Remarkable polyhedra related to set functions, games and capacities

Michel Grabisch

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2016, vol. 24, issue 2, No 1, 326 pages

Abstract: 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; 91A; 06A06 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (29)

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Working Paper: Remarkable polyhedra related to set functions, games and capacities (2016)
Working Paper: Remarkable polyhedra related to set functions, games and capacities (2016)
Working Paper: Remarkable polyhedra related to set functions, games and capacities (2016)
Working Paper: Remarkable polyhedra related to set functions, games and capacities (2016)
Working Paper: Remarkable polyhedra related to set functions, games and capacities (2016)
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DOI: 10.1007/s11750-016-0421-4

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