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Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections

Banks, Jeffrey S. and Duggan, John and Le Breton, Michel (2002) Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections. Journal of Economic Theory, 103 (1). pp. 88-105. ISSN 0022-0531. doi:10.1006/jeth.2001.2825.

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We prove that the support of mixed strategy equilibria of two-player, symmetric, zero-sum games lies in the uncovered set, a concept originating in the theory of tournaments, and the spatial theory of politics. We allow for uncountably infinite strategy spaces, and as a special case, we obtain a long-standing claim to the same effect, due to R. McKelvey (Amer. J. Polit. Sci.30 (1986), 283–314), in the political science literature. Further, we prove the nonemptiness of the uncovered set under quite general assumptions, and we establish, under various assumptions, the coanalyticity and measurability of this set. In the concluding section, we indicate how the inclusion result may be extended to multiplayer, non-zero-sum games.

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Additional Information:© 2001 Elsevier Science (USA). Received October 18, 1998; final version received March 28, 2001; published online November 7, 2001. Jeff Banks passed away on December 21, 2000. The second and third authors express their respect and admiration for Jeff as a colleague and dear friend. His contributions to our profession, great as they were, were cut unduly short. We will miss him. We thank an anonymous referee for constructive comments.
Subject Keywords:Nash equilibrium; undominated strategies; uncovered set
Issue or Number:1
Record Number:CaltechAUTHORS:20160524-092601151
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Official Citation:Jeffrey S Banks, John Duggan, Michel Le Breton, Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections, Journal of Economic Theory, Volume 103, Issue 1, March 2002, Pages 88-105, ISSN 0022-0531, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:67295
Deposited By: Ruth Sustaita
Deposited On:24 May 2016 16:36
Last Modified:11 Nov 2021 00:30

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