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Mixed Equilibrium in a Downsian Model with a Favored Candidate

Aragones, Enriqueta and Palfrey, Thomas R. (2002) Mixed Equilibrium in a Downsian Model with a Favored Candidate. Journal of Economic Theory, 103 (1). pp. 131-161. ISSN 0022-0531. doi:10.1006/jeth.2001.2821.

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This paper examines competition in the standard one-dimensional Downsian model of two-candidate elections, but where one candidate (A) enjoys an advantage over the other candidate (D). Voters' preferences are Euclidean, but any voter will vote for candidate A over candidate D unless D is closer to her ideal point by some fixed distance δ. The location of the median voter's ideal point is uncertain, and its distribution is commonly known by both candidates. The candidates simultaneously choose locations to maximize the probability of victory. Pure strategy equilibria often fail to exist in this model, except under special conditions about δ and the distribution of the median ideal point. We solve for the essentially unique symmetric mixed equilibrium with no-gaps, show that candidate A adopts more moderate policies than candidate D, and obtain some comparative statics results about the probability of victory and the expected distance between the two candidates' policies. We find that both players' equilibrium strategies converge to the expected median voter as A's advantage shrinks to 0.

Item Type:Article
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URLURL TypeDescription ItemWorking Paper
Palfrey, Thomas R.0000-0003-0769-8109
Additional Information:© 2001 Elsevier Science. Received 1 March 2000, Revised 22 February 2001, Available online 25 May 2002. Aragones acknowledges financial support by the Generalitat de Catalunya Grant 1999SGR 00157 and the Universitat Pompeu Fabra Grant COFREA99.003 and the hospitality of CBRSS at Harvard University. Palfrey acknowledges financial support from the National Science Foundation, Grants SBR-9631627 and INT-9815573. We are grateful to Tim Groseclose and an anonymous referee for detailed comments on an earlier draft, and to Andrew Postlewaite for several helpful discussions. The paper has also benefited from suggestions by participants at the Wallis Conference on Candidate Entry, Exit, and Positioning, University of Rochester, June 2000, the Games 2000 Congress in Bilbao, July 2000, and seminars at Columbia University and Universitat Pompeu Fabra.
Funding AgencyGrant Number
Generalitat de Catalunya1999SGR 00157
Universitat Pompeu FabraCOFREA99.003
Subject Keywords:spatial competition; mixed strategies; candidate quality
Issue or Number:1
Classification Code:JEL: C72, D72
Record Number:CaltechAUTHORS:20170808-084105843
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Official Citation:Enriqueta Aragones, Thomas R Palfrey, Mixed Equilibrium in a Downsian Model with a Favored Candidate, Journal of Economic Theory, Volume 103, Issue 1, March 2002, Pages 131-161, ISSN 0022-0531, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79909
Deposited By: Tony Diaz
Deposited On:08 Aug 2017 16:51
Last Modified:15 Nov 2021 17:51

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