Remarkable polyhedra related to set functions, games

Michel Grabisch

Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne

Abstract: Set functions are widely used in many domains of Operations Research (cooperative game theory, decision under risk and uncertainty, combinatorial optimization) under different names (TU-game, capacity, nonadditive measure, pseudo-Boolean function, etc…). Remarkable families of set functions form polyhedra, e.g., the polytope of capacities, the polytope of p-additive capacities, the cone of supermodular games, etc…. Also, the core of a set function, defined as the set of additive set functions dominating that set function, is a polyhedron which is of fundamental importance in game theory, decision making and combinatorial optimization. This survey paper gives an overview of these notions and studies all these polyhedra

Keywords: TU-game; capacity; nonadditive measure; pseudo-Boolean function; Möbius transform; supermodular game; p-additive game; multichoice game; core (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Pages: 25 pages
Date: 2016-11
New Economics Papers: this item is included in nep-gth
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:mse:cesdoc:16081

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