The expected number of Nash equilibria of a normal form game

McLennan, Andrew (2005) The expected number of Nash equilibria of a normal form game. Econometrica, 73 1: 141-174. doi:10.1111/j.1468-0262.2005.00567.x

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Author McLennan, Andrew
Title The expected number of Nash equilibria of a normal form game
Journal name Econometrica   Check publisher's open access policy
ISSN 0012-9682
Publication date 2005
Sub-type Article (original research)
DOI 10.1111/j.1468-0262.2005.00567.x
Open Access Status Not Open Access
Volume 73
Issue 1
Start page 141
End page 174
Total pages 34
Place of publication Chichester, United Kingdom
Publisher Wiley-Blackwell Publishing
Language eng
Abstract Fix finite pure strategy sets S1,..., S,,, and let S = S, x... x S-n. 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-A. For given nonempty T-1 subset of S-1,..., T-n subset of S-n we give a computationally implementable formula for the mean number of Nash equilibria in which each agent i's mixed strategy has support T-i. 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 Ti. The second may be construed as the "probability" that such an equilibrium remains an equilibrium when the strategies in the sets S-i\T-i become available.
Keyword Nash equilibrium
Number of equilibria
Computational complexity
Random games
Algebraic geometry
Rotational invariance
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: Excellence in Research Australia (ERA) - Collection
School of Economics Publications
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Created: Wed, 17 Oct 2007, 13:23:49 EST