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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. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    3. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February.
    4. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    5. Berger, Ulrich, 2007. "Brown's original fictitious play," Journal of Economic Theory, Elsevier, vol. 135(1), pages 572-578, July.
    6. Leslie, David S. & Collins, E.J., 2006. "Generalised weakened fictitious play," Games and Economic Behavior, Elsevier, vol. 56(2), pages 285-298, August.
    7. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
    8. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
    9. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
    10. Berger, Ulrich, 2005. "Fictitious play in 2 x n games," Journal of Economic Theory, Elsevier, vol. 120(2), pages 139-154, February.
    11. 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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