Canonical Representation of Set Functions

Itzhak Gilboa and David Schmeidler

No 986, Discussion Papers from Northwestern University, Center for Mathematical Studies in Economics and Management Science

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.

Date: 1992-04
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Working Paper: Canonical Representation of Set Functions (1995)
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