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

Tadeusz Radzik ()
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Tadeusz Radzik: Wrocław University of Science and Technology

Mathematical Methods of Operations Research, 2017, vol. 86, issue 1, No 6, 149-170

Abstract: 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.

Keywords: Extended TU-game; Extended value; Axiomatization; The Shapley value; The equal division value; The egalitarian Shapley value; The least square prenucleolus (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s00186-017-0587-z

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