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Bargaining with an Agenda

  • Barry O'Neill
  • Dov Samet
  • Zvi Wiener
  • Eyal Winter

We propose a new framework for bargaining in which the process follows an agenda. The agenda is represented by a family, parameterized by time, of increasing sets of joint utilities for possible agreements. This is in contrast to the single set used in the standard framework. The set at each time involves all possible agreements on the issues discussed up to that time. A \emph{bargaining solution} for an agenda specifies a path of agreements, one for each time. We characterize axiomatically a solution that is ordinal, meaning that it is covariant with order- preserving transformations of the utility representations. It can be viewed as the limit of a step-by-step bargaining process in which the agreement point of the last negotiation becomes the disagreement point for the next. The stepwise agreements may follow the Nash solution, the Kalai-Smorodinsky solution or many others, and the ordinal solution will still emerge as the steps tend to zero. Shapley showed that ordinal solutions exist for the standard framework for three players but not for two; the present framework generates an ordinal solution for any number of bargainers, in particular for two.

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Paper provided by EconWPA in its series Game Theory and Information with number 0110004.

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Length: 19 pages
Date of creation: 31 Oct 2001
Date of revision:
Handle: RePEc:wpa:wuwpga:0110004
Note: Type of Document - ; pages: 19
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  1. Safra, Zvi & Samet, Dov, 2004. "An ordinal solution to bargaining problems with many players," Games and Economic Behavior, Elsevier, vol. 46(1), pages 129-142, January.
  2. Sprumont, Yves, 1998. "Ordinal Cost Sharing," Journal of Economic Theory, Elsevier, vol. 81(1), pages 126-162, July.
  3. Clara Ponsati & Joel Watson, 1998. "Multiple-Issue Bargaining and Axiomatic Solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(4), pages 501-524.
  4. Lin Zhou, 1997. "The Nash Bargaining Theory with Non-Convex Problems," Econometrica, Econometric Society, vol. 65(3), pages 681-686, May.
  5. Chaim Fershtman, 1986. "The Importance of the Agenda in Bargaining," Discussion Papers 689, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Winter, Eyal, 1997. "Negotiations in multi-issue committees," Journal of Public Economics, Elsevier, vol. 65(3), pages 323-342, September.
  7. Maschler,Michael Owen,Guillermo & Peleg,Bezalel, 1987. "Paths leadings to the Nash set," Discussion Paper Serie A 135, University of Bonn, Germany.
  8. Perea, Andrés & Nicolò, Antonio, 2000. "A non-welfarist solution for two-person bargaining situations," UC3M Working papers. Economics 7222, Universidad Carlos III de Madrid. Departamento de Economía.
  9. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  10. Thomson, W., 1989. "Cooperative Models Of Bargaining," RCER Working Papers 177, University of Rochester - Center for Economic Research (RCER).
  11. Daniel J. Seidmann & Eyal Winter, 1998. "A Theory of Gradual Coalition Formation," Review of Economic Studies, Oxford University Press, vol. 65(4), pages 793-815.
  12. Ehud Kalai, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Discussion Papers 179, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  13. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May.
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