# On an extension of the concept of TU-games and their values

On an extension of the concept of TU-games and their values We propose a new more general approach to TU-games and their efficient values, significantly different from the classical one. It leads to extended TU-games described by a triplet $$(N,v,\Omega )$$ ( N , v , Ω ) , where (N, v) is a classical TU-game on a finite grand coalition N, and $$\Omega \in {\mathbb {R}}$$ Ω ∈ R is a game worth to be shared between the players in N. Some counterparts of the Shapley value, the equal division value, the egalitarian Shapley value and the least square prenucleolus are defined and axiomatized on the set of all extended TU-games. As simple corollaries of the obtained results, we additionally get some new axiomatizations of the Shapley value and the egalitarian Shapley value. Also the problem of independence of axioms is widely discussed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Methods of Operations Research Springer Journals

# On an extension of the concept of TU-games and their values

, Volume 86 (1) – Apr 11, 2017
22 pages

/lp/springer_journal/on-an-extension-of-the-concept-of-tu-games-and-their-values-erXu32XS8I
Publisher
Springer Berlin Heidelberg
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Operations Research/Decision Theory; Business and Management, general
ISSN
1432-2994
eISSN
1432-5217
D.O.I.
10.1007/s00186-017-0587-z
Publisher site
See Article on Publisher Site

### Abstract

We propose a new more general approach to TU-games and their efficient values, significantly different from the classical one. It leads to extended TU-games described by a triplet $$(N,v,\Omega )$$ ( N , v , Ω ) , where (N, v) is a classical TU-game on a finite grand coalition N, and $$\Omega \in {\mathbb {R}}$$ Ω ∈ R is a game worth to be shared between the players in N. Some counterparts of the Shapley value, the equal division value, the egalitarian Shapley value and the least square prenucleolus are defined and axiomatized on the set of all extended TU-games. As simple corollaries of the obtained results, we additionally get some new axiomatizations of the Shapley value and the egalitarian Shapley value. Also the problem of independence of axioms is widely discussed.

### Journal

Mathematical Methods of Operations ResearchSpringer Journals

Published: Apr 11, 2017

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