Cooperative Games on Accessible Union Stable Systems

Agents participating in different kind of organizations, usually take different positions in some relational structure. The aim of this paper is to introduce a new framework taking into account both communication and hierachical features derived from this participation. In fact, this new set or network structure unifies and generalizes well-known models from the literature, such as communication networks and hierarchies. We introduce and analyze accessible union stable systems where union stability reflects the communication network and accessibility describes the hierarchy. Particular cases of these new structures are the sets of connected coalitions in a communication graph, antimatroids (and therefore also sets of feasible coalitions in permission structures) and augmenting systems which have numerous applications in the literature. We give special attention to th e class of cycle-free accessible union stable systems. We also consider cooperative games with restricted cooperation where the set of feasible coalitions is an accessible union stable system, and provide an axiomatization of an extension of the Shapley value to this class of games.