IDEAS home Printed from https://ideas.repec.org/p/wrk/wcreta/82.html
   My bibliography  Save this paper

A Difficulty in Characterising Mixed Nash Equilibria in a Strategic Market Game

Author

Listed:
  • Bailey, Ralph W.

    (Department of Economics, University of Birmingham)

  • Kozlovskaya, Maria

    (Economics, Finance and Entrepreneurship Department, Aston Business School)

  • Ray, Indrajit

    (Cardiff Business School)

Abstract

We analyse the conditions for a strategy profile to be an equilibrium in a specific buy and sell strategic market game, with two goods, using best responses of a player against random bids from the opponents. The difficulty in characterising mixed Nash equilbria is that the expected utility is not quasiconcave in strategies. We still prove that any mixed strategy Nash equilibrium profile in which every player faces only two random bids is trivial, that is, is a convex combination of some pure strategy Nash equilibria; moreover, we show that the outcome (the price and the allocations) is deterministic in such an equilibrium.

Suggested Citation

  • Bailey, Ralph W. & Kozlovskaya, Maria & Ray, Indrajit, 2023. "A Difficulty in Characterising Mixed Nash Equilibria in a Strategic Market Game," CRETA Online Discussion Paper Series 82, Centre for Research in Economic Theory and its Applications CRETA.
    • Handle: RePEc:wrk:wcreta:82
    as

    Download full text from publisher

    File URL: https://warwick.ac.uk/fac/soc/economics/research/centres/creta/papers/manage/creta82_-_maria_kozlovskaya.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Forges, Francoise & Peck, James, 1995. "Correlated Equilibrium and Sunspot Equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 33-50, January.
    2. Dmitry Levando, 2012. "A Survey Of Strategic Market Games," Economic Annals, Faculty of Economics and Business, University of Belgrade, vol. 57(194), pages 63-106, July - Se.
    3. Dubey, Pradeep & Shubik, Martin, 1978. "A theory of money and financial institutions. 28. The non-cooperative equilibria of a closed trading economy with market supply and bidding strategies," Journal of Economic Theory, Elsevier, vol. 17(1), pages 1-20, February.
    Full references (including those not matched with items on IDEAS)

    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. Peck, James, 2003. "Large market games with demand uncertainty," Journal of Economic Theory, Elsevier, vol. 109(2), pages 283-299, April.
    2. Hens, Thorsten & Pilgrim, Beate, 2004. "Sunspot Equilibria and the Transfer Paradox," Discussion Papers 2004/14, Norwegian School of Economics, Department of Business and Management Science.
    3. Thorsten Hens & Beate Pilgrim & Janos Mayer, "undated". "Existence of Sunspot Equilibria and Uniqueness of Spot Market Equilibria: The Case of Intrinsically Complete Markets," IEW - Working Papers 188, Institute for Empirical Research in Economics - University of Zurich.
    4. DeMichelis, Stefano & Germano, Fabrizio, 2000. "On the Indices of Zeros of Nash Fields," Journal of Economic Theory, Elsevier, vol. 94(2), pages 192-217, October.
    5. Michael Powers & Martin Shubik & Shun Yao, 1998. "Insurance market games: Scale effects and public policy," Journal of Economics, Springer, vol. 67(2), pages 109-134, June.
    6. Régis Breton & Bertrand Gobillard, 2005. "Robustness of equilibrium price dispersion in finite market games," Post-Print halshs-00257207, HAL.
    7. Koutsougeras, L., 1999. "Market Games with Multiple Trading Posts," Discussion Paper 1999-40, Tilburg University, Center for Economic Research.
    8. Indrajit Ray & Sonali Gupta, 2013. "Coarse correlated equilibria in linear duopoly games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 541-562, May.
    9. Thorsten Hens & Beate Pilgrim, 2004. "Sunspot equilibria and the transfer paradox," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(3), pages 583-602, October.
    10. Duffy, John & Matros, Alexander & Temzelides, Ted, 2011. "Competitive behavior in market games: Evidence and theory," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1437-1463, July.
    11. KOUTSOUGERAS, Leonidas, 1999. "Market games with multiple trading posts," LIDAM Discussion Papers CORE 1999018, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Leonidas Koutsougeras, 2007. "From strategic to price taking behavior," Economics Discussion Paper Series 0717, Economics, The University of Manchester.
    13. Acharya, Sushant & Benhabib, Jess & Huo, Zhen, 2021. "The anatomy of sentiment-driven fluctuations," Journal of Economic Theory, Elsevier, vol. 195(C).
    14. Alex Dickson & Simone Tonin, 2021. "An introduction to perfect and imperfect competition via bilateral oligopoly," Journal of Economics, Springer, vol. 133(2), pages 103-128, July.
    15. Friedman, Daniel & Rabanal, Jean Paul & Rud, Olga A. & Zhao, Shuchen, 2022. "On the empirical relevance of correlated equilibrium," Journal of Economic Theory, Elsevier, vol. 205(C).
    16. Indrajit Ray & Sonali Gupta, 2013. "Coarse correlated equilibria in linear duopoly games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 541-562, May.
    17. Leonidas C. Koutsougeras & Claudia Meo, 2018. "An asymptotic analysis of strategic behavior for exchange economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(2), pages 301-325, August.
    18. John Duffy & Alexander Matros & Ted Temzelides, 2008. "Competitive Behavior in Market Games: Evidence and Theory," Working Paper 366, Department of Economics, University of Pittsburgh, revised Jul 2010.
    19. Goenka, Aditya & Kelly, David L. & Spear, Stephen E., 1998. "Endogenous Strategic Business Cycles," Journal of Economic Theory, Elsevier, vol. 81(1), pages 97-125, July.
    20. Powers, Michael R. & Shubik, Martin, 2001. "Toward a theory of reinsurance and retrocession," Insurance: Mathematics and Economics, Elsevier, vol. 29(2), pages 271-290, October.

    More about this item

    Keywords

    Mixed bids ; Mixed strategy Nash equilibrium ; strategic market games JEL codes: C72;
    All these keywords.

    JEL classification:

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

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:wrk:wcreta:82. 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: Margaret Nash (email available below). General contact details of provider: https://edirc.repec.org/data/dewaruk.html .

    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.