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Conditioning Capacities and Choquet Integrals: The Role of Comonotony

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Author Info

  • Alain Chateauneuf
  • Robert Kast
  • André Lapied

Abstract

Choquet integrals and capacities play a crucial role in modern decision theory. Comonotony is a central concept for these theories because the main property of a Choquet integral is its additivity for comonotone functions. We consider a Choquet integral representation of preferences showing uncertainty aversion (pessimism) and propose axioms on time consistency which yield a candidate for conditional Choquet integrals. An other axiom characterizes the role of comonotony in the use of information. We obtain two conditioning rules for capacities which amount to the well-known Bayes' and Dempster–Schafer's updating rules. We are allowed to interpret both of them as a lack of confidence in information in a dynamic extension of pessimism. Copyright Kluwer Academic Publishers 2001

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Bibliographic Info

Article provided by Springer in its journal Theory and Decision.

Volume (Year): 51 (2001)
Issue (Month): 2 (December)
Pages: 367-386

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Handle: RePEc:kap:theord:v:51:y:2001:i:2:p:367-386

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Web page: http://www.springerlink.com/link.asp?id=100341

Related research

Keywords: Choquet integral; Comonotony; Time consitency; Conditionnal capacities;

References

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  1. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  2. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
  3. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  4. Cohen, M. & Gilboa, I. & Jaffray, J.Y. & Schmeidler, D., 2000. "An experimental study of updating ambiguous beliefs," Risk, Decision and Policy, Cambridge University Press, vol. 5(02), pages 123-133, June.
  5. Kast, R. & Lapied, A., 1997. "A Decision Theoretic Approach to Bid-Ask Spreads," G.R.E.Q.A.M. 97a17, Universite Aix-Marseille III.
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Citations

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Cited by:
  1. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2011. "A representation of preferences by the Choquet integral with respect to a 2-additive capacity," Theory and Decision, Springer, vol. 71(3), pages 297-324, September.
  2. André Lapied & Pascal Toquebeuf, 2011. "Dynamically consistent CEU preferences," Working Papers halshs-00856193, HAL.
  3. Robert Kast & André Lapied & Pascal Toquebeuf, 2008. "Updating Choquet Integrals , Consequentialism and Dynamic Consistency," ICER Working Papers - Applied Mathematics Series 04-2008, ICER - International Centre for Economic Research.
  4. repec:ebl:ecbull:v:4:y:2005:i:10:p:1-6 is not listed on IDEAS
  5. André Lapied & Pascal Toquebeuf, 2011. "A note on "Re-examining the law of iterated expectations for Choquet decision makers"," Working Papers halshs-00856184, HAL.
  6. André Lapied & Robert Kast, 2009. "Updating Choquet valuation and discounting information arrivals," Working Papers halshs-00410532, HAL.
  7. Robert Kast & André Lapied, 2007. "Dynamically Consistent Conditional Choquet Capacities," ICER Working Papers - Applied Mathematics Series 20-2007, ICER - International Centre for Economic Research.
  8. André Lapied & Thomas Rongiconi, 2013. "Ambiguity as a Source of Temptation: Modeling Unstable Beliefs," Working Papers halshs-00797631, HAL.
  9. Takashi Ui & Atsushi Kajii, 2005. "Equivalence of the Dempster-Shafer rule and the maximum likelihood rule implies convexity," Economics Bulletin, AccessEcon, vol. 4(10), pages 1-6.
  10. repec:hal:cesptp:halshs-00625708 is not listed on IDEAS
  11. André Lapied & Pascal Tocquebeuf, 2007. "Consistent Dynamice Choice And Non-Expected Utility Preferences," Working Papers halshs-00353880, HAL.
  12. Robert Kast & André Lapied, 2008. "Valuing future cash flows with non separable discount factors and non additive subjective measures: Conditional Choquet Capacities on Time and on Uncertainty," Working Papers 08-09, LAMETA, Universtiy of Montpellier, revised Jun 2008.
  13. Lapied, André & Toquebeuf, Pascal, 2012. "Dynamically consistent CEU preferences on f-convex events," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 252-256.
  14. Robert Kast & André Lapied & Pascal Toquebeuf, 2012. "Updating Choquet capacities: a general framework," Economics Bulletin, AccessEcon, vol. 32(2), pages 1495-1503.
  15. repec:hal:cesptp:halshs-00625706 is not listed on IDEAS

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