IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v89y2015icp122-125.html
   My bibliography  Save this article

Symmetric zero-sum games with only asymmetric equilibria

Author

Listed:
  • Xefteris, Dimitrios

Abstract

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825614001675
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2014.12.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Cao, Zhigang & Yang, Xiaoguang, 2018. "Symmetric games revisited," Mathematical Social Sciences, Elsevier, vol. 95(C), pages 9-18.
    3. Shiran Rachmilevitch, 2023. "Symmetric games with only asymmetric equilibria: examples with continuous payoff functions," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 65-68, April.
    4. Ajay Kumar Bhurjee & Geetanjali Panda, 2017. "Optimal strategies for two-person normalized matrix game with variable payoffs," Operational Research, Springer, vol. 17(2), pages 547-562, July.
    5. Rachmilevitch, Shiran, 2016. "Approximate equilibria in strongly symmetric games," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 52-57.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xefteris, Dimitrios, 2014. "Mixed equilibria in runoff elections," Games and Economic Behavior, Elsevier, vol. 87(C), pages 619-623.
    2. Dimitrios Xefteris, 2018. "Candidate valence in a spatial model with entry," Public Choice, Springer, vol. 176(3), pages 341-359, September.
    3. Tsakas, Nikolas & Xefteris, Dimitrios, 2018. "Electoral competition with third party entry in the lab," Journal of Economic Behavior & Organization, Elsevier, vol. 148(C), pages 121-134.
    4. Steffen Huck & Vicki Knoblauch & Wieland Müller, 2006. "Spatial Voting with Endogenous Timing," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 162(4), pages 557-570, December.
    5. Steffen Huck & Wieland M¸ller, 2002. "The East End, the West End, and King's Cross: on Clustering in the Four-Player Hotelling Game," Economic Inquiry, Western Economic Association International, vol. 40(2), pages 231-240, April.
    6. Tarbush, Bassel, 2018. "Hotelling competition and the gamma distribution," Games and Economic Behavior, Elsevier, vol. 111(C), pages 222-240.
    7. Joep Sloun, 2023. "Rationalizable behavior in the Hotelling–Downs model of spatial competition," Theory and Decision, Springer, vol. 95(2), pages 309-335, August.
    8. Hummel, Patrick, 2010. "On the nature of equilibria in a Downsian model with candidate valence," Games and Economic Behavior, Elsevier, vol. 70(2), pages 425-445, November.
    9. Omer Ben-Porat & Moshe Tennenholtz, 2019. "Multiunit Facility Location Games," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 865-889, August.
    10. Dimitrios Xefteris & Iván Barreda-Tarrazona & Aurora García-Gallego & Nikolaos Georgantzis, 2018. "Catalog Competition: Equilibrium Characterization and experimental evidence," Working Papers 2018/08, Economics Department, Universitat Jaume I, Castellón (Spain).
    11. Baye, Michael R. & Kovenock, Dan & de Vries, Casper G., 1992. "It takes two to tango: Equilibria in a model of sales," Games and Economic Behavior, Elsevier, vol. 4(4), pages 493-510, October.
    12. Drezner, Zvi & Eiselt, H.A., 2024. "Competitive location models: A review," European Journal of Operational Research, Elsevier, vol. 316(1), pages 5-18.
    13. Andrea Mangani & Paolo Patelli, 2002. "The Max-Min Principle of Product Differentiation: An Experimental Analysis," LEM Papers Series 2002/05, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    14. 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.
    15. Jeffrey S. Rosenthal, 2019. "Many-Candidate Nash Equilibria for Elections Involving Random Selection," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 279-293, March.
    16. Toshihiro Matsumura & Noriaki Matsushima, 2009. "Cost differentials and mixed strategy equilibria in a Hotelling model," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 43(1), pages 215-234, March.
    17. Jaideep Roy & Marcin Dziubinski, 2008. "Electoral Competition amongst Citizen-candidates and Downsian Politicians," CEDI Discussion Paper Series 08-10, Centre for Economic Development and Institutions(CEDI), Brunel University.
    18. Arnaud Dellis, 2022. "Does Party Polarization Affect the Electoral Prospects of a New Centrist Candidate?," Games, MDPI, vol. 13(4), pages 1-20, July.
    19. Zhiyong Huang, 2011. "The mixed strategy equilibrium of the three-firm location game with discrete location choices," Economics Bulletin, AccessEcon, vol. 31(3), pages 2109-2116.
    20. Arnaud Dellis & Alexandre Gauthier-Belzile & Mandar Oak, 2017. "Policy Polarization and Strategic Candidacy in Elections under the Alternative-Vote Rule," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 173(4), pages 565-590, December.

    More about this item

    Keywords

    Symmetric game; Symmetric equilibrium; Zero-sum game;
    All these keywords.

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:89:y:2015:i:c:p:122-125. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.