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When Winning is the Only Thing: Pure Strategy Nash Equilibria in a Three-Candidate Spatial Voting Model

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  • Richard Chisik

    (Department of Economics, Ryerson University, Toronto, Canada)

  • Robert J. Lemke

    (Department of Economics, Lake Forest College, Lake Forest, Illiniois)

Abstract

It is well-known that there are no pure strategy Nash equilibria (PSNE) in the standard three-candidate spatial voting model when candidates maximize their share of the vote. When all that matters to the candidates is winning the election, however, we show that PSNE do exist. We provide a complete characterization of such equilibria and then extend our results to elections with an arbitrary number of candidates. Finally, when two candidates face the potential entrant of a third, we show that PSNE no longer exist, however, they do exist when the number of existing candidates is at least three.

Suggested Citation

  • Richard Chisik & Robert J. Lemke, 2010. "When Winning is the Only Thing: Pure Strategy Nash Equilibria in a Three-Candidate Spatial Voting Model," Working Papers 021, Ryerson University, Department of Economics.
    • Handle: RePEc:rye:wpaper:wp021
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    References listed on IDEAS

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    1. Martin J. Osborne, 1995. "Spatial Models of Political Competition under Plurality Rule: A Survey of Some Explanations of the Number of Candidates and the Positions They Take," Canadian Journal of Economics, Canadian Economics Association, vol. 28(2), pages 261-301, May.
    2. Osborne Martin J., 1993. "Candidate Positioning and Entry in a Political Competition," Games and Economic Behavior, Elsevier, vol. 5(1), pages 133-151, January.
    3. Myerson, Roger B. & Weber, Robert J., 1993. "A Theory of Voting Equilibria," American Political Science Review, Cambridge University Press, vol. 87(1), pages 102-114, March.
    4. Greenberg, Joseph & Shepsle, Kenneth, 1987. "The Effect of Electoral Rewards in Multiparty Competition with Entry," American Political Science Review, Cambridge University Press, vol. 81(2), pages 525-537, June.
    5. Osborne, Martin J., 2000. "Entry-deterring policy differentiation by electoral candidates," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 41-62, July.
    6. Thomas R. Palfrey, 1984. "Spatial Equilibrium with Entry," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(1), pages 139-156.
    7. Myerson, Roger B., 1999. "Theoretical comparisons of electoral systems," European Economic Review, Elsevier, vol. 43(4-6), pages 671-697, April.
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    Cited by:

    1. Haldun Evrenk, 2009. "Three-candidate competition when candidates have valence: the base case," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(1), pages 157-168, January.
    2. Cahan, Dodge & McCabe-Dansted, John & Slinko, Arkadii, 2018. "Asymmetric equilibria in spatial competition under weakly concave scoring rules," Economics Letters, Elsevier, vol. 167(C), pages 71-74.
    3. Dodge Cahan & Arkadii Slinko, 2018. "Electoral competition under best-worst voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(2), pages 259-279, August.

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    More about this item

    Keywords

    Voting; spatial equilibrium; location models; entry.;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D0 - Microeconomics - - General
    • H8 - Public Economics - - Miscellaneous Issues
    • R1 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics

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