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k -additive upper approximation of TU-games

Michel Grabisch and Agnieszka Rusinowska ()
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Agnieszka Rusinowska: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: We study the problem of an upper approximation of a TU-game by a-additive game under the constraint that both games yield the same Shapley value. The best approximation is obtained by minimizing the sum of excesses with respect to the original game, which yields an LP problem. We show that for any game with at most 4 players all vertices of the polyhedron of feasible solutions are optimal, and we give an explicit formula of the value of the LP problem for a particular class of games.

Date: 2020-07
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Published in Operations Research Letters, Elsevier, 2020, 48 (4), pp.487-492. ⟨10.1016/j.orl.2020.06.001⟩

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DOI: 10.1016/j.orl.2020.06.001

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