Extending the Nash solution to choice problems with reference points
AbstractIn 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 InfoPaper provided by Department of Business and Economics, University of Southern Denmark in its series Discussion Papers of Business and Economics with number 13/2012.
Length: 16 pages
Date of creation: 13 Aug 2012
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Bargaining problem; Nash set; Shapley NTU value;
Other versions of this item:
- Sudhölter, Peter & Zarzuelo, José M., 2013. "Extending the Nash solution to choice problems with reference points," Games and Economic Behavior, Elsevier, vol. 80(C), pages 219-228.
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
- C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-08-23 (All new papers)
- NEP-GTH-2012-08-23 (Game Theory)
- NEP-HPE-2012-08-23 (History & Philosophy of Economics)
- NEP-MIC-2012-08-23 (Microeconomics)
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