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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. 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.
    3. 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).
    4. 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.
    5. Pascal Toquebeuf, 2016. "Choquet expected utility with affine capacities," Theory and Decision, Springer, vol. 81(2), pages 177-187, August.
    6. Craig S. Webb, 2017. "Piecewise linear rank-dependent utility," Theory and Decision, Springer, vol. 82(3), pages 403-414, March.
    7. Adam Dominiak & Ani Guerdjikova, 2021. "Pessimism and optimism towards new discoveries," Theory and Decision, Springer, vol. 90(3), pages 321-370, May.
    8. 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.
    9. Georgalos, Konstantinos, 2021. "Dynamic decision making under ambiguity: An experimental investigation," Games and Economic Behavior, Elsevier, vol. 127(C), pages 28-46.
    10. Horie, Mayumi, 2013. "Reexamination on updating Choquet beliefs," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 467-470.

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