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Title:The Expected Number of Nash Equilibria of a Normal Form Game PDF Logo
Authors:McLennan, Andrew
Issue Date:2001
Series/Report no.:Minnesota working papers / University of Minnesota, Center for Economic Research, Department of Economics 315
Abstract:Fix finite pure strategy sets S1, . . ., Sn, and let S = S1 x . . .x Sn. 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 IRS. For given nonempty T1 c S1, . . ., Tn c Sn we give a computationally implementable formula for the mean number of Nash equilibria in which each agent i's mixed strategy has support Ti. 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 SinTi become available. Journal of Economic Literature Classification Number C72.
Document Type:Working Paper
Appears in Collections:Minnesota Working Papers, Department of Economics - Center for Economic Research, University of Minnesota

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