Remarkable polyhedra related to set functions, games and capacities

Michel Grabisch

PSE-Ecole d'économie de Paris (Postprint) from HAL

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, decicion making and com-binatorial optimization. This survey paper gives an overview of these notions and studies all these polyhedra.

Keywords: pseudo-Boolean function; Möbius trans-form; nonadditive measure; capacity; core; multichoice game; supermodular game; p-additive game; TU-game (search for similar items in EconPapers)
Date: 2016-07
Note: View the original document on HAL open archive server: https://hal.science/hal-01372858v1
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Citations: View citations in EconPapers (4)

Published in TOP, 2016, 24 (2), pp.301-326. ⟨10.1007/s11750-016-0421-4⟩

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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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Persistent link: https://EconPapers.repec.org/RePEc:hal:pseptp:hal-01372858

DOI: 10.1007/s11750-016-0421-4

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