International Journal of Game Theory (1991) 20:53-63 On Non-Transferable Utility Games with Coalition Structnre ByE. Winter 2 Abstract: We introduce a solution function for Non-transferable Utility (NTU) games when prior coalition structure isgiven. This solution function generalizes both the Harsanyi solution function for NTU games and the Owen solution for TU games with coalition structure. 1 Introduction Many political and economic confrontations are characterized by having some prior description of the cooperative structure of the players. These structures, which are influenced either by utility considerations of the players or by ideological aspects in political situations, may reflect binding agreements between the players, pressure groups, or even descriptions of channels of negotiation between the players. In each of these cases the structures are assumed to affect the bargaining position of the players, and hence the final allocation of the utility between them. Many papers, such as Aumann and Dreze [1], Hart and Kurz [4], [5], Myerson [11], Owen [12], Winter [14] in the theory of cooperative games have responded to such situations, typically by generalizing solutions (such as the Shapley value) to situations as such. However, most of these works use the prior assumption that utili- ty in such situations is transferable. In this paper we shall treat those situations described above when utility is not necessarily transferable. Games without side payments are widely recognized as a satisfactory formula- tion of trading in markets. When one considers international trading, the aspect of integration and cooperation becomes extremely relevant. Governments can in- tervene in international transactions by issuing regulations and by forming agreements with other countries' governments. One can find many such examples in economic history, especially in the European economy. In 1948 Belgium, the Netherlands and Luxemburg formed a customs union which was later merged (in 1958) to the European Economic Community. In 1960, Britain, Norway, Sweden, Denmark, Austria, Switzerland and Portugal formed the European Free Trade Area I would like to thank Sergiu Hart, Bezalel Peleg and Shmuel Zamir for some conversations and constructive remarks on an earlier version of this paper. Part of this research was sup- ported by the Sonderforschungsbereich 303 in the university of Bonn. Dr. Eyal Winter, Department of Economics, Faculty of Arts and Sciences, University of Pitt- sburgh, Pittsburgh, PA 152 60, USA. 0020-7276/91/1/53-63 $2.50 9 1991 Physica-Verlag, Heidelberg