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Fictitious play property of the Nash demand game

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  • In, Younghwan

Abstract

We show that the Nash demand game has the fictitious play property. We also show that almost every fictitious play process and its associated belief path converge to a pure-strategy Nash equilibrium in the Nash demand game.

Suggested Citation

  • In, Younghwan, 2014. "Fictitious play property of the Nash demand game," Economics Letters, Elsevier, vol. 122(3), pages 408-412.
  • Handle: RePEc:eee:ecolet:v:122:y:2014:i:3:p:408-412
    DOI: 10.1016/j.econlet.2013.12.017
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    References listed on IDEAS

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    1. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
    2. Berger, Ulrich, 2005. "Fictitious play in 2 x n games," Journal of Economic Theory, Elsevier, vol. 120(2), pages 139-154, February.
    3. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    4. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February.
    5. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    6. Berger, Ulrich, 2007. "Brown's original fictitious play," Journal of Economic Theory, Elsevier, vol. 135(1), pages 572-578, July.
    7. Leslie, David S. & Collins, E.J., 2006. "Generalised weakened fictitious play," Games and Economic Behavior, Elsevier, vol. 56(2), pages 285-298, August.
    8. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
    9. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945.
    10. Monderer, Dov & Shapley, Lloyd S., 1996. "Fictitious Play Property for Games with Identical Interests," Journal of Economic Theory, Elsevier, vol. 68(1), pages 258-265, January.
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    Cited by:

    1. Roberto Serrano, 2020. "Sixty-Seven Years of the Nash Program: Time for Retirement?," Working Papers 2020-20, Brown University, Department of Economics.
    2. Roberto Serrano, 2021. "Sixty-seven years of the Nash program: time for retirement?," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 35-48, March.
    3. Aryandoust, Arsam & Lilliestam, Johan, 2017. "The potential and usefulness of demand response to provide electricity system services," Applied Energy, Elsevier, vol. 204(C), pages 749-766.

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    More about this item

    Keywords

    Bargaining; Nash demand game; Fictitious play;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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