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Bargaining with an agenda

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

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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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 48 (2004)
Issue (Month): 1 (July)
Pages: 139-153

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Handle: RePEc:eee:gamebe:v:48:y:2004:i:1:p:139-153
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. Lin Zhou, 1997. "The Nash Bargaining Theory with Non-Convex Problems," Econometrica, Econometric Society, vol. 65(3), pages 681-686, May.
  2. Seidmann, Daniel J & Winter, Eyal, 1998. "A Theory of Gradual Coalition Formation," Review of Economic Studies, Wiley Blackwell, vol. 65(4), pages 793-815, October.
  3. Winter, Eyal, 1997. "Negotiations in multi-issue committees," Journal of Public Economics, Elsevier, vol. 65(3), pages 323-342, September.
  4. Thomson, W., 1989. "Cooperative Models Of Bargaining," RCER Working Papers 177, University of Rochester - Center for Economic Research (RCER).
  5. Clara Ponsati & Joel Watson, 1998. "Multiple-Issue Bargaining and Axiomatic Solutions," International Journal of Game Theory, Springer, vol. 26(4), pages 501-524.
  6. Maschler,Michael Owen,Guillermo & Peleg,Bezalel, 1987. "Paths leadings to the Nash set," Discussion Paper Serie A 135, University of Bonn, Germany.
  7. Chaim Fershtman, 1986. "The Importance of the Agenda in Bargaining," Discussion Papers 689, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-18, May.
  9. Zvi Safra & Dov Samet, 2003. "An ordinal solution to bargaining problems with many players," Game Theory and Information 0310002, EconWPA.
  10. 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.
  11. Sprumont, Y., 1996. "Ordinal Cost Sharing," Cahiers de recherche 9624, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  12. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
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