A shapley value for games with authorization structure

Abstract

A cooperative TU-game consists of a set of players and a characteristic function which determines the maximal gain or minimal cost that every subset of players can achieve when they decide to cooperate, regardless of the actions that the other players take. It is often assumed that the players are free to participate in any coalition, but in some situations there are dependency relationships among the players that restrict their capacity to cooperate within some coalitions. Those relationships must be taken into account if we want to distribute the profits fairly. To do this, several models have been introduced in literature. In this chapter we describe one of those models for games with restricted cooperation. This model is more general than others in several ways. For instance, it allows us to deal with non-hierarchical or non-transitive dependency relationships. In addition, it can be adapted to consider fuzzy dependency relationships, which arise in situations in which each player has a degree of freedom to cooperate within a coalition.