Remarkable polyhedra related to set functions, games and capacities

Michel Grabisch

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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 trans- form; supermodular game; p-additive game; multichoice game; core; jeux à utilité transférable; coopération restreinte; jeux avec contraintes de précédence; coeur; sommet (search for similar items in EconPapers)
Date: 2016-11
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01412292v1
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Citations: View citations in EconPapers (16)

Published in 2016

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Related works:
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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