Games on concept lattices: Shapley value and core

Ulrich Faigle (), Michel Grabisch, Andres Jiménez-Losada and Manuel Ordóñez
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Andres Jiménez-Losada: ETSI - Escuela Técnica Superior de Ingenieros de Sevilla
Manuel Ordóñez: ETSI - Escuela Técnica Superior de Ingenieros de Sevilla

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

Abstract: We introduce cooperative TU-games on concept lattices, where a concept is a pair (S, S ′) with S being a subset of players or objects, and S ′ a subset of attributes. Any such game induces a game on the set of players/objects, which appears to be a TU-game whose collection of feasible coalitions is a lattice closed under intersection, and a game on the set of attributes. We propose a Shapley value for each type of game, axiomatize it, and investigate the geometrical properties of the core (non-emptiness, boundedness, pointedness, extremal rays). In particular, we derive the equivalence of the intent and extent core for the class of distributive concepts.

Keywords: cooperative game; restricted cooperation; concept lattice; core; Shapley value (search for similar items in EconPapers)
Date: 2016
Note: View the original document on HAL open archive server: https://hal.science/hal-01379699v1
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Citations: View citations in EconPapers (3)

Published in Discrete Applied Mathematics, 2016, 198, pp.29 - 47. ⟨10.1016/j.dam.2015.08.004⟩

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Related works:
Working Paper: Games on concept lattices: Shapley value and core (2016)
Working Paper: Games on concept lattices: Shapley value and core (2016)
Working Paper: Games on concept lattices: Shapley value and core (2014)
Working Paper: Games on concept lattices: Shapley value and core (2014)
Working Paper: Games on concept lattices: Shapley value and core (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:pseptp:hal-01379699

DOI: 10.1016/j.dam.2015.08.004

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