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Updating Choquet Integrals , Consequentialism and Dynamic Consistency

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  • Robert Kast

    ()

  • André Lapied

    ()

  • Pascal Toquebeuf

    ()

Abstract

Choquet capacities have been used to represent decision makers’ beliefs in order to generalise the expected utility approach. Conditional capacities have to be defined for dynamic choice situations where information may modify the decision maker future beliefs. Several updating rules have been proposed in the literature. We derive them from a general approach based on conditional Choquet expectations. Conversely, depending on the updating rule adopted, the conditional Choquet integral can take different values. Conditional Choquet Expected Utility are derived from axioms on preferences. However, it is now well-known in decision theory that if preferences satisfy simultaneously dynamic consistency and consequentialism axioms their representation is restricted to classical Expected Utility. We show that the rule proposed by Chateauneuf, Kast and Lapied (2001) is the only one to satisfy dynamic consistency with a nonnecessary additive capacity

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Bibliographic Info

Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 04-2008.

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Length: 25 pages
Date of creation: Jun 2008
Date of revision:
Handle: RePEc:icr:wpmath:04-2008

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Keywords: Conditional Choquet expectation; Conditional capacity; Updating rules; Choquet Expected Utility; Dynamic consistency; Consequentialism.;

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References

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  1. Denneberg, Dieter, 2002. "Conditional expectation for monotone measures, the discrete case," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 105-121, April.
  2. Lehrer, Ehud, 2005. "Updating non-additive probabilities-- a geometric approach," Games and Economic Behavior, Elsevier, vol. 50(1), pages 42-57, January.
  3. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  4. Itzhak Gilboa & David Schmeidler, 1991. "Updating Ambiguous Beliefs," Discussion Papers 924, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-68, December.
  6. Hammond, P.J. & , ., 1987. "Consequentialist foundations for expected utility," CORE Discussion Papers 1987016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. repec:ebl:ecbull:v:4:y:2006:i:19:p:1-6 is not listed on IDEAS
  8. Alain Chateauneuf & Robert Kast & André Lapied, 2001. "Conditioning Capacities and Choquet Integrals: The Role of Comonotony," Theory and Decision, Springer, vol. 51(2), pages 367-386, December.
  9. Karni, Edi & Schmeidler, David, 1991. "Atemporal dynamic consistency and expected utility theory," Journal of Economic Theory, Elsevier, vol. 54(2), pages 401-408, August.
  10. André Lapied & Pascal Toquebeuf, 2009. "Consistent dynamic choice and non-expected utility preferences," Working Papers hal-00416214, HAL.
  11. André Lapied & Pascal Tocquebeuf, 2007. "Consistent Dynamice Choice And Non-Expected Utility Preferences," Working Papers halshs-00353880, HAL.
  12. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer, vol. 20(1), pages 83-92.
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Cited by:
  1. Miklos Rasonyi & Andrea M. Rodrigues, 2012. "Optimal Portfolio Choice for a Behavioural Investor in Continuous-Time Markets," Papers 1202.0628, arXiv.org, revised Apr 2013.
  2. André Lapied & Robert Kast, 2010. "Dynamically consistent Choquet random walk and real investments," Working Papers 10-21, LAMETA, Universtiy of Montpellier, revised 2010.
  3. 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.

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