Generalized additive games

A transferable utility (TU) game with n players specifies a vector of $$2^n-1$$ 2 n - 1 real numbers, i.e. a number for each non-empty coalition, and this can be difficult to handle for large n. Therefore, several models from the literature focus on interaction situations which are characterized by a compact representation of a TU-game, and such that the worth of each coalition can be easily computed. Sometimes, the worth of each coalition is computed from the values of single players by means of a mechanism describing how the individual abilities interact within groups of players. In this paper we introduce the class of Generalized additive games (GAGs), where the worth of a coalition $$S { \subseteq } N$$ S ⊆ N is evaluated by means of an interaction filter, that is a map $$\mathcal {M}$$ M which returns the valuable players involved in the cooperation among players in S. Moreover, we investigate the subclass of basic GAGs, where the filter $$\mathcal {M}$$ M selects, for each coalition S, those players that have friends but not enemies in S. We show that well-known classes of TU-games can be represented in terms of such basic GAGs, and we investigate the problem of computing the core and the semivalues for specific families of GAGs.