The Core of Convex Multi-choice Cooperative Games with a Priori Unions

The paper deals with the concepts of core and Weber set with a priori unions of multi-choice games. As far as we know, the approach to multi-choice games with a priori unions has never been studied from the coalitional point of view. Thus we define the coalitional core and coalitional Weber set and characterize the class of convex multi-choice games with a priori unions by means of the relationships between both solution concepts.