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Products of convex measures: A Fubini theorem

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Christian Bauer ()

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Abstract

The concept of qualitative di¤erences in information, i.e. the distinction between risk and ambiguity, builds the framework of a growing strand of economic research. For non additive set functions as used in the Choquet Expected Utility framework, the independent product in general is not unique and the Fubini theorem is restricted to slice-comonotonic functions. In this paper, we use the representation theorem of [Gilboa and Schmeidler(1995)] to extend the Möbius product for non additive set functions to non finite spaces. The uniqueness result of [Ghirardato(1997)] for belief functions is also extended to non finite spaces. For this unique product, one side of the Fubini theorem holds for all integrable functions if one of the marginals either is a probability or a convex combination of a chain of unanimity games.

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Article provided by Department of Economics, Economics I, Bayreuth University in its journal Macroeconomics.

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Handle: RePEc:uba:hadfwe:prod-cap_2003-04

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Related research
Keywords: Knightian uncertainty; multivariate capacity; product measure; totally monotone measure; Choqet integral;

Find related papers by JEL classification:
D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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References listed on IDEAS
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  1. Mukerji, S. & Song Shin, H., 1997. "Equilibrium Departures From Common Knowledge in Games With Non-Additive Expected Utility," Economics Papers 137, Economics Group, Nuffield College, University of Oxford.
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  3. Antoine Billot & Alain Chateauneuf & Itzhak Gilboa & Jean-Marc Tallon, 2000. "Sharing Beliefs: Between Agreeing and Disagreeing," Econometrica, Econometric Society, vol. 68(3), pages 685-694, May.
    Other versions:
  4. Larry G. Epstein & JianJun Miao, 2001. "A Two-Person Dynamic Equilibrium under Ambiguity," RCER Working Papers 478, University of Rochester - Center for Economic Research (RCER). [Downloadable!]
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  5. Olivier Jeanne & Andrew K. Rose, 2002. "Noise Trading And Exchange Rate Regimes," The Quarterly Journal of Economics, MIT Press, vol. 117(2), pages 537-569, May. [Downloadable!] (restricted)
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  6. Heinemann, Frank & Illing, Gerhard, 2002. "Speculative attacks: unique equilibrium and transparency," Journal of International Economics, Elsevier, vol. 58(2), pages 429-450, December. [Downloadable!] (restricted)
  7. Itzhak Gilboa & David Schmeidler, 1992. "Canonical Representation of Set Functions," Discussion Papers 986, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  9. Larry G. Epstein, 2001. "Sharing Ambiguity," American Economic Review, American Economic Association, vol. 91(2), pages 45-50, May. [Downloadable!] (restricted)
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  12. Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
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  13. Ghirardato, Paolo, 1995. "On Independence For Non-Additive Measures, With a Fubini Theorem," Working Papers 940, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
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  14. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June. [Downloadable!] (restricted)
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Cited by:
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  1. Roman Kozhan & Michael Zarichnyi, 2008. "Nash equilibria for games in capacities," Economic Theory, Springer, vol. 35(2), pages 321-331, May. [Downloadable!] (restricted)
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