Axiomatizations of symmetrically weighted solutions

John Kleppe (), Hans Reijnierse () and Peter Sudhölter
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John Kleppe: CentER and Department of Econometrics and Operations Research, Postal: Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands

No 3/2013, Discussion Papers on Economics from University of Southern Denmark, Department of Economics

Abstract: If the excesses of the coalitions in a transferable utility game are weighted, then we show that the arising weighted modifications of the well-known (pre)nucleolus and (pre)kernel satisfy the equal treatment property if and only if the weight system is symmetric in the sense that the weight of a subcoalition of a grand coalition may only depend on the grand coalition and the size of the subcoalition. Hence, the symmetrically weighted versions of the (pre)nucleolus and the (pre)kernel are symmetric, i.e., invariant under symmetries of a game. They may, however, violate anonymity, i.e., they may depend on the names of the players. E.g., a symmetrically weighted nucleolus may assign the classical nucleolus to one game and the per capita nucleolus to another game. We generalize Sobolev's axiomatization of the prenucleolus and its modification for the nucleolus as well as Peleg's axiomatization of the prekernel to the symmetrically weighted versions. Only the reduced games have to be replaced by suitably modified reduced games whose definitions may depend on the weight system. Moreover, it is shown that a solution may only satisfy the mentioned sets of modified axioms if the weight system is symmetric.

Keywords: TU game; nucleolus; kernel (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Pages: 18 pages
Date: 2013-02-01
New Economics Papers: this item is included in nep-gth, nep-hpe and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Related works:
Journal Article: Axiomatizations of symmetrically weighted solutions (2016)
Working Paper: Axiomatizations Of Symmetrically Weighted Solutions (2013)
Working Paper: Axiomatizations Of Symmetrically Weighted Solutions (2013)
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