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

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Author Info
Alejandro Saporiti () (Economics, University of Manchester)

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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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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
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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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Related research
Keywords: Electoral competition mixed motivations discontinuous games Nash equilibrium.

Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Models of Political Processes: Rent-seeking, Elections, Legislatures, and Voting Behavior
D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy-Making and Implementation

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References listed on IDEAS
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  1. Steffen Hoernig, 2007. "Bertrand Games and Sharing Rules," Economic Theory, Springer, vol. 31(3), pages 573-585, June. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
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  3. Ignacio Ortuño Orti´n, 2002. "Ideological versus Downsian political competition," Social Choice and Welfare, Springer, vol. 19(3), pages 551-567. [Downloadable!] (restricted)
  4. Hinich, Melvin J., 1977. "Equilibrium in spatial voting: The median voter result is an artifact," Journal of Economic Theory, Elsevier, vol. 16(2), pages 208-219, December. [Downloadable!] (restricted)
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  5. 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.
  6. Aragones, Enriqueta & Palfrey, Thomas R., 2002. "Mixed Equilibrium in a Downsian Model with a Favored Candidate," Journal of Economic Theory, Elsevier, vol. 103(1), pages 131-161, March. [Downloadable!] (restricted)
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  7. Duggan, John & Fey, Mark, 2005. "Electoral competition with policy-motivated candidates," Games and Economic Behavior, Elsevier, vol. 51(2), pages 490-522, May. [Downloadable!] (restricted)
    Other versions:
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