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Existence and uniqueness of Nash equilibrium in electoral competition games: The hybrid case

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  • Alejandro Saporiti

    () (Economics, University of Manchester)

Abstract

This paper analyzes the traditional unidimensional, two-party electoral competition game when parties have mixed motivations, in the sense that they are interested in winning the election, but also in the policy implemented after the contest. In spite of having discontinuous payoffs, this game, refer to as the hybrid election game, is shown to be payoff secure and reciprocally upper semi-continuous. Conditional payoffs, however, are not quasi-concave. Hence, the existence of a pure strategy Nash equilibrium (PSNE) is ensured only if parties have homogenous interests in power. In that case, an equilibrium not only exists, but it is also unique. Instead, if parties have heterogeneous motivations, depending upon the relationship between the electoral uncertainty, the aggregate opportunism and its distribution across parties, a psne may or may not exist. The mixed extension, however, is always better reply secure. Therefore, a mixed strategy Nash equilibrium do indeed exist. These results generalize previous existence results in unidimensional electoral competition.

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Bibliographic Info

Paper provided by University of Rochester - Wallis Institute of Political Economy in its series Wallis Working Papers with number WP50.

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Length: 25 pages
Date of creation: Dec 2007
Date of revision:
Handle: RePEc:roc:wallis:wp50

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Postal: University of Rochester, Wallis Institute, Harkness 109B Rochester, New York 14627 U.S.A.

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Keywords: Electoral competition; mixed motivations; discontinuous games; Nash equilibrium.;

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  1. Enriqueta Aragonès & Thomas R. Palfrey, 2004. "Electoral Competition Between Between Two Candidates of Different Quality: The Effects of Candidate Ideology and Private Information," Working Papers 60, Barcelona Graduate School of Economics.
  2. John Duggan & Mark Fey, . "Electoral Competition with Policy-Motivated Candidates," Wallis Working Papers WP19, University of Rochester - Wallis Institute of Political Economy.
  3. Aragones, Enriqueta & Palfrey, Thomas. R., 2000. "Mixed Equilibrium in a Downsian Model With a Favored Candidate," Working Papers 1102, California Institute of Technology, Division of the Humanities and Social Sciences.
  4. Steffen Hoernig, 2007. "Bertrand Games and Sharing Rules," Economic Theory, Springer, vol. 31(3), pages 573-585, June.
  5. Bernhardt, Dan & Duggan, John & Squintani, Francesco, 2007. "Electoral competition with privately-informed candidates," Games and Economic Behavior, Elsevier, vol. 58(1), pages 1-29, January.
  6. Weingast, Barry R. & Wittman, Donald, 2008. "The Oxford Handbook of Political Economy," OUP Catalogue, Oxford University Press, number 9780199548477, July.
  7. Hinich, M., 1976. "Equilibrium in Spatial Voting: The Median Voter Result is an Artifact," Working Papers 119, California Institute of Technology, Division of the Humanities and Social Sciences.
  8. John E. Roemer, 1997. "Political-economic equilibrium when parties represent constituents: The unidimensional case," Social Choice and Welfare, Springer, vol. 14(4), pages 479-502.
  9. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
  10. Ignacio Ortuño Orti´n, 2002. "Ideological versus Downsian political competition," Social Choice and Welfare, Springer, vol. 19(3), pages 551-567.
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Cited by:
  1. Alejandro Saporiti, 2013. "Power Sharing and Electoral Equilibrium," The School of Economics Discussion Paper Series 1301, Economics, The University of Manchester.
  2. Michalis Drouvelis & Alejandro Saporiti & Nicolaas J Vriend, 2011. "Political Motivations and Electoral Competition: Equilibrium Analysis and Experimental Evidence," Discussion Papers 11-15, Department of Economics, University of Birmingham.
  3. Alejandro Saporiti, 2010. "Power, ideology, and electoral competition," The School of Economics Discussion Paper Series 1003, Economics, The University of Manchester.
  4. Hummel, Patrick, 2010. "Flip-flopping from primaries to general elections," Journal of Public Economics, Elsevier, vol. 94(11-12), pages 1020-1027, December.

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