Semi-marginalistic Values for Set Games

Concerning the solution theory for set games, the paper focuses on a family of values, each of which allocates to any player some type of marginalistic contribution with respect to any coalition containing the player. For any value of the relevant family, an axiomatization is given by means of three properties, namely one type of an efficiency property, the equal treatment property and one type of a monotonicity property. We present one proof technique which is based on the decomposition of any arbitrary set game into a union of simple set games, the value of which are much easier to determine. A simple set game is associated with an arbitrary, but fixed item of the universe.