The Shapley Value for Games with Restricted Cooperation

Abstract

The traditional assumption in cooperative game theory is that every coalition is feasible and can form to attain its payoff. However, in many real life situations not every group of players has the opportunity to cooperate and to collect their own payoff. We say that we deal with cooperative games with restricted cooperation when not all coalitions can form. In this paper we will deal with generalizations of the Shapley value for games with restricted cooperation. Three solutions for games with restricted cooperation will be considered. One of them (the Myerson value) is well known. Two others are based on the same principle: to construct some restricted game and to use the Shapley value for this game. We consider the class of all solutions which can be constructed in an analogous way. We will show that this class coincides with the class of all solutions with balanced contribution property. Also each solution from this class can be described by either a potential function or a consistency property.