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The Product of Capacities and Belief Functions

Author

Listed:
  • : Ebbe Hendon

    (Institute of Economics, University of Copenhagen)

  • Hans Jørgen Jacobsen

    (Institute of Economics, University of Copenhagen)

  • Birgitte Sloth

    (Institute of Economics, University of Copenhagen)

  • Torben Tranæs

    (Institute of Economics, University of Copenhagen)

Abstract

Capacities (monotone, non-additive set functions) have been suggested to describe situations of uncertainty. We examine the question of how to define the product of two independent capacities. In particular, for the product of two belief functions (totally monotone capacities), there is a unique minimal product belief function. This is characterized in several ways.

Suggested Citation

  • : Ebbe Hendon & Hans Jørgen Jacobsen & Birgitte Sloth & Torben Tranæs, 1993. "The Product of Capacities and Belief Functions," Discussion Papers 93-04, University of Copenhagen. Department of Economics.
  • Handle: RePEc:kud:kuiedp:9304
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    References listed on IDEAS

    as
    1. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, vol. 71(2), pages 443-484, November.
    2. Hendon, Ebbe & Jacobsen, Hans JØrgen & Sloth, Birgitte & TranÆs, Torben, 1994. "Expected Utility with Lower Probabilities," Journal of Risk and Uncertainty, Springer, vol. 8(2), pages 197-216, March.
    3. Dow James & Werlang Sergio Ribeiro Da Costa, 1994. "Nash Equilibrium under Knightian Uncertainty: Breaking Down Backward Induction," Journal of Economic Theory, Elsevier, vol. 64(2), pages 305-324, December.
    4. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    5. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Christian Bauer, 2012. "Products of non-additive measures: a Fubini-like theorem," Theory and Decision, Springer, vol. 73(4), pages 621-647, October.
    2. Ralph W. Bailey & Jürgen Eichberger & David Kelsey, 2005. "Ambiguity and Public Good Provision in Large Societies," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 7(5), pages 741-759, December.
    3. Klaus Nehring, 2006. "Bernoulli Without Bayes: A Theory of Utility-Sophisticated Preferences under Ambiguity," Economics Working Papers 0072, Institute for Advanced Study, School of Social Science.
    4. Sujoy Mukerji & Jean-Marc Tallon, 2001. "Ambiguity Aversion and Incompleteness of Financial Markets," Review of Economic Studies, Oxford University Press, vol. 68(4), pages 883-904.
    5. repec:bos:wpaper:wp2013-001 is not listed on IDEAS
    6. Ebbe Groes & Hans Jørgen Jacobsen & Birgitte Sloth & Torben Tranaes, 1998. "Nash Equilibrium with Lower Probabilities," Theory and Decision, Springer, vol. 44(1), pages 37-66, January.
    7. repec:dau:papers:123456789/7324 is not listed on IDEAS
    8. Kin Chung Lo, 1998. "Epistemic Conditions for Agreement and Stochastic Independence of epsilon-Contaminated Beliefs," Working Papers 1998_02, York University, Department of Economics.
    9. Eichberger, Jürgen & Oechssler, Jörg & Schnedler, Wendelin, 2012. "How do people cope with an ambiguous situation when it becomes even more ambiguous?," Working Papers 0528, University of Heidelberg, Department of Economics.
    10. Epstein, Larry G. & Schneider, Martin, 2003. "IID: independently and indistinguishably distributed," Journal of Economic Theory, Elsevier, vol. 113(1), pages 32-50, November.
    11. Lo, Kin Chung, 2006. "Agreement and stochastic independence of belief functions," Mathematical Social Sciences, Elsevier, vol. 51(1), pages 1-22, January.
    12. Lo, Kin Chung, 2000. "Epistemic conditions for agreement and stochastic independence of [epsi]-contaminated beliefs," Mathematical Social Sciences, Elsevier, vol. 39(2), pages 207-234, March.
    13. Epstein, Larry G. & Seo, Kyoungwon, 2015. "Exchangeable capacities, parameters and incomplete theories," Journal of Economic Theory, Elsevier, vol. 157(C), pages 879-917.
    14. 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).
    15. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
    16. repec:hal:journl:halshs-00130444 is not listed on IDEAS
    17. Denneberg, Dieter, 2002. "Conditional expectation for monotone measures, the discrete case," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 105-121, April.

    More about this item

    Keywords

    uncertainty; capacities; non-additive measures; lower probabilities; belief functions;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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