A new approach to the core and Weber set of multichoice games |
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Authors: | Michel Grabisch Lijue Xie |
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Institution: | 1.CERMSEM,Maison des Sciences Economiques,Paris,France;2.Université Paris I - Panthéon-Sorbonne,Paris,France |
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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 the set of imputations
may be unbounded, which makes its application questionable. A second definition is proposed, imposing normalization at each
level, causing the core to be a convex compact 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 coincidence in the convex case remain valid. A last section makes a comparison with the
core defined by Van den Nouweland et al.
A preliminary and short version of this paper has been presented at 4th Logic, Game Theory and Social Choice meeting, Caen,
France, June 2005 (Xie and Grabisch 2005). |
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Keywords: | Multichoice game Lattice Core |
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