Canonical Representation of Set Functions

Itzhak Gilboa and David Schmeidler

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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.

Keywords: cooperative game; unanimity game; nonadditive measure; Choquet integral (search for similar items in EconPapers)
Date: 1995-02
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Citations: View citations in EconPapers (24)

Published in Mathematical Methods of Operations Research, 1995, Vol.20, n°1, pp.197-212. ⟨10.1287/moor.20.1.197⟩

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Working Paper: Canonical Representation of Set Functions (1992)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00481346

DOI: 10.1287/moor.20.1.197

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