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

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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File URL: http://www.wallis.rochester.edu/WallisPapers/wallis_50.pdf
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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
Contact details of provider: Postal: University of Rochester, Wallis Institute, Harkness 109B Rochester, New York 14627 U.S.A.

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  1. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 27-41, January.
  2. 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.
  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. Duggan, John & Fey, Mark, 2005. "Electoral competition with policy-motivated candidates," Games and Economic Behavior, Elsevier, vol. 51(2), pages 490-522, May.
  5. John Duggan, 2003. "Electoral Competition with Privately Informed Candidates," Theory workshop papers 505798000000000029, UCLA Department of Economics.
  6. Richard Ball, 1999. "Discontinuity and non-existence of equilibrium in the probabilistic spatial voting model," Social Choice and Welfare, Springer, vol. 16(4), pages 533-555.
  7. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65, pages 135.
  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. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 1-26, January.
  10. Ignacio Ortuño Orti´n, 2002. "Ideological versus Downsian political competition," Social Choice and Welfare, Springer, vol. 19(3), pages 551-567.
  11. Weingast, Barry R. & Wittman, Donald, 2008. "The Oxford Handbook of Political Economy," OUP Catalogue, Oxford University Press, number 9780199548477, March.
  12. John Ferejohn, 1986. "Incumbent performance and electoral control," Public Choice, Springer, vol. 50(1), pages 5-25, January.
  13. Steffen Hoernig, 2007. "Bertrand Games and Sharing Rules," Economic Theory, Springer, vol. 31(3), pages 573-585, June.
  14. 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.
  15. Jean-FranÚois Laslier, 2000. "Interpretation of electoral mixed strategies," Social Choice and Welfare, Springer, vol. 17(2), pages 283-292.
  16. 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.
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