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On the implementation of the L-Nash bargaining solution in two-person bargaining games

  • Ferenc Forgó


  • János Fülöp


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    The “Nash program” initiated by Nash (Econometrica 21:128–140, 1953) is a research agenda aiming at representing every axiomatically determined cooperative solution to a game as a Nash outcome of a reasonable noncooperative bargaining game. The L-Nash solution first defined by Forgó (Interactive Decisions. Lecture Notes in Economics and Mathematical Systems, vol 229. Springer, Berlin, pp 1–15, 1983) is obtained as the limiting point of the Nash bargaining solution when the disagreement point goes to negative infinity in a fixed direction. In Forgó and Szidarovszky (Eur J Oper Res 147:108–116, 2003), the L-Nash solution was related to the solution of multiciteria decision making and two different axiomatizations of the L-Nash solution were also given in this context. In this paper, finite bounds are established for the penalty of disagreement in certain special two-person bargaining problems, making it possible to apply all the implementation models designed for Nash bargaining problems with a finite disagreement point to obtain the L-Nash solution as well. For another set of problems where this method does not work, a version of Rubinstein’s alternative offer game (Econometrica 50:97–109, 1982) is shown to asymptotically implement the L-Nash solution. If penalty is internalized as a decision variable of one of the players, then a modification of Howard’s game (J Econ Theory 56:142–159, 1992) also implements the L-Nash solution. Copyright Springer-Verlag 2008

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    Article provided by Springer in its journal Central European Journal of Operations Research.

    Volume (Year): 16 (2008)
    Issue (Month): 4 (December)
    Pages: 359-377

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    Handle: RePEc:spr:cejnor:v:16:y:2008:i:4:p:359-377
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    1. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    2. Binmore, K. & Osborne, M.J. & Rubinstein, A., 1989. "Noncooperative Models Of Bargaining," Papers 89-26, Michigan - Center for Research on Economic & Social Theory.
    3. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 252, David K. Levine.
    4. (*), Y. Stephen Chiu & Ani Dasgupta, 1998. "On implementation via demand commitment games," International Journal of Game Theory, Springer, vol. 27(2), pages 161-189.
    5. Forgo, F. & Szidarovszky, F., 2003. "On the relation between the Nash bargaining solution and the weighting method," European Journal of Operational Research, Elsevier, vol. 147(1), pages 108-116, May.
    6. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
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