Games on lattices, multichoice games and the Shapley value: a new approach

Michel Grabisch and Fabien Lange ()
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Fabien Lange: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

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Abstract: Multichoice games have been introduced by Hsiao and Raghavan as a generalization of classical cooperative games. An important notion in cooperative game theory is the core of the game, as it contains the rational imputations for players. We propose two definitions for the core of a multichoice game, the first one is called the precore and is a direct generalization of the classical definition. We show that the precore coincides with the definition proposed by Faigle, and that it contains unbounded imputations, which makes its application questionable. A second definition is proposed, imposing normalization at each level, causing the core to be a convex closed set. We study its properties, introducing balancedness and marginal worth vectors, and defining the Weber set and the pre-Weber set. We show that the classical properties of inclusion of the (pre)core into the (pre)-Weber set as well as their equality remain valid. A last section makes a comparison with the core defined by van den Nouweland et al.

Keywords: multichoice game; lattice; core (search for similar items in EconPapers)
Date: 2007-02
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00178916v1
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Citations: View citations in EconPapers (45)

Published in Mathematical Methods of Operations Research, 2007, 65 (1), pp.153-167. ⟨10.1007/s00186-006-0109-x⟩

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Related works:
Journal Article: Games on lattices, multichoice games and the shapley value: a new approach (2007)
Working Paper: Games on lattices, multichoice games and the Shapley value: a new approach (2007)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-00178916

DOI: 10.1007/s00186-006-0109-x

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