We consider several related set extensions of the core and the anticore of games with transferable utility. An … polytopes with a core-like structure. One of these polytopes is the <InlineEquation ID="IEq1"> <EquationSource Format … all these sets coincide. These three sets also coincide with the core for balanced games and with the anticore for …

the NSPKs and NSPNs and their relations to the positive prekernel and to the positive core. It turns out that any NSPK is … them being subsolutions of the positive core. We show that any NSPN is a subsolution of the positive core provided that it …

We prove that the core on the set of all transferable utility games with players contained in a universe of at least … also characterize the core on certain subsets of games, e.g., on the set of totally balanced games, on the set of balanced … games, and on the set of superadditive games. Suitable extensions of these properties yield an axiomatization of the core on …