Cooperative games with nontransferable utility on antimatroids

This paper introduces a new family of nontransferable utility (NTU) games with partial cooperation. Games with transferable utility (TU) restricted by antimatroids were studied since 2004. Antimatroids are known combinatorial structures which are interpreted in games as dependency situations among a group of agents, and they generalize several other hierarchical structures studied in the literature. Now we define projected NTU games over antimatroids following the same idea. We have needed to build a new theory about projections between two coalitions. In this case, an outcome is feasible for a coalition if and only if its projection is feasible in the NTU game. This paper studies several properties of the projected games and the relations between these games and the original game for some interesting cases: TU games, hyperplane games and bargaining problems.