Continuity of Choquet Integrals of Supermodular Capacities

Abstract

We prove the continuity of the Choquet integral of supermodular capacities, in L ∞ with respect to the weak*-topology, employing a useful relationship between convex games and their Choquet integrals. The main result is applied to generalized fair division problems, and the existence of Pareto optimal α-allocations is demonstrated for the case of nonadditive measures. MSC 2000: Primary: 28B05, 28E10; secondary: 91A12. © Springer-Verlag Berlin Heidelberg 2010.