (πlogN/2)M−1/M. Letting M=N→∞, the expected number of Nash equilibria is exp(NM+O(logN)), where M≈0.281644 is a constant, and almost all equilibria have each player assigning positive probability to approximately 31.5915 percent of her pure strategies. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1016/j.geb.2004.10.008 | Games and Economic Behavior |
Keywords | Field | DocType |
C72 | Binary logarithm,Combinatorics,Mathematical economics,Statistical mechanics,Real roots,System of polynomial equations,Expected value,Nash equilibrium,Mathematics,Computational complexity theory | Journal |
Volume | Issue | ISSN |
51 | 2 | 0899-8256 |
Citations | PageRank | References |
19 | 3.82 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Andrew McLennan | 1 | 40 | 5.20 |
| Johannes Berg | 2 | 41 | 6.32 |