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Symmetric zero-sum games with only asymmetric equilibria


  • Xefteris, Dimitrios


We know that a) two-player symmetric zero-sum games with non-empty equilibrium sets always admit symmetric equilibria and that b) two-player and multiplayer symmetric non-zero-sum games might have only asymmetric equilibria (Fey, 2012). But what about multiplayer symmetric zero-sum games? This paper shows that these games might also have only asymmetric equilibria. One of the examples employed to illustrate this point is the three-candidate version of the popular Hotelling–Downs model of electoral competition. This demonstrates that symmetric games with only asymmetric equilibria are not technical paradoxes but are integrated in economics and political science literature for quite a while.

Suggested Citation

  • Xefteris, Dimitrios, 2015. "Symmetric zero-sum games with only asymmetric equilibria," Games and Economic Behavior, Elsevier, vol. 89(C), pages 122-125.
  • Handle: RePEc:eee:gamebe:v:89:y:2015:i:c:p:122-125
    DOI: 10.1016/j.geb.2014.12.001

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    References listed on IDEAS

    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. 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.
    3. Fey, Mark, 2012. "Symmetric games with only asymmetric equilibria," Games and Economic Behavior, Elsevier, vol. 75(1), pages 424-427.
    4. 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. repec:spr:jogath:v:46:y:2017:i:2:d:10.1007_s00182-016-0540-z is not listed on IDEAS
    2. Dimitrios Xefteris & Didier Laussel & Michel Le Breton, 2017. "Simple centrifugal incentives in spatial competition," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 357-381, May.
    3. Rachmilevitch, Shiran, 2016. "Approximate equilibria in strongly symmetric games," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 52-57.

    More about this item


    Symmetric game; Symmetric equilibrium; Zero-sum game;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games


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