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The product of capacities and belief functions

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  • Hendon, Ebbe
  • Jacobsen, Hans Jorgen
  • Sloth, Birgitte
  • Tranaes, Torben

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.

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Bibliographic Info

Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 32 (1996)
Issue (Month): 2 (October)
Pages: 95-108

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Handle: RePEc:eee:matsoc:v:32:y:1996:i:2:p:95-108

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Web page: http://www.elsevier.com/locate/inca/505565

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References

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  1. Kin Chung Lo, 1995. "Equilibrium in Beliefs Under Uncertainty," Working Papers ecpap-95-02, University of Toronto, Department of Economics.
  2. 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.
  3. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  4. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  5. Hendon, Ebbe, et al, 1994. "Expected Utility with Lower Probabilities," Journal of Risk and Uncertainty, Springer, vol. 8(2), pages 197-216, March.
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Citations

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Cited by:
  1. Lefort, Jean-Philippe & Chateauneuf, Alain, 2008. "Some Fubini Theorems on product σ-algebras for non-additive measures," Economics Papers from University Paris Dauphine 123456789/7324, Paris Dauphine University.
  2. 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.
  3. repec:hal:journl:halshs-00130444 is not listed on IDEAS
  4. repec:bos:wpaper:wp2013-001 is not listed on IDEAS
  5. Denneberg, Dieter, 2002. "Conditional expectation for monotone measures, the discrete case," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 105-121, April.
  6. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
  7. Larry Epstein & Martin Schneider, 2002. "IID: Independently and Indistinguishably Distributed," RCER Working Papers 496, University of Rochester - Center for Economic Research (RCER).
  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. repec:hal:cesptp:halshs-00174539 is not listed on IDEAS
  11. Lo, Kin Chung, 2006. "Agreement and stochastic independence of belief functions," Mathematical Social Sciences, Elsevier, vol. 51(1), pages 1-22, January.
  12. Christian Bauer, 2012. "Products of non-additive measures: a Fubini-like theorem," Theory and Decision, Springer, vol. 73(4), pages 621-647, October.
  13. 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).
  14. 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.

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