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Bargaining with an Agenda

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

Abstract

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.

Suggested Citation

  • Barry O'Neill & Dov Samet & Zvi Wiener & Eyal Winter, 2001. "Bargaining with an Agenda," Game Theory and Information 0110004, EconWPA.
  • Handle: RePEc:wpa:wuwpga:0110004
    Note: Type of Document - ; pages: 19
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    References listed on IDEAS

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    1. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    2. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    3. 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.
    4. Lin Zhou, 1997. "The Nash Bargaining Theory with Non-Convex Problems," Econometrica, Econometric Society, vol. 65(3), pages 681-686, May.
    5. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    6. Thomson, William, 1994. "Cooperative 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 2, chapter 35, pages 1237-1284 Elsevier.
    7. Nicolò, Antonio & Perea, Andrés, 2000. "A non-welfarist solution for two-person bargaining situations," UC3M Working papers. Economics 7222, Universidad Carlos III de Madrid. Departamento de Economía.
    8. Sprumont, Yves, 1998. "Ordinal Cost Sharing," Journal of Economic Theory, Elsevier, vol. 81(1), pages 126-162, July.
    9. Fershtman, Chaim, 1990. "The importance of the agenda in bargaining," Games and Economic Behavior, Elsevier, vol. 2(3), pages 224-238, September.
    10. Maschler,Michael Owen,Guillermo & Peleg,Bezalel, 1987. "Paths leadings to the Nash set," Discussion Paper Serie A 135, University of Bonn, Germany.
    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. 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.
    13. Winter, Eyal, 1997. "Negotiations in multi-issue committees," Journal of Public Economics, Elsevier, vol. 65(3), pages 323-342, September.
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    Cited by:

    1. Diskin, A. & Koppel, M. & Samet, D., 2011. "Generalized Raiffa solutions," Games and Economic Behavior, Elsevier, vol. 73(2), pages 452-458.
    2. de Clippel, Geoffroy & Bejan, Camelia, 2011. "No profitable decompositions in quasi-linear allocation problems," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1995-2012, September.
    3. Perez-Castrillo, David & Wettstein, David, 2006. "An ordinal Shapley value for economic environments," Journal of Economic Theory, Elsevier, vol. 127(1), pages 296-308, March.
    4. Joan Esteban & József Sákovics, 2008. "A Theory of Agreements in the Shadow of Conflict: The Genesis of Bargaining Power," Theory and Decision, Springer, vol. 65(3), pages 227-252, November.
    5. Julian J. Arevalo, 2005. "Gradual Nash Bargaining with Endogenous Agenda: A Path-Dependent Model," Game Theory and Information 0502004, EconWPA.
    6. Kibris, Ozgur, 2004. "Egalitarianism in ordinal bargaining: the Shapley-Shubik rule," Games and Economic Behavior, Elsevier, vol. 49(1), pages 157-170, October.
    7. Joan-Maria Esteban & József Sákovics, 2005. "A Theory of Agreements in the Shadow of Conflict," Working Papers 255, Barcelona Graduate School of Economics.
    8. Amparo Mármol & Clara Ponsatí, 2008. "Bargaining over multiple issues with maximin and leximin preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(2), pages 211-223, February.
    9. Aviad Heifetz & Clara Ponsati, 2007. "All in good time," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 521-538, April.
    10. Christopher Waller & Guillaume Rocheteau, 2005. "Bargaining in Monetary Economies," 2005 Meeting Papers 55, Society for Economic Dynamics.
    11. Julián Arévalo, 2004. "Negociación Nash Gradual con Agenda Endógena: Un Modelo Trayectoria-Dependiente," Game Theory and Information 0407001, EconWPA.
    12. 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.
    13. Samet, Dov, 2009. "What if Achilles and the tortoise were to bargain? An argument against interim agreements," MPRA Paper 23370, University Library of Munich, Germany.
    14. Nicolo, Antonio & Perea, Andres, 2005. "Monotonicity and equal-opportunity equivalence in bargaining," Mathematical Social Sciences, Elsevier, vol. 49(2), pages 221-243, March.
    15. Joan Esteban & József Sákovics, 2002. "Endogenous bargaining power," Economics Working Papers 644, Department of Economics and Business, Universitat Pompeu Fabra.
    16. Boragan Aruoba, S. & Rocheteau, Guillaume & Waller, Christopher, 2007. "Bargaining and the value of money," Journal of Monetary Economics, Elsevier, vol. 54(8), pages 2636-2655, November.
    17. Calvo, Emilio & Peters, Hans, 2005. "Bargaining with ordinal and cardinal players," Games and Economic Behavior, Elsevier, vol. 52(1), pages 20-33, July.
    18. Nosal, Ed & Rocheteau, Guillaume, 2013. "Pairwise trade, asset prices, and monetary policy," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 1-17.
    19. Vidal-Puga, Juan, 2015. "A non-cooperative approach to the ordinal Shapley–Shubik rule," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 111-118.

    More about this item

    Keywords

    bargaining; ordinal utility;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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