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Cores of Cooperative Games, Superdifferentials of Functions, and the Minkowski Difference of Sets

By Vladimir I. Danilov and Gleb A. Koshevoy


AbstractLet v be a cooperative (TU) game and v=v1−v2 be a decomposition of v as a difference of two convex games v1 and v2. Then the core C(v) of the game v has a similar decomposition C(v)=C(v1)⊖C(v2), where ⊖ denotes the Minkowski difference. We prove such a decomposition as a consequence of two claims: the core of a game is equal to the superdifferential of its continuation, known as the Choquet integral, and the superdifferential of a difference of two concave functions equals the Minkowski difference of corresponding superdifferentials

Publisher: Academic Press.
Year: 2000
DOI identifier: 10.1006/jmaa.2000.6756
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