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Axiomatic Bargaining on Economic Enviornments with Lott

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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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
Contact details of provider: Postal: Department of Economics, Brown University, Providence, RI 02912

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  4. 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.
  5. Elisha A. Pazner & David Schmeidler, 1975. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," Discussion Papers 174, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Peters, H.J.M. & Tijs, S.H., 1985. "Characterization of all individually monotonic bargaining solutions," Other publications TiSEM 52f5a6d5-dcac-4fec-9b8e-9, Tilburg University, School of Economics and Management.
  7. 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.
  8. 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.
  9. Burgos, Albert & Grant, Simon & Kajii, Atsushi, 2002. "Bargaining and Boldness," Games and Economic Behavior, Elsevier, vol. 38(1), pages 28-51, January.
  10. Kibris, Ozgur, 2004. "Egalitarianism in ordinal bargaining: the Shapley-Shubik rule," Games and Economic Behavior, Elsevier, vol. 49(1), pages 157-170, October.
  11. de Clippel, Geoffroy & Eliaz, Kfir, 2012. "Reason-based choice: a bargaining rationale for the attraction and compromise effects," Theoretical Economics, Econometric Society, vol. 7(1), January.
  12. DUTTA, Bhaskar & JACKSON, Matthew O. & LE BRETON, Michel, 1999. "Strategic candidacy and voting procedures," CORE Discussion Papers 1999011, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  13. Roger B. Myerson, 1982. "Two-Person Bargaining Problems with Incomplete Infonnation," Discussion Papers 527, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  14. Geoffroy de Clippel & Camelia Bejan, 2009. "No Profitable Decomposition in Quasi-Linear Allocation Problems," Working Papers 2009-6, Brown University, Department of Economics.
  15. Peters, Hans & Wakker, Peter, 1991. "Independence of Irrelevant Alternatives and Revealed Group Preferences," Econometrica, Econometric Society, vol. 59(6), pages 1787-1801, November.
  16. Aumann, Robert J & Kurz, Mordecai, 1977. "Power and Taxes," Econometrica, Econometric Society, vol. 45(5), pages 1137-61, July.
  17. 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.
  18. 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.
  19. Roemer, John E., 1988. "Axiomatic bargaining theory on economic environments," Journal of Economic Theory, Elsevier, vol. 45(1), pages 1-31, June.
  20. Campbell, Donald E, 1992. "Implementation of Social Welfare Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(3), pages 525-33, August.
  21. Hanany, Eran, 2007. "Appeals immune bargaining solution with variable alternative sets," Games and Economic Behavior, Elsevier, vol. 59(1), pages 72-84, April.
  22. Chambers, Christopher P., 2005. "Allocation rules for land division," Journal of Economic Theory, Elsevier, vol. 121(2), pages 236-258, April.
  23. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  24. Marc Fleurbaey, 2003. "On the informational basis of social choice," Social Choice and Welfare, Springer, vol. 21(2), pages 347-384, October.
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