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A Fictitious-Play Model of Bargaining To Implement the Nash Solution

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  • Younghwan In

    (National University of Singapore)

Abstract

We present a fictitious-play model of bargaining, where two bargainers play the Nash demand game repeatedly. The bargainers make a deliberate decision on their demands in the initial period and then follow a fictitious play process subsequently. If the bargainers are patient, the set of epsilon -equilibria of the initial-demand game is in a neighborhood of the division corresponding to the Nash bargaining solution. As the bargainers make a more accurate comparison of payoffs and become more patient accordingly, the set of epsilon-equilibria shrinks and the only equilibrium left is the division of the Nash bargaining solution.

Suggested Citation

  • Younghwan In, 2005. "A Fictitious-Play Model of Bargaining To Implement the Nash Solution," Departmental Working Papers wp0509, National University of Singapore, Department of Economics.
  • Handle: RePEc:nus:nusewp:wp0509
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    File URL: http://www.fas.nus.edu.sg/ecs/pub/wp/wp0509.pdf
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    References listed on IDEAS

    as
    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    3. Martin J. Osborne & Ariel Rubinstein, 2005. "Bargaining and Markets," Levine's Bibliography 666156000000000515, UCLA Department of Economics.
    4. Tore Ellingsen, 1997. "The Evolution of Bargaining Behavior," The Quarterly Journal of Economics, Oxford University Press, vol. 112(2), pages 581-602.
    5. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
    6. Ken Binmore & Larry Samuelson & Petyon Young, 2003. "Equilibrium Selection in Bargaining Models," Levine's Bibliography 506439000000000466, UCLA Department of Economics.
    7. Juana Santamaria-Garcia, 2004. "Equilibrium Selection In The Nash Demand Game. An Evolutionary Approach," Working Papers. Serie AD 2004-34, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    8. JÃrg Oechssler & Frank Riedel, 2001. "Evolutionary dynamics on infinite strategy spaces," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 17(1), pages 141-162.
    9. Binmore, Ken & Samuelson, Larry & Young, Peyton, 2003. "Equilibrium selection in bargaining models," Games and Economic Behavior, Elsevier, vol. 45(2), pages 296-328, November.
    10. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February.
    11. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
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    More about this item

    Keywords

    fictitious play; Nash demand game; epsilon-equilibrium; Nash bargaining solution; Nash program.;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • 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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