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Equilibrium in a discrete Downsian model given a non-minimal valence advantage and linear loss functions

  • Xefteris, Dimitrios

This note complements Aragonès and Palfrey [Aragonés, E., Palfrey, T., 2002. Mixed strategy equilibrium in a Downsian model with a favored candidate. Journal of Economic Theory 103, 131–161.] and Hummel [Hummel, P., 2010. On the nature of equilibriums in a Downsian model with candidate valence. Games and Economic Behavior 70 (2), 425–445.] by characterizing an essentially unique mixed strategy Nash equilibrium in a two-candidate Downsian model where one candidate enjoys a non-minimal non-policy advantage over the other candidate. The policy space is unidimensional and discrete (even number of equidistant locations), the preferences of the median voter are not known to the candidates and voter’s preferences on the policy space are represented by linear loss functions. We find that if the uncertainty about the median voter’s preferences is sufficiently low, then the mixed strategy σˆA= play the two intermediate locations with probability12 for the advantaged candidate and the mixed strategy σˆD= play the least liberal location that guarantees positive probability of election givenσˆAwith probability12and the least conservative strategy that guarantees positive probability of election givenσˆAwith probability12 for the disadvantaged candidate, constitute a Nash equilibrium of the game for any admissible value of the non-policy advantage.

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Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 65 (2013)
Issue (Month): 2 ()
Pages: 150-153

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Handle: RePEc:eee:matsoc:v:65:y:2013:i:2:p:150-153
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505565

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  1. Helios Herrera & David K. Levine & Cesar Martinelli, 2005. "Policy Platforms, Campaign Spending and Voter Participation," Working Papers 0503, Centro de Investigacion Economica, ITAM.
  2. Ashworth, Scott & Bueno de Mesquita, Ethan, 2009. "Elections with platform and valence competition," Games and Economic Behavior, Elsevier, vol. 67(1), pages 191-216, September.
  3. Aragonès, Enriqueta & Xefteris, Dimitrios, 2012. "Candidate quality in a Downsian model with a continuous policy space," Games and Economic Behavior, Elsevier, vol. 75(2), pages 464-480.
  4. Alexei Zakharov, 2009. "A model of candidate location with endogenous valence," Public Choice, Springer, vol. 138(3), pages 347-366, March.
  5. Norman Schofield, 2007. "The Mean Voter Theorem: Necessary and Sufficient Conditions for Convergent Equilibrium," Review of Economic Studies, Oxford University Press, vol. 74(3), pages 965-980.
  6. Ansolabehere, Stephen & Snyder, James M, Jr, 2000. " Valence Politics and Equilibrium in Spatial Election Models," Public Choice, Springer, vol. 103(3-4), pages 327-36, June.
  7. Xefteris, Dimitrios, 2012. "Spatial electoral competition with a probabilistically favored candidate," Economics Letters, Elsevier, vol. 116(1), pages 96-98.
  8. JuanD. Carrillo & Micael Castanheira, 2008. "Information and Strategic Political Polarisation," Economic Journal, Royal Economic Society, vol. 118(530), pages 845-874, 07.
  9. Dix, Manfred & Santore, Rudy, 2002. "Candidate ability and platform choice," Economics Letters, Elsevier, vol. 76(2), pages 189-194, July.
  10. Xefteris, Dimitrios, 2012. "Mixed strategy equilibrium in a Downsian model with a favored candidate: A comment," Journal of Economic Theory, Elsevier, vol. 147(1), pages 393-396.
  11. Adams, James, 1999. " Policy Divergence in Multicandidate Probabilistic Spatial Voting," Public Choice, Springer, vol. 100(1-2), pages 103-22, July.
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