In this paper, we study the position value for games in which partial cooperation 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 value is provided for a specific class of union stable systems.
Conditions under 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 provided.