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The Maximal Number of Regular Totally Mixed Nash Equilibria

McKelvey, Richard D. and McLennan, Andrew (1994) The Maximal Number of Regular Totally Mixed Nash Equilibria. Social Science Working Paper, 865. California Institute of Technology , Pasadena, CA. (Unpublished)

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Let S=∏^n_(i=1) Si be the strategy space for a finite n-person game. Let (S10,…, Sn0) ϵ S be any strategy n-tuple, and let Ti = Si - {si0}, i = 1, ..., n. We show that the maximum number of regular totally mixed Nash equilibria to a game with strategy sets Si is the number of partitions P = {P1,…, Pn} of UiTi such that, for each i, #Pi = #Ti and Pi ∩ Ti = ∅. The bound is tight, as we give a method for constructing a game with the maximum number of equilibria.

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Additional Information:This research was supported in part by National Science Foundation grants SBR-9308862 to the University of Minnesota and SBR-9308637 to the California Institute of Technology. We benefited from stimulating discussions with Victor Reiner and Michel leBreton. Published as McKelvey, Richard D., and Andrew McLennan. "The maximal number of regular totally mixed Nash equilibria." Journal of Economic Theory 72, no. 2 (1997): 411-425.
Group:Social Science Working Papers
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Series Name:Social Science Working Paper
Issue or Number:865
Classification Code:JEL: C72
Record Number:CaltechAUTHORS:20170823-152433647
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80745
Deposited By: Jacquelyn Bussone
Deposited On:30 Aug 2017 20:37
Last Modified:03 Oct 2019 18:34

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