Canonical Representation of Set Functions
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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- Itzhak Gilboa & David Schmeidler, 1992. "Additive Representation of Non-Additive Measures and the Choquet Integral," Discussion Papers 985, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Gilboa, Itzhak & Lehrer, Ehud, 1991.
International Journal of Game Theory,
Springer, vol. 20(2), pages 129-47.
- Itzhak Gilboa & David Schmeidler, 1991.
"Updating Ambiguous Beliefs,"
924, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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