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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
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    References listed on IDEAS

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    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. Amir, Rabah & Sahi, Siddharta & Shubik, Martin & Yao, Shuntian, 1990. "A strategic market game with complete markets," Journal of Economic Theory, Elsevier, vol. 51(1), pages 126-143, June.
    4. 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.
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    JEL classification:

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

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