k -additive upper approximation of TU-games

Michel Grabisch (1, 2) , Agnieszka Rusinowska (1, 2)

1 CES - Centre d'économie de la Sorbonne
2 PSE - Paris School of Economics

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.

Domaines: Economies et finances; Mathématique discrète [cs.DM]

Michel Grabisch, Agnieszka Rusinowska. k -additive upper approximation of TU-games. Operations Research Letters, 2020, 48 (4), pp.487-492. ⟨10.1016/j.orl.2020.06.001⟩. ⟨halshs-02860802⟩