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Neo-additive capacities and updating

  • Eichberger, Jürgen
  • Grant, Simon
  • Lefort, Jean-Philippe

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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Paper provided by University of Heidelberg, Department of Economics in its series Working Papers with number 0490.

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Date of creation: 04 Nov 2009
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Handle: RePEc:awi:wpaper:0490
Note: This paper is part of http://archiv.ub.uni-heidelberg.de/volltextserver/view/schriftenreihen/sr-3.html
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  1. Epstein Larry G. & Le Breton Michel, 1993. "Dynamically Consistent Beliefs Must Be Bayesian," Journal of Economic Theory, Elsevier, vol. 61(1), pages 1-22, October.
  2. Meglena Jeleva & Stephane Rossignol, 2009. "Political decision of risk reduction: the role of trust," Public Choice, Springer, vol. 139(1), pages 83-104, April.
  3. 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..
  4. Klibanoff, Peter & Hanany, Eran, 2007. "Updating preferences with multiple priors," Theoretical Economics, Econometric Society, vol. 2(3), September.
  5. Jurgen Eichberger & Simon Grant & David Kelsey, 2006. "Updating Choquet Beliefs," Discussion Papers 0607, Exeter University, Department of Economics.
  6. Grant, Simon & Eichberger, Jürgen & Kelsey, David, 2004. "CEU Preferences and Dynamic Consistency," Sonderforschungsbereich 504 Publications 04-47, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  7. 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.
  8. 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.
  9. Eichberger, Jürgen & Kelsey, David & Schipper, Burkhard, 2003. "Ambiguity and Social Interaction," Sonderforschungsbereich 504 Publications 03-30, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  10. 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.
  11. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
  12. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  13. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer, vol. 20(1), pages 83-92.
  14. Eichberger, Jürgen & Kelsey, David, 2003. "Sequential Two-Player Games with Ambiguity," Sonderforschungsbereich 504 Publications 03-27, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  15. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  16. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
  17. Eichberger, Jürgen & Grant, Simon & Kelsey, David, 2010. "Comparing three ways to update Choquet beliefs," Economics Letters, Elsevier, vol. 107(2), pages 91-94, May.
  18. Eichberger, J. & Kelsey, D., 1995. "Uncertainty Aversion and Preferences for Randomisation," Department of Economics - Working Papers Series 476, The University of Melbourne.
  19. 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.
  20. Dow, James & Werlang, Sergio Ribeiro da Costa, 1992. "Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio," Econometrica, Econometric Society, vol. 60(1), pages 197-204, January.
  21. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
  22. 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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