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The Maximal Number of Regular Totally Mixed Nash Equilibria

McKelvey, Richard D. and McLennan, Andrew (1997) The Maximal Number of Regular Totally Mixed Nash Equilibria. Journal of Economic Theory, 72 (2). pp. 411-425. ISSN 0022-0531. doi:10.1006/jeth.1996.2214.

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LetS=∏^n_(i=1) S_ibe the strategy space for a finite n-person game. Let (s_(10),…, s_(n0))∈Sbe any strategyn-tuple, and let T_i=S_i−{s_(i0)},i=1, …, n. We show that the maximum number of regular totally mixed Nash equilibria of a game with strategy sets S_iis the number of partitions P={P_1,…,P_n} of ∪_i T_i such that, for each i, |P_i|=|T_i| and P_i∩T_i=∅. The bound is tight, as we give a method for constructing a game with the maximum number of equilibria. Journal of Economic Literature Classification Number C72.

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Additional Information:© 1997 Academic Press. Received 26 July 1994, Revised 5 February 1996. This research was supported in part by National Science Foundation Grant SBR-9308862 to the University of Minnesota and Grant SBR-9308637 to the California Institute of Technology. We benefited from stimulating discussions with Victor Reiner and Michel Le Breton, and an anonymous referee made many excellent suggestions.
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Official Citation:Richard D McKelvey, Andrew McLennan, The Maximal Number of Regular Totally Mixed Nash Equilibria, Journal of Economic Theory, Volume 72, Issue 2, 1997, Pages 411-425, ISSN 0022-0531, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81185
Deposited By: Ruth Sustaita
Deposited On:06 Sep 2017 17:48
Last Modified:15 Nov 2021 19:41

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