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Canonical Representation of Set Functions

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  • Itzhak Gilboa
  • David Schmeidler

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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Bibliographic Info

Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 986.

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Date of creation: Apr 1992
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Handle: RePEc:nwu:cmsems:986

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Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
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Web page: http://www.kellogg.northwestern.edu/research/math/
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  1. 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.
  2. Itzhak Gilboa & David Schmeidler, 1991. "Updating Ambiguous Beliefs," Discussion Papers 924, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Gilboa, Itzhak & Lehrer, Ehud, 1991. "Global Games," International Journal of Game Theory, Springer, vol. 20(2), pages 129-47.
    • Itzhak Gilboa & Ehud Lehrer, 1990. "Global Games," Discussion Papers 922, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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Cited by:
  1. Massimo Marinacci, 1995. "Decomposition and Representation of Coalitional Games," Discussion Papers 1152, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. De Waegenaere, A.M.B. & Wakker, P.P., 1997. "Choquet Integrals With Respect to Non-Monotonic Set Functions," Discussion Paper 1997-44, Tilburg University, Center for Economic Research.
  3. Alain Chateauneuf & Jean-Philippe Lefort, 2006. "Some Fubini theorems on sigma-algebras for non additive measures," Cahiers de la Maison des Sciences Economiques b06086, Université Panthéon-Sorbonne (Paris 1).
  4. Simon Grant & Atsushi Kajii, 2005. "Probabilistically Sophisticated Multiple Priors," KIER Working Papers 608, Kyoto University, Institute of Economic Research.
  5. Zaier Aouani, 2004. "Exact capacities and star shaped distorted probabilities," Cahiers de la Maison des Sciences Economiques b04117, Université Panthéon-Sorbonne (Paris 1).

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