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. https://resolver.caltech.edu/CaltechAUTHORS:20170906-095820143
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Abstract
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.
| Item Type: | Article | ||||||||||||
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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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| Issue or Number: | 2 | ||||||||||||
| DOI: | 10.1006/jeth.1996.2214 | ||||||||||||
| Record Number: | CaltechAUTHORS:20170906-095820143 | ||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170906-095820143 | ||||||||||||
| 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, http://dx.doi.org/10.1006/jeth.1996.2214. (http://www.sciencedirect.com/science/article/pii/S0022053196922140) | ||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
| ID Code: | 81185 | ||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||
| Deposited By: | Ruth Sustaita | ||||||||||||
| Deposited On: | 06 Sep 2017 17:48 | ||||||||||||
| Last Modified: | 15 Nov 2021 19:41 |
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