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Bargaining with nonanonymous disagreement: Monotonic rules

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  • KIbrIs, Özgür
  • TapkI, Ipek Gürsel

Abstract

We analyze bargaining situations where the agents' payoffs from disagreement depend on who among them breaks down the negotiations. We model such problems as a superset of the standard domain of Nash [Nash, J.F., 1950. The bargaining problem. Econometrica 18, 155-162]. On our extended domain, we analyze the implications of two central properties which, on the Nash domain, are known to be incompatible: strong monotonicity [Kalai, E., 1977. Proportional solutions to bargaining situations: Interpersonal utility comparisons. Econometrica 45, 1623-1630] and scale invariance [Nash, J.F., 1950. The bargaining problem. Econometrica 18, 155-162]. We first show that a class of monotone path rules uniquely satisfy strong monotonicity, scale invariance, weak Pareto optimality, and "continuity". We also show that dropping scale invariance from this list characterizes the whole class of monotone path rules. We then introduce a symmetric monotone path rule that we call the Cardinal Egalitarian rule and show that it is weakly Pareto optimal, strongly monotonic, scale invariant, symmetric and that it is the only rule to satisfy these properties on a class of two-agent problems.

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Bibliographic Info

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

Volume (Year): 68 (2010)
Issue (Month): 1 (January)
Pages: 233-241

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Handle: RePEc:eee:gamebe:v:68:y:2010:i:1:p:233-241

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Web page: http://www.elsevier.com/locate/inca/622836

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Keywords: Disagreement matrix Axiomatic Monotonicity Monotone path rule Cardinal Egalitarian rule;

References

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  1. Volij, Oscar & Dagan, Nir & Winter, Eyal, 2002. "A Characterization of the Nash Bargaining Solution," Staff General Research Papers 5259, Iowa State University, Department of Economics.
  2. Corominas-Bosch, Margarida, 2000. "Bargaining with asymmetric threat points," Economics Letters, Elsevier, vol. 69(3), pages 333-339, December.
  3. Thomson, William, 1981. "Nash's Bargaining Solution and Utilitarian Choice Rules," Econometrica, Econometric Society, vol. 49(2), pages 535-38, March.
  4. 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.
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  13. Damme, E.E.C. van & Peters, H., 1991. "Characterizing the Nash and Raiffa bargaining solutions by disagreement point axioms," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154419, Tilburg University.
  14. Livne, Zvi, 1986. "The bargaining problem: axioms concerning changes in the conflict point," Economics Letters, Elsevier, vol. 21(2), pages 131-134.
  15. Kaushik Basu, 1996. "Bargaining with set-valued disagreement," Social Choice and Welfare, Springer, vol. 13(1), pages 61-74, January.
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Cited by:
  1. Kıbrıs, Özgür & Tapkı, İpek Gürsel, 2011. "Bargaining with nonanonymous disagreement: Decomposable rules," Mathematical Social Sciences, Elsevier, vol. 62(3), pages 151-161.

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