The position value for union stable systems

In this paper, we study the position value for games in which partial coope ration exist, that is based on a union stable coalition system. The concept of basis is introduced for these systems, allowing for a definition of the position value. Moreover, an axiomatic characterization of the position va lue is provided for a specific class of union stable systems. Conditions un der which convexity is inherited from the underlying game to the conference game, and the position value is a core vector of the restricted game are p rovided. 1991 Mathematics Subject Classification: 90D12.