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Limit Solutions for Finite Horizon Bargaining Problems

Author

Listed:
  • Haruo Imai

    (Kyoto Institute of Economic Research, Kyoto University, Kyoto, Japan)

  • Hannu Salonen

    (Department of Economics and PCRC, University of Turku, 20014 Turku, Finland)

Abstract

We investigate a random proposer bargaining game with a dead line. A bounded time interval is divided into bargaining periods of equal length and we study the limit of the subgame perfect equilibrium outcome as the number of bargaining periods goes to infinity while the dead line is kept fixed. This limit is close to the Raiffa solution when the time horizon is very short. If the dead line goes to infinity the limit outcome converges to the time preference Nash solution. The limit outcome is given an axiomatic characterization as well.

Suggested Citation

  • Haruo Imai & Hannu Salonen, 2009. "Limit Solutions for Finite Horizon Bargaining Problems," Discussion Papers 51, Aboa Centre for Economics.
  • Handle: RePEc:tkk:dpaper:dp51
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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. Chae, Suchan, 1993. "The n-person Nash bargaining solution with time preference," Economics Letters, Elsevier, vol. 41(1), pages 21-24.
    4. Coles, Melvyn G. & Muthoo, Abhinay, 2003. "Bargaining in a non-stationary environment," Journal of Economic Theory, Elsevier, vol. 109(1), pages 70-89, March.
    5. Salonen, Hannu, 1988. "Decomposable solutions for N -- person bargaining games," European Journal of Political Economy, Elsevier, vol. 4(3), pages 333-347.
    6. Eyal Winter & Oscar Volij & Nir Dagan, 2002. "A characterization of the Nash bargaining solution," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(4), pages 811-823.
    7. Roth, Alvin E & Murnighan, J Keith & Schoumaker, Francoise, 1988. "The Deadline Effect in Bargaining: Some Experimental Evidence," American Economic Review, American Economic Association, vol. 78(4), pages 806-823, September.
    8. Ma, Ching-To Albert & Manove, Michael, 1993. "Bargaining with Deadlines and Imperfect Player Control," Econometrica, Econometric Society, vol. 61(6), pages 1313-1339, November.
    9. Shaked, Avner & Sutton, John, 1984. "Involuntary Unemployment as a Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 52(6), pages 1351-1364, November.
    10. Coles, Melvyn G. & Wright, Randall, 1998. "A Dynamic Equilibrium Model of Search, Bargaining, and Money," Journal of Economic Theory, Elsevier, vol. 78(1), pages 32-54, January.
    11. Hans Peters & Eric Van Damme, 1991. "Characterizing the Nash and Raiffa Bargaining Solutions by Disagreement Point Axioms," Mathematics of Operations Research, INFORMS, vol. 16(3), pages 447-461, August.
    12. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    13. Fershtman Chaim & Seidmann Daniel J., 1993. "Deadline Effects and Inefficient Delay in Bargaining with Endogenous Commitment," Journal of Economic Theory, Elsevier, vol. 60(2), pages 306-321, August.
    14. Sjostrom, Tomas, 1991. "Stahl's bargaining model," Economics Letters, Elsevier, vol. 36(2), pages 153-157, June.
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    More about this item

    Keywords

    Nash solution; Raiffa solution; bargaining;

    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

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