Harsanyi Power Solutions for Games on Union Stable Systems

This paper analyzes Harsanyi power solutions for cooperative games in which partial cooperation is based on union stable systems. These structures contain as particular cases the widely studied communication graph games and permission structures, among others. In this context, we provide axiomatic characterizations of the Harsanyi power solutions which distribute the Harsanyi dividends proportional to weights determined by a power measure for union stable systems. Moreover, the well-known Myerson value is exactly the Harsanyi power solution for the equal power measure, and on a special subclass of union stable systems the position value coincides with the Harsanyi power solution obtained for the influence power measure.