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Generalized neo-additive capacities and updating

  • Jürgen Eichberger
  • Simon Grant
  • Jean-Philippe Lefort

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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File URL: http://hdl.handle.net/10.1111/j.1742-7363.2012.00189.x
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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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  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 & 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.
  3. Cesaltina Pacheco Pires, 2002. "A Rule For Updating Ambiguous Beliefs," Theory and Decision, Springer, vol. 53(2), pages 137-152, September.
  4. Grant, Simon & Chateauneuf, A. & Eichberger, J., 2002. "Choice under Uncertainty with the Best and Worst in Mind: Neo-additive Capacities," Working Papers 2002-10, Rice University, Department of Economics.
  5. Eichberger, J. & Kelsey, D., 1995. "Uncertainty Aversion and Preferences for Randomisation," Department of Economics - Working Papers Series 476, The University of Melbourne.
  6. 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..
  7. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  8. Eichberger, Jürgen & Grant, Simon & Kelsey, David, 2010. "Comparing three ways to update Choquet beliefs," Economics Letters, Elsevier, vol. 107(2), pages 91-94, May.
  9. 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.
  10. 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.
  11. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer, vol. 20(1), pages 83-92.
  12. Meglena Jeleva & Stephane Rossignol, 2009. "Political decision of risk reduction: the role of trust," Public Choice, Springer, vol. 139(1), pages 83-104, April.
  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. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  15. Eichberger, Jurgen & Grant, Simon & Kelsey, David, 2005. "CEU preferences and dynamic consistency," Mathematical Social Sciences, Elsevier, vol. 49(2), pages 143-151, March.
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