Semivalues as power indices

Semivalues as power indices

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Article ID: iaor20043247
Country: Netherlands
Volume: 149
Issue: 3
Start Page Number: 676
End Page Number: 687
Publication Date: Sep 2003
Journal: European Journal of Operational Research
Authors: , ,
Abstract:

A restricted notion of semivalue as a power index, i.e. as a value on the lattice of simple games, is axiomatically introduced by using the symmetry, positivity and dummy player standard properties together with the transfer property. The main theorem, that parallels the existing statement for semivalues on general cooperative games, provides a combinatorial definition of each semivalue on simple games in terms of weighting coefficients, and shows the crucial role of the transfer property in this class of games. A similar characterization is also given that refers to unanimity coefficients, which describe the action of the semivalue on unanimity games. We then combine the notion of induced semivalue on lower cardinalities with regularity and obtain a series of characteristic properties of regular semivalues on simple games, that concern null and nonnull players, subgames, quotients, and weighted majority games.

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