Gerard van der Laan 3

By a cooperative game in coalitional structure or shortly coalitional game we mean the standard cooperative non-transferable utility game described by a set of payos for each coalition that is a nonempty subset of the grand coalition of all players. It is well-known that balancedness is a sucient condition for the nonemptiness of the core of such a cooperative non-transferable utility game. For this result any information on the internal organization of the coalition is neglected. In this paper we generalize the concept of coalitional games and allow for organiza-tional structure within coalitions. For a subset of players any arbitrarily given structural relation represented by a graph is allowed for. We then consider non-transferable utility games in which a possibly empty set of payo vectors is assigned to any graph on every subset of players. Such a game will be called a cooperative game in graph structure or shortly graph game. A payo vector lies in the core of the game if there is no graph on a group of players which can make all of its members better o. We dene the balanced-core of a graph game as a renement of the core. To do so