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Journal Articles Mathematical Methods of Operations Research Year : 1995

Canonical Representation of Set Functions

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Abstract

The representation of a cooperative transferable utility game as a linear combination of unanimity games may be viewed as an isomorphism between not-necessarily additive set functions on the players space and additive ones on the coalitions space. We extend the unanimity-basis representation to general (infinite) spaces of players, study spaces of games of games which satisfy certain properties and provide some conditions for sigma-additivity of the resulting additive set function (on the space of coalitions). These results also allow us to extend some representations of the Choquet integral from finite to infinite spaces.

Dates and versions

hal-00481346 , version 1 (06-05-2010)

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Itzhak Gilboa, David Schmeidler. Canonical Representation of Set Functions. Mathematical Methods of Operations Research, 1995, Vol.20, n°1, pp.197-212. ⟨10.1287/moor.20.1.197⟩. ⟨hal-00481346⟩

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