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Bargaining with nonanonymous disagreement: Decomposable rules

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  • Kıbrıs, Özgür
  • Tapkı, İpek 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 (1950). We first show that this domain extension creates a very large number of new rules. In particular, decomposable rules (which are extensions of rules from the Nash domain) constitute a nowhere dense subset of all possible rules. For them, we analyze the process through which “good” properties of rules on the Nash domain extend to ours. We then enquire whether the counterparts of some well-known results on the Nash (1950) domain continue to hold for decomposable rules on our extended domain. We first show that an extension of the Kalai–Smorodinsky bargaining rule uniquely satisfies the Kalai and Smorodinsky (1975) properties. This uniqueness result, however, turns out to be an exception. We characterize the uncountably large classes of decomposable rules that survive the Nash (1950), Kalai (1977), and Thomson (1981) properties.

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Bibliographic Info

Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 62 (2011)
Issue (Month): 3 ()
Pages: 151-161

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Handle: RePEc:eee:matsoc:v:62:y:2011:i:3:p:151-161

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Web page: http://www.elsevier.com/locate/inca/505565

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  1. Chun, Youngsub & Thomson, William, 1992. "Bargaining problems with claims," Mathematical Social Sciences, Elsevier, vol. 24(1), pages 19-33, August.
  2. 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.
  3. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  4. Sunil Gupta & Zvi A. Livne, 1988. "Resolving a Conflict Situation with a Reference Outcome: An Axiomatic Model," Management Science, INFORMS, vol. 34(11), pages 1303-1314, November.
  5. Chun, Y. & Thomson, W., 1988. "Nash Solution And Uncertain Disagreement Points," RCER Working Papers 134, University of Rochester - Center for Economic Research (RCER).
  6. Martin J. Osborne & Ariel Rubinstein, 2005. "Bargaining and Markets," Levine's Bibliography 666156000000000515, UCLA Department of Economics.
  7. Nir Dagan & Oscar Volij & Eyal Winter, 2000. "A Characterization of the Nash Bargaining Solution," Economic theory and game theory 018, Nir Dagan, revised 21 Sep 2000.
  8. Shaked, Avner & Sutton, John, 1984. "Involuntary Unemployment as a Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 52(6), pages 1351-64, November.
  9. repec:cup:cbooks:9780521343831 is not listed on IDEAS
  10. Corominas-Bosch, Margarida, 2000. "Bargaining with asymmetric threat points," Economics Letters, Elsevier, vol. 69(3), pages 333-339, December.
  11. Livne, Zvi, 1986. "The bargaining problem: axioms concerning changes in the conflict point," Economics Letters, Elsevier, vol. 21(2), pages 131-134.
  12. Thomson, William, 1987. "Monotonicity of bargaining solutions with respect to the disagreement point," Journal of Economic Theory, Elsevier, vol. 42(1), pages 50-58, June.
  13. Chun, Youngsub & Thomson, William, 1990. "Bargaining with Uncertain Disagreement Points," Econometrica, Econometric Society, vol. 58(4), pages 951-59, July.
  14. Alvin E Roth, 2008. "Axiomatic Models of Bargaining," Levine's Working Paper Archive 122247000000002376, David K. Levine.
  15. Kaushik Basu, 1996. "Bargaining with set-valued disagreement," Social Choice and Welfare, Springer, vol. 13(1), pages 61-74, January.
  16. JÕzsef SÂkovics & Clara PonsatÎ, 1998. "Rubinstein bargaining with two-sided outside options," Economic Theory, Springer, vol. 11(3), pages 667-672.
  17. KIbrIs, Özgür & TapkI, Ipek Gürsel, 2010. "Bargaining with nonanonymous disagreement: Monotonic rules," Games and Economic Behavior, Elsevier, vol. 68(1), pages 233-241, January.
  18. Livne, Zvi A., 1988. "The bargaining problem with an uncertain conflict outcome," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 287-302, June.
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