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Multilateral Value for TU Cooperative Games

A value of a TU Cooperative game represents an assessment by a player of her gains for participating in a coalition. One of the most important values in the literature of TU games is the Shapley value [18]. It is indeed an aggregation of the marginal contributions of a player based on her bilateral interactions. In this paper we introduce a new value for TU Cooperative games. The notion of multilateral interaction of a player is proposed that accounts not only for the player’s own inclusion or exclusion in a coalition as considered in computing the Shapley value but also for her influence on her peers in their decision of joining or leaving the coalition together. We characterize this value by the axioms of linearity, anonymity, efficiency and a new axiom: the axiom of parasite player. A parasite player extracts worths of other players. Our model makes her role less significant in presence of multilateral interactions.