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Generalized neo-additive capacities and updating

Author

Listed:
  • Jürgen Eichberger

    (Universität Heidelberg [Heidelberg] = Heidelberg University)

  • Simon Grant

    (AUTRES)

  • Jean-Philippe Lefort

    (LEDa - Laboratoire d'Economie de Dauphine - IRD - Institut de Recherche pour le Développement - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Jürgen Eichberger & Simon Grant & Jean-Philippe Lefort, 2012. "Generalized neo-additive capacities and updating," Post-Print hal-01615858, HAL.
    • Handle: RePEc:hal:journl:hal-01615858
    DOI: 10.1111/j.1742-7363.2012.00189.x
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    Cited by:

    1. Giraud, Raphaël & Thomas, Lionel, 2017. "Ambiguity, optimism, and pessimism in adverse selection models," Journal of Economic Theory, Elsevier, vol. 171(C), pages 64-100.
    2. Baillon, Aurélien & Bleichrodt, Han & Li, Chen & Wakker, Peter P., 2021. "Belief hedges: Measuring ambiguity for all events and all models," Journal of Economic Theory, Elsevier, vol. 198(C).
    3. Pascal Toquebeuf, 2016. "Choquet expected utility with affine capacities," Theory and Decision, Springer, vol. 81(2), pages 177-187, August.
    4. Craig Webb, 2015. "Piecewise additivity for non-expected utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 371-392, October.
    5. Horie, Mayumi, 2013. "Reexamination on updating Choquet beliefs," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 467-470.
    6. Adam Dominiak & Ani Guerdjikova, 2021. "Special Issue on Ambiguity and Strategic Interactions in Honor of Jürgen Eichberger," Theory and Decision, Springer, vol. 90(3), pages 301-307, May.
    7. Emy Lécuyer & Jean-Philippe Lefort, 2021. "Put–call parity and generalized neo-additive pricing rules," Theory and Decision, Springer, vol. 90(3), pages 521-542, May.
    8. Adam Dominiak & Ani Guerdjikova, 2021. "Pessimism and optimism towards new discoveries," Theory and Decision, Springer, vol. 90(3), pages 321-370, May.
    9. Georgalos, Konstantinos, 2021. "Dynamic decision making under ambiguity: An experimental investigation," Games and Economic Behavior, Elsevier, vol. 127(C), pages 28-46.
    10. Craig S. Webb, 2017. "Piecewise linear rank-dependent utility," Theory and Decision, Springer, vol. 82(3), pages 403-414, March.

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