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

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Author Info
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.

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

Find related papers by 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, and Information

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  1. Roberto Serrano, 2004. "Fifty Years of the Nash Program, 1953-2003," Working Papers 2004-20, Brown University, Department of Economics. [Downloadable!]
    Other versions:
  2. Ellingsen, Tore, 1997. "The Evolution of Bargaining Behavior," The Quarterly Journal of Economics, MIT Press, vol. 112(2), pages 581-602, May.
    Other versions:
  3. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January. [Downloadable!] (restricted)
  4. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April. [Downloadable!] (restricted)
  5. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April. [Downloadable!] (restricted)
  6. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February. [Downloadable!] (restricted)
  7. Binmore, Ken & Samuelson, Larry & Young, Peyton, 2003. "Equilibrium selection in bargaining models," Games and Economic Behavior, Elsevier, vol. 45(2), pages 296-328, November. [Downloadable!] (restricted)
  8. Ken Binmore & Ariel Rubinstein & Asher Wolinsky, 1986. "The Nash Bargaining Solution in Economic Modelling," RAND Journal of Economics, The RAND Corporation, vol. 17(2), pages 176-188, Summer. [Downloadable!] (restricted)
  9. Martin J. Osborne & Ariel Rubinstein, 2005. "Bargaining and Markets," Levine's Bibliography 666156000000000515, UCLA Department of Economics. [Downloadable!]
  10. Ken Binmore & Larry Samuelson & Petyon Young, 2003. "Equilibrium Selection in Bargaining Models," Levine's Bibliography 506439000000000466, UCLA Department of Economics. [Downloadable!]
  11. Oechssler, Joerg, and Frank Riedel, . "Evolutionary Dynamics on Infinite Strategy Spaces," Discussion Paper Serie A 606, University of Bonn, Germany. [Downloadable!]
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  12. 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). [Downloadable!]
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