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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)

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    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.

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    File URL: http://www.fas.nus.edu.sg/ecs/pub/wp/wp0509.pdf
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    Bibliographic Info

    Paper provided by National University of Singapore, Department of Economics in its series Departmental Working Papers with number wp0509.

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    Date of creation: Jan 2005
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    Handle: RePEc:nus:nusewp:wp0509

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

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    1. 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).
    2. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    3. Oechssler, Joerg & Frank Riedel, 1999. "Evolutionary Dynamics on Infinite Strategy Spaces," Discussion Paper Serie A 606, University of Bonn, Germany.
    4. Binmore, Ken & Samuelson, Larry & Young, Peyton, 2003. "Equilibrium selection in bargaining models," Games and Economic Behavior, Elsevier, vol. 45(2), pages 296-328, November.
    5. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February.
    6. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
    7. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    8. Ellingsen, Tore, 1995. "The Evolution of Bargaining Behavior," Working Paper Series in Economics and Finance 61, Stockholm School of Economics.
    9. Ken Binmore & Larry Samuelson & Petyon Young, 2003. "Equilibrium Selection in Bargaining Models," Levine's Bibliography 506439000000000466, UCLA Department of Economics.
    10. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    11. Debreu,Gerard Introduction by-Name:Hildenbrand,Werner, 1986. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521335614, October.
    12. Martin J. Osborne & Ariel Rubinstein, 2005. "Bargaining and Markets," Levine's Bibliography 666156000000000515, UCLA Department of Economics.
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