Subcalculus for set functions and cores of TU games. (Q1394991)

Let \((N, v)\) be a measure game in the sense of Aumann and Shapley (1974). This paper establishes a simple but elegant characterization of the core of \((N, v)\), \(\text{core}(v)\), in terms of the superdifferential of \(v\), \(\partial v\): \(\text{core}(v)= \partial v(E)\sqcap\partial v(E^c)\), for any linear set \(E\). Further conditions are given which guarantee the nonemptiness of the core and which guarantee that the core is a singleton.