Marginal contributions in games with externalities

Abstract

In this work we explore games with externalities, where our basic approach is rooted in the concept of marginal contributions of players to coalitions. We considered the general case where a player (in a coalition S) may join another coalition after leaving S. We then show that the standard translation of Shapley's four axioms to games with externalities is not sufficient to obtain a unique value. Finally, we provide an axiomatic characterization for the family of solutions for games with externalities satisfying those axioms that traditionally are used to characterize the Shapley value in the absence of externalities. In particular, we show that every such solution is a linear combination of marginal contributions of players and provide an interpretation as a bargaining process.