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Multiple-Issue Bargaining and Axiomatic Solutions

Author

Listed:
  • Clara Ponsati

    (Department d'Economia i Historia Econoica, Universitat Autonoma, Barcelona 08193, Spain, e-mail: cponsati@cc.uab.es)

  • Joel Watson

    (Department of Economics, 0508, University of California, San Diego, La Jolla, CA 92093-0508, USA, e-mail: jwatson@weber.ucsd.edu)

Abstract

We study two-person, multiple-issue bargaining problems and identify four procedures by which the bargaining may take place. Drawing on some logic from non-cooperative game theory, we propose axioms which relate the outcomes of the procedures. We also promote a weak monotonicity axiom on solutions, called issue-by-issue monotonicity, which is geared toward multiple-issue bargaining. Our main result concerns the relationship between a sequential bargaining procedure - with the rule that agreements are implemented only after all issues are resolved - and global bargaining (in which all issues are negotiated simultaneously). If a bargaining solution predicts the same outcome with these two procedures, then we say that it satisfies agenda independence. We prove that a solution satisfies axioms of efficiency, symmetry, scale invariance, issue-by-issue monotonicity, and agenda independence if and only if it is the Nash solutions. This result provides new intuition for Nash's independence of irrelevant alternatives axiom. Among other results, we show that a solution is invariant to all four of the procedures and satisfies efficiency and symmetry if and only if it is the utilitarian solution with equal weights. We comment on the results of other authors who address multiple-issue bargaining.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jogath:v:26:y:1998:i:4:p:501-524
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Busch, Lutz-Alexander & Horstmann, Ignatius J., 2002. "The game of negotiations: ordering issues and implementing agreements," Games and Economic Behavior, Elsevier, vol. 41(2), pages 169-191, November.
    4. O'Neill, Barry & Samet, Dov & Wiener, Zvi & Winter, Eyal, 2004. "Bargaining with an agenda," Games and Economic Behavior, Elsevier, vol. 48(1), pages 139-153, July.
    5. Joan Esteban & József Sákovics, 2002. "Endogenous bargaining power," Economics Working Papers 644, Department of Economics and Business, Universitat Pompeu Fabra.
    6. Ephraim Zehavi & Amir Leshem, 2018. "On the Allocation of Multiple Divisible Assets to Players with Different Utilities," Computational Economics, Springer;Society for Computational Economics, vol. 52(1), pages 253-274, June.
    7. Bossert, Walter & Peters, Hans, 2000. "Multi-attribute decision-making in individual and social choice," Mathematical Social Sciences, Elsevier, vol. 40(3), pages 327-339, November.
    8. Joan-Maria Esteban & József Sákovics, 2005. "A Theory of Agreements in the Shadow of Conflict," Working Papers 255, Barcelona Graduate School of Economics.
    9. Gayer, Gabrielle & Persitz, Dotan, 2016. "Negotiation across multiple issues," Theoretical Economics, Econometric Society, vol. 11(3), September.
    10. Amparo M. Mármol Conde & Clara Ponsatí Obiols, 2006. "Bargaining Multiple Issues with Leximin Preferences," Economic Working Papers at Centro de Estudios Andaluces E2006/05, Centro de Estudios Andaluces.
    11. Harri Ehtamo & Raimo P. Hämäläinen, 2001. "Interactive Multiple‐Criteria Methods for Reaching Pareto Optimal Agreements in Negotiations," Group Decision and Negotiation, Springer, vol. 10(6), pages 475-491, November.
    12. Joan Esteban & Jozsef Sakovics, 1999. "Why do lions get the lion's share? A Hobbesian theory of agreements," Edinburgh School of Economics Discussion Paper Series 37, Edinburgh School of Economics, University of Edinburgh.
    13. Katsuhide Fujita & Takayuki Ito & Mark Klein, 2012. "A Secure and Fair Protocol that Addresses Weaknesses of the Nash Bargaining Solution in Nonlinear Negotiation," Group Decision and Negotiation, Springer, vol. 21(1), pages 29-47, January.
    14. Chwolka, Anne & Raith, Matthias G., 2001. "Group preference aggregation with the AHP - implications for multiple-issue agendas," European Journal of Operational Research, Elsevier, vol. 132(1), pages 176-186, July.
    15. M. Hinojosa & A. Mármol & L. Monroy, 2005. "Generalized Maximin Solutions in Multicriteria Bargaining," Annals of Operations Research, Springer, vol. 137(1), pages 243-255, July.
    16. Naeve-Steinweg, E., 2004. "The averaging mechanism," Games and Economic Behavior, Elsevier, vol. 46(2), pages 410-424, February.

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