Extending the Nash solution to choice problems with reference points

Peter Sudhölter and José Zarzuelo ()

No 13/2012, Discussion Papers on Economics from University of Southern Denmark, Department of Economics

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.

Keywords: Bargaining problem; Nash set; Shapley NTU value (search for similar items in EconPapers)
JEL-codes: C71 C78 (search for similar items in EconPapers)
Pages: 16 pages
Date: 2012-08-13
New Economics Papers: this item is included in nep-gth, nep-hpe and nep-mic
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Journal Article: Extending the Nash solution to choice problems with reference points (2013)
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