On the implementation of the L-Nash bargaining solution in two-person bargaining games
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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Volume (Year): 16 (2008)
Issue (Month): 4 (December)
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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Rubinstein, Ariel, 1982.
"Perfect Equilibrium in a Bargaining Model,"
Econometric Society, vol. 50(1), pages 97-109, January.
- Binmore, Ken & Osborne, Martin J. & Rubinstein, Ariel, 1992.
"Noncooperative models of bargaining,"
Handbook of Game Theory with Economic Applications,
in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 7, pages 179-225
- (*), Y. Stephen Chiu & Ani Dasgupta, 1998. "On implementation via demand commitment games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(2), pages 161-189.
- Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
- Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
- 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.
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