Cores of cooperative games, superdifferentials of functions, and the Minkowski difference of sets

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:247

Article

Danilov, VI ; Koshevoy, GA

关键词: totally monotone game;    support function;    inverse Mobius transform;    Minkowski sum;   

DOI  :  10.1006/jmaa.2000.6756

来源: Elsevier

【 摘 要 】

Let upsilon he a cooperative (TU) game and upsilon = upsilon(1) - upsilon(2) be a decomposition of Let upsilon he a cooperative (TU) game and upsilon = upsilon(1) - upsilon(2) be a decomposition of upsilon as a difference of two convex games upsilon(1) and upsilon(2). Then the core C(upsilon) of the game upsilon has a similar decomposition C(upsilon) = C(upsilon(1)) - C(upsilon(2)), 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. (C) 2000 Academic Press.

【 授权许可】

Free