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Axiomatic Bargaining on Economic Enviornments with Lott

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Abstract

Most contributions in axiomatic bargaining are phrased in the space of utilities. This comes in sharp contrast with standards in most other fields of economic theory. The present paper shows how Nash’s original axiomatic system can be rephrased in a natural class of economic environments with lotteries, and how his uniqueness result can be recovered, provided one completes the system with a property of independence with respect to preferences over unfeasible alternatives. Similar results can be derived for the Kalai-Smorodinsky solution if and only if bargaining may involve multiple goods. The paper also introduces a distinction between welfarism and cardinal welfarism, and emphasizes that the Nash solution is ordinally invariant on the class of von Neumann-Morgensterm preferences.

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File URL: http://www.brown.edu/Departments/Economics/Papers/2009/2009-5_paper.pdf
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Bibliographic Info

Paper provided by Brown University, Department of Economics in its series Working Papers with number 2009-5.

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Date of creation: 2009
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Handle: RePEc:bro:econwp:2009-5

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Postal: Department of Economics, Brown University, Providence, RI 02912

Related research

Keywords: Bargaining; Welfarism; Nash; Kalai-Smorodinsky; Expected Utility;

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  1. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  2. 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.
  3. John A. Weymark, 2000. "Candidate Stability and Nonbinary Social Choice," Vanderbilt University Department of Economics Working Papers 0029, Vanderbilt University Department of Economics, revised Feb 2001.
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  8. 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.
  9. Geoffroy de Clippel & Kfir Eliaz, 2009. "Reason-Based Choice: A Bargaining Rationale for the Attraction and Compromise Effects," Working Papers 2009-4, Brown University, Department of Economics.
  10. Dutta, Bhaskar & Jackson, Matthew O & Le Breton, Michel, 2001. "Strategic Candidacy and Voting Procedures," Econometrica, Econometric Society, vol. 69(4), pages 1013-37, July.
  11. Grant, Simon & Kajii, Atsushi, 1995. "A Cardinal Characterization of the Rubinstein-Safra-Thomson Axiomatic Bargaining Theory," Econometrica, Econometric Society, vol. 63(5), pages 1241-49, September.
  12. Rubinstein, Ariel & Safra, Zvi & Thomson, William, 1992. "On the Interpretation of the Nash Bargaining Solution and Its Extension to Non-expected Utility Preferences," Econometrica, Econometric Society, vol. 60(5), pages 1171-86, September.
  13. Roemer, John E., 1988. "Axiomatic bargaining theory on economic environments," Journal of Economic Theory, Elsevier, vol. 45(1), pages 1-31, June.
  14. Hanany, Eran, 2007. "Appeals immune bargaining solution with variable alternative sets," Games and Economic Behavior, Elsevier, vol. 59(1), pages 72-84, April.
  15. Chambers, Christopher P., 2005. "Allocation rules for land division," Journal of Economic Theory, Elsevier, vol. 121(2), pages 236-258, April.
  16. Samet, Dov & Safra, Zvi, 2005. "A family of ordinal solutions to bargaining problems with many players," Games and Economic Behavior, Elsevier, vol. 50(1), pages 89-106, January.
  17. Aumann, Robert J & Kurz, Mordecai, 1977. "Power and Taxes," Econometrica, Econometric Society, vol. 45(5), pages 1137-61, July.
  18. Zvi Safra & Dov Samet, 2003. "An ordinal solution to bargaining problems with many players," Game Theory and Information 0310002, EconWPA.
  19. Peters, Hans & Wakker, Peter, 1991. "Independence of Irrelevant Alternatives and Revealed Group Preferences," Econometrica, Econometric Society, vol. 59(6), pages 1787-1801, November.
  20. Grether, David M & Plott, Charles R, 1982. "Nonbinary Social Choice: An Impossibility Theorem," Review of Economic Studies, Wiley Blackwell, vol. 49(1), pages 143-49, January.
  21. Marc Fleurbaey, 2003. "On the informational basis of social choice," Social Choice and Welfare, Springer, vol. 21(2), pages 347-384, October.
  22. Peters, H.J.M. & Tijs, S.H., 1985. "Characterization of all individually monotonic bargaining solutions," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154267, Tilburg University.
  23. Karni, Edi & Schmeidler, David, 1976. "Independence of nonfeasible alternatives, and independence of nonoptimal alternatives," Journal of Economic Theory, Elsevier, vol. 12(3), pages 488-493, June.
  24. Kibris, Ozgur, 2004. "Egalitarianism in ordinal bargaining: the Shapley-Shubik rule," Games and Economic Behavior, Elsevier, vol. 49(1), pages 157-170, October.
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Cited by:
  1. Yves Sprumont, 2013. "On relative egalitarianism," Social Choice and Welfare, Springer, vol. 40(4), pages 1015-1032, April.
  2. Geoffroy de Clippel & Camelia Bejan, 2009. "No Profitable Decomposition in Quasi-Linear Allocation Problems," Working Papers 2009-6, Brown University, Department of Economics.
  3. Yves SPRUMONT, 2009. "Relative Egalitarianism and Related Criteria," Cahiers de recherche 02-2009, Centre interuniversitaire de recherche en économie quantitative, CIREQ.

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