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Asymmetric equilibria in spatial competition under weakly concave scoring rules

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  • Cahan, Dodge
  • McCabe-Dansted, John
  • Slinko, Arkadii

Abstract

The Hotelling–Downs model of spatial competition is used to investigate the strategic position-taking behavior of firms or political parties under scoring rules. Previous studies of non-convergent Nash equilibria – equilibria in which divergent positions are chosen – found that they often do not exist and, when they do, they are fairly symmetric. In particular, this is true for convex scoring rules (Cahan and Slinko, 2017). Here, we investigate non-convergent equilibria for the broad class of weakly concave scoring rules. Surprisingly, we find that only asymmetric equilibria can exist, and we present several examples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ecolet:v:167:y:2018:i:c:p:71-74
    DOI: 10.1016/j.econlet.2018.03.020
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    References listed on IDEAS

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    1. B. Curtis Eaton & Richard G. Lipsey, 1975. "The Principle of Minimum Differentiation Reconsidered: Some New Developments in the Theory of Spatial Competition," Review of Economic Studies, Oxford University Press, vol. 42(1), pages 27-49.
    2. Jean-François Laslier & François Maniquet, 2010. "Classical Electoral Competition Under Approval Voting," Studies in Choice and Welfare, in: Jean-François Laslier & M. Remzi Sanver (ed.), Handbook on Approval Voting, chapter 0, pages 415-429, Springer.
    3. Arnaud Dellis & Mandar Oak, 2016. "Multiple votes, multiple candidacies and polarization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 1-38, January.
    4. Richard Chisik & Robert Lemke, 2006. "When winning is the only thing: pure strategy Nash equilibria in a three-candidate spatial voting model," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(1), pages 209-215, January.
    5. Xefteris, Dimitrios, 2016. "Stability in electoral competition: A case for multiple votes," Journal of Economic Theory, Elsevier, vol. 161(C), pages 76-102.
    6. Aragonès, Enriqueta & Xefteris, Dimitrios, 2012. "Candidate quality in a Downsian model with a continuous policy space," Games and Economic Behavior, Elsevier, vol. 75(2), pages 464-480.
    7. 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.
    8. Dodge Cahan & Arkadii Slinko, 2017. "Nonconvergent Electoral Equilibria under Scoring Rules: Beyond Plurality," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 19(2), pages 445-460, April.
    9. Myerson, Roger B., 1999. "Theoretical comparisons of electoral systems," European Economic Review, Elsevier, vol. 43(4-6), pages 671-697, April.
    10. Jean-François Laslier & M. Remzi Sanver (ed.), 2010. "Handbook on Approval Voting," Studies in Choice and Welfare, Springer, number 978-3-642-02839-7, December.
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    Cited by:

    1. Dominic Keehan & Dodge Cahan & John McCabe-Dansted & Arkadii Slinko, 2022. "Equilibria on a circular market when consumers do not always buy from the closest firm," Review of Economic Design, Springer;Society for Economic Design, vol. 26(3), pages 285-306, September.
    2. Dodge Cahan & Hongjia H. Chen & Louis Christie & Arkadii Slinko, 2021. "Spatial competition on 2-dimensional markets and networks when consumers don’t always go to the closest firm," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 945-970, December.

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    More about this item

    Keywords

    Spatial competition; Nash equilibrium; Scoring rules; Asymmetric equilibrium; Agglomeration;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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