The Probabilistic Representative Values

Abstract

In this paper we define a new family of solutions for the class of cooperative games with transferable utility, in which the set of players exhibits a structure of a priori unions. This family is deeply connected with the Shapley value for games with transferable utility but, moreover, we assume a solidarity strong connection among all the components of each union. As a consequence of this, they are disposed to delegate one coalition of members of the union to negotiate with the other unions, and, therefore, each union will have a representative coalition. Furthermore, three interesting solutions that belong to this family of values are studied, as well as the non cooperative selection of the best representative coalition for each union.

Keywords: TU-games with unions, Shapley value, representative coalition

JEL Classification: C71, C72