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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. Alvin E Roth, 2008. "Axiomatic Models of Bargaining," Levine's Working Paper Archive 122247000000002376, David K. Levine.
  2. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  3. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-30, October.
  4. Chun, Y. & Thomson, W., 1988. "Nash Solution And Uncertain Disagreement Points," RCER Working Papers 134, University of Rochester - Center for Economic Research (RCER).
  5. Livne, Zvi A., 1988. "The bargaining problem with an uncertain conflict outcome," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 287-302, June.
  6. KIbrIs, Özgür & TapkI, Ipek Gürsel, 2010. "Bargaining with nonanonymous disagreement: Monotonic rules," Games and Economic Behavior, Elsevier, vol. 68(1), pages 233-241, January.
  7. JÕzsef SÂkovics & Clara PonsatÎ, 1998. "Rubinstein bargaining with two-sided outside options," Economic Theory, Springer, vol. 11(3), pages 667-672.
  8. Corominas-Bosch, Margarida, 2000. "Bargaining with asymmetric threat points," Economics Letters, Elsevier, vol. 69(3), pages 333-339, December.
  9. Chun, Youngsub & Thomson, William, 1990. "Bargaining with Uncertain Disagreement Points," Econometrica, Econometric Society, vol. 58(4), pages 951-59, July.
  10. Chun, Y. & Thomson, W., 1989. "Bargaining Problems With Claims," RCER Working Papers 189, University of Rochester - Center for Economic Research (RCER).
  11. Martin J. Osborne & Ariel Rubinstein, 2005. "Bargaining and Markets," Levine's Bibliography 666156000000000515, UCLA Department of Economics.
  12. 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.
  13. 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.
  14. Livne, Zvi, 1986. "The bargaining problem: axioms concerning changes in the conflict point," Economics Letters, Elsevier, vol. 21(2), pages 131-134.
  15. 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.
  16. 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.
  17. Kaushik Basu, 1996. "Bargaining with set-valued disagreement," Social Choice and Welfare, Springer, vol. 13(1), pages 61-74, January.
  18. repec:cup:cbooks:9780521343831 is not listed on IDEAS
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