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Extending the Nash solution to choice problems with reference points

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  • Sudhölter, Peter

    ()
    (Department of Business and Economics)

  • Zarzuelo, José M.

    ()
    (Faculty of Economics and Business Administration)

Abstract

In 1985 Aumann axiomatized the Shapley NTU value by non-emptiness, efficiency, unanimity, scale covariance, conditional additivity, and independence of irrelevant alternatives. We show that, when replacing unanimity by "unanimity for the grand coalition" and translation covariance, these axioms characterize the Nash solution on the class of n-person choice problems with reference points. A classical bargaining problem consists of a convex feasible set that contains the disagreement point here called reference point. The feasible set of a choice problem does not necessarily contain the reference point and may not be convex. However, we assume that it satisfies some standard properties. Our result is robust so that the characterization is still valid for many subclasses of choice problems, among those is the class of classical bargaining problems. Moreover, we show that each of the employed axioms – including independence of irrelevant alternatives – may be logically independent of the remaining axioms.

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Bibliographic Info

Paper provided by Department of Business and Economics, University of Southern Denmark in its series Discussion Papers of Business and Economics with number 13/2012.

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Length: 16 pages
Date of creation: 13 Aug 2012
Date of revision:
Handle: RePEc:hhs:sdueko:2012_013

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Postal: Department of Business and Economics, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
Phone: 65 50 32 33
Fax: 65 50 32 37
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Web page: http://www.sdu.dk/ivoe
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Keywords: Bargaining problem; Nash set; Shapley NTU value;

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  1. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  2. Herrero, Maria Jose, 1989. "The nash program: Non-convex bargaining problems," Journal of Economic Theory, Elsevier, vol. 49(2), pages 266-277, December.
  3. Marco Mariotti & Antonio Villar, 2005. "The Nash rationing problem," International Journal of Game Theory, Springer, vol. 33(3), pages 367-377, 09.
  4. Peters, Hans & Vermeulen, Dries, 2006. "WPO, COV and IIA bargaining solutions," Research Memorandum 021, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  5. Conley, John P. & Wilkie, Simon, 1996. "An Extension of the Nash Bargaining Solution to Nonconvex Problems," Games and Economic Behavior, Elsevier, vol. 13(1), pages 26-38, March.
  6. A. Rubinstein & L. Zhou, 1998. "Choice Problems with a "Reference" Point," Princeton Economic Theory Papers 00s3, Economics Department, Princeton University.
  7. Bezalel Peleg & Peter Sudhölter & José Zarzuelo, 2012. "On the impact of independence of irrelevant alternatives: the case of two-person NTU games," SERIEs, Spanish Economic Association, vol. 3(1), pages 143-156, March.
  8. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer, vol. 18(4), pages 389-407.
  9. Mariotti, Marco, 1998. "Extending Nash's Axioms to Nonconvex Problems," Games and Economic Behavior, Elsevier, vol. 22(2), pages 377-383, February.
  10. Hans Peters & Dries Vermeulen, 2012. "WPO, COV and IIA bargaining solutions for non-convex bargaining problems," International Journal of Game Theory, Springer, vol. 41(4), pages 851-884, November.
  11. Aumann, Robert J, 1985. "An Axiomatization of the Non-transferable Utility Value," Econometrica, Econometric Society, vol. 53(3), pages 599-612, May.
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