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Canonical Representation of Set Functions

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.
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Submitted on : Thursday, May 6, 2010 - 2:29:03 PM
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Itzhak Gilboa, David Schmeidler. Canonical Representation of Set Functions. Mathematical Methods of Operations Research, Springer Verlag, 1995, Vol.20, n°1, pp.197-212. ⟨10.1287/moor.20.1.197⟩. ⟨hal-00481346⟩



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