Supermodular NTU-games

An NTU-game consists of payoff sets for every coalition of players. We introduce the concept of supermodularity of a game to guarantee that all its marginal vectors are in the core. As solution we propose a set of payoff vectors that is determined by the average of all marginal vectors, the Shapley set. Conditions are given under which the Shapley set is in the core of the game or is a set of bargaining solutions of a well-defined bargaining problem.