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Generalized neo-additive capacities and updating

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  • Jürgen Eichberger
  • Simon Grant
  • Jean-Philippe Lefort

Abstract

This paper shows that, for CEU preferences, the axioms consquentialism, state independence and conditional certainty equivalent consistency under updating characterise a family of capacities, called Genralised Neo-Additive Capacities (GNAC). This family contains as special cases among others neo-additive capacities as introduced by Chateauneuf, Eichberger, and Grant(2007), Hurwicz capacities, and ε-contaminations. Moreover, we will show that the convex version of a GNAC is the only capacity for which the core of the Full-Bayesian Updates of a capacity, introduced by Jaffray (1992), equals the set of Bayesian updates of the probability distributions in the core of the original capacity.

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Bibliographic Info

Article provided by The International Society for Economic Theory in its journal International Journal of Economic Theory.

Volume (Year): 8 (2012)
Issue (Month): 3 (09)
Pages: 237-257

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Handle: RePEc:bla:ijethy:v:8:y:2012:i:3:p:237-257

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References

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  1. Itzhak Gilboa & David Schmeidler, 1991. "Updating Ambiguous Beliefs," Discussion Papers 924, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Eichberger, Jurgen & Grant, Simon & Kelsey, David, 2005. "CEU preferences and dynamic consistency," Mathematical Social Sciences, Elsevier, vol. 49(2), pages 143-151, March.
  3. Eichberger, Jurgen & Kelsey, David, 1996. "Uncertainty Aversion and Preference for Randomisation," Journal of Economic Theory, Elsevier, vol. 71(1), pages 31-43, October.
  4. Sarin, Rakesh & Wakker, Peter P, 1998. "Revealed Likelihood and Knightian Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 16(3), pages 223-50, July-Aug..
  5. Chateauneuf, Alain & Eichberger, Jürgen & Grant, Simon, 2003. "Choice under Uncertainty with the Best and Worst in Mind: Neo-additive Capacities," Sonderforschungsbereich 504 Publications 03-10, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
  6. Wakker, Peter P, 2001. "Testing and Characterizing Properties of Nonadditive Measures through Violations of the Sure-Thing Principle," Econometrica, Econometric Society, vol. 69(4), pages 1039-59, July.
  7. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  8. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer, vol. 20(1), pages 83-92.
  9. Meglena Jeleva & Stephane Rossignol, 2009. "Political decision of risk reduction: the role of trust," Public Choice, Springer, vol. 139(1), pages 83-104, April.
  10. Eichberger, Jürgen & Grant, Simon & Kelsey, David, 2010. "Comparing three ways to update Choquet beliefs," Economics Letters, Elsevier, vol. 107(2), pages 91-94, May.
  11. Joshua C. Teitelbaum, 2007. "A Unilateral Accident Model under Ambiguity," The Journal of Legal Studies, University of Chicago Press, vol. 36(2), pages 431-477, 06.
  12. Eichberger, Jurgen & Kelsey, David, 2002. "Strategic Complements, Substitutes, and Ambiguity: The Implications for Public Goods," Journal of Economic Theory, Elsevier, vol. 106(2), pages 436-466, October.
  13. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
  14. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  15. Cesaltina Pacheco Pires, 2002. "A Rule For Updating Ambiguous Beliefs," Theory and Decision, Springer, vol. 53(2), pages 137-152, September.
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Cited by:
  1. Horie, Mayumi, 2013. "Reexamination on updating Choquet beliefs," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 467-470.

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