Convex and exact games with non-transferable utility

We generalize exactness to games with non-transferable utility (NTU). A game is exact if for each coalition there is a core allocation on the boundary of its payoff set. Convex games with transferable utility are well-known to be exact. We consider ve generalizations of convexity in the NTU setting. We show that each of ordinal, coalition merge, individual merge and marginal convexity can be uni¯ed under NTU exactness. We provide an example of a cardinally convex game which is not NTU exact. Finally, we relate the classes of Π-balanced, totally Π-balanced, NTU exact, totally NTU exact, ordinally convex, cardinally convex, coalition merge convex, individual merge convex and marginal convex games to one another

On the core, the Weber set and convexity in games with a priori unions

This paper deals with the concepts of core and Weber set with a priori unions à la Owen. As far as we know, the Owen approach to games with a priori unions has never been studied from the coalitional stability point of view. Thus we introduce the coalitional core and coalitional Weber set and characterize the class of convex games with a priori unions by means of the relationships between both solution concepts.Cooperative games A priori unions Coalitional core Coalitional Weber set Convexity