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Mixed equilibria in runoff elections

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  • Xefteris, Dimitrios

Abstract

We demonstrate that the Hotelling–Downs model with runoff voting always admits symmetric mixed strategy equilibria for any (even or odd) number of office-motivated candidates (provided they are at least four). In specific, (a) we show that the game does not admit any symmetric atomless equilibrium, (b) we fully characterize a class of symmetric atomic mixed equilibria which exist for any distribution of the voters' ideal policies and (c) we argue that these equilibria are more robust than pure strategy equilibria to introduction of uncertainty about the voters' preferences.

Suggested Citation

  • Xefteris, Dimitrios, 2014. "Mixed equilibria in runoff elections," Games and Economic Behavior, Elsevier, vol. 87(C), pages 619-623.
    • Handle: RePEc:eee:gamebe:v:87:y:2014:i:c:p:619-623
    DOI: 10.1016/j.geb.2013.09.002
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    References listed on IDEAS

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    1. Osborne Martin J., 1993. "Candidate Positioning and Entry in a Political Competition," Games and Economic Behavior, Elsevier, vol. 5(1), pages 133-151, January.
    2. Haan, Marco & Volkerink, Bjorn, 2001. "A runoff system restores the principle of minimum differentiation," European Journal of Political Economy, Elsevier, vol. 17(1), pages 157-162, March.
    3. Brusco, Sandro & Dziubiński, Marcin & Roy, Jaideep, 2012. "The Hotelling–Downs model with runoff voting," Games and Economic Behavior, Elsevier, vol. 74(2), pages 447-469.
    4. Shaked, A, 1982. "Existence and Computation of Mixed Strategy Nash Equilibrium for 3-Firms Location Problem," Journal of Industrial Economics, Wiley Blackwell, vol. 31(1-2), pages 93-96, September.
    5. Fey, Mark, 2012. "Symmetric games with only asymmetric equilibria," Games and Economic Behavior, Elsevier, vol. 75(1), pages 424-427.
    6. Matsushima, Noriaki, 2007. "Uncertainty of voters' preferences and differentiation in a runoff system," European Journal of Political Economy, Elsevier, vol. 23(4), pages 1185-1189, December.
    7. Osborne, Martin J & Pitchik, Carolyn, 1986. "The Nature of Equilibrium in a Location Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 223-237, February.
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    Cited by:

    1. Xefteris, Dimitrios, 2016. "Stability in electoral competition: A case for multiple votes," Journal of Economic Theory, Elsevier, vol. 161(C), pages 76-102.
    2. Ewerhart Christian, 2015. "Mixed Equilibrium in a Pure Location Game: The Case of n≥4$$n \ge 4$$ Firms," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 15(2), pages 457-472, July.
    3. Christian Ewerhart, 2014. "Mixed equilibrium in a pure location game: the case of n ≥ 4 firms," ECON - Working Papers 168, Department of Economics - University of Zurich.

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    More about this item

    Keywords

    Runoff voting; Mixed strategies; Hotelling–Downs;
    All these keywords.

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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