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Bargaining, conditional consistency, and weighted lexicographic Kalai-Smorodinsky Solutions

Listed author(s):
  • Bram Driesen

    ()

    (University of Glasgow, Adam Smith Business School)

Abstract We reconsider the class of weighted Kalai-Smorodinsky solutions of Dubra (Econ Lett 73:131–136, 2001), and using methods of Imai (Econometrica 51:389–401, 1983), extend their characterization to the domain of multilateral bargaining problems. Aside from standard axioms in the literature, this result involves a new property that weakens the axiom Bilateral Consistency (Lensberg, J Econ Theory 45:330–341, 1988), by making the notion of consistency dependent on how ideal values in a reduced problem change relative to the original problem.

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Article provided by Springer & The Society for Social Choice and Welfare in its journal Social Choice and Welfare.

Volume (Year): 46 (2016)
Issue (Month): 4 (April)
Pages: 777-809

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Handle: RePEc:spr:sochwe:v:46:y:2016:i:4:d:10.1007_s00355-015-0936-x
DOI: 10.1007/s00355-015-0936-x
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  1. Anbarci, Nejat & Sun, Ching-jen, 2013. "Asymmetric Nash bargaining solutions: A simple Nash program," Economics Letters, Elsevier, vol. 120(2), pages 211-214.
  2. Thomson,William & Lensberg,Terje, 2006. "Axiomatic Theory of Bargaining with a Variable Number of Agents," Cambridge Books, Cambridge University Press, number 9780521027038, December.
  3. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
  4. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
  5. Mark A. Chen, 2000. "Individual monotonicity and the leximin solution," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 353-365.
  6. Imai, Haruo, 1983. "Individual Monotonicity and Lexicographic Maxmin Solution," Econometrica, Econometric Society, vol. 51(2), pages 389-401, March.
  7. Chun, Youngsub & Thomson, William, 1992. "Bargaining problems with claims," Mathematical Social Sciences, Elsevier, vol. 24(1), pages 19-33, August.
  8. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  9. Peters, Hans & Tijs, Stef & Zarzuelo, Jose, 1994. "A reduced game property for the Kalai-Smorodinsky and egalitarian bargaining solutions," Mathematical Social Sciences, Elsevier, vol. 27(1), pages 11-18, February.
  10. Dubra, Juan, 2001. "An asymmetric Kalai-Smorodinsky solution," Economics Letters, Elsevier, vol. 73(2), pages 131-136, November.
  11. Roth, Alvin E., 1977. "Independence of irrelevant alternatives, and solutions to Nash's bargaining problem," Journal of Economic Theory, Elsevier, vol. 16(2), pages 247-251, December.
  12. Driesen, Bram, 2012. "Proportional concessions and the leximin solution," Economics Letters, Elsevier, vol. 114(3), pages 288-291.
  13. 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.
  14. Britz, Volker & Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2010. "Non-cooperative support for the asymmetric Nash bargaining solution," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1951-1967, September.
  15. Bossert, Walter, 1993. "An alternative solution to bargaining problems with claims," Mathematical Social Sciences, Elsevier, vol. 25(3), pages 205-220, May.
  16. Chang, Chih & Liang, Meng-Yu, 1998. "A characterization of the lexicographic Kalai-Smorodinsky solution for n=3," Mathematical Social Sciences, Elsevier, vol. 35(3), pages 307-319, May.
  17. Laruelle, Annick & Valenciano, Federico, 2008. "Noncooperative foundations of bargaining power in committees and the Shapley-Shubik index," Games and Economic Behavior, Elsevier, vol. 63(1), pages 341-353, May.
  18. John C. Harsanyi & Reinhard Selten, 1972. "A Generalized Nash Solution for Two-Person Bargaining Games with Incomplete Information," Management Science, INFORMS, vol. 18(5-Part-2), pages 80-106, January.
  19. Chih Chang & Yan-An Hwang, 1999. "A characterization of the leximin solution of the bargaining problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(3), pages 395-400, July.
  20. repec:spr:compst:v:49:y:1999:i:3:p:395-400 is not listed on IDEAS
  21. Lensberg, Terje, 1988. "Stability and the Nash solution," Journal of Economic Theory, Elsevier, vol. 45(2), pages 330-341, August.
  22. Chun, Youngsub & Peters, Hans, 1991. "The lexicographic equal-loss solution," Mathematical Social Sciences, Elsevier, vol. 22(2), pages 151-161, October.
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