Generalized additive games
Résumé
A transferable utility (TU) game with n players specifies a vector of 2n−12n−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⊆NS⊆N is evaluated by means of an interaction filter, that is a map MM which returns the valuable players involved in the cooperation among players in S. Moreover, we investigate the subclass of basic GAGs, where the filter MM 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.