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Conditional Preference Orders and their Numerical Representations

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  • Samuel Drapeau
  • Asgar Jamneshan

Abstract

We provide an axiomatic system modeling conditional preference orders which is based on conditional set theory. Conditional numerical representations are introduced, and a conditional version of the theorems of Debreu on the existence of numerical representations is proved. The conditionally continuous representations follow from a conditional version of Debreu's Gap Lemma the proof of which relies on a conditional version of the axiom of choice, free of any measurable selection argument. We give a conditional version of the von Neumann and Morgenstern representation as well as automatic conditional continuity results, and illustrate them by examples.

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  • Samuel Drapeau & Asgar Jamneshan, 2014. "Conditional Preference Orders and their Numerical Representations," Papers 1410.5466, arXiv.org, revised Jan 2016.
  • Handle: RePEc:arx:papers:1410.5466
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    References listed on IDEAS

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    Cited by:

    1. Asgar Jamneshan & Michael Kupper & José Miguel Zapata-García, 2020. "Parameter-Dependent Stochastic Optimal Control in Finite Discrete Time," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 644-666, August.
    2. Marco Maggis & Andrea Maran, 2018. "Stochastic Dynamic Utilities and Inter-Temporal Preferences," Papers 1803.05244, arXiv.org, revised Feb 2020.
    3. Asgar Jamneshan & Michael Kupper & José Miguel Zapata-García, 0. "Parameter-Dependent Stochastic Optimal Control in Finite Discrete Time," Journal of Optimization Theory and Applications, Springer, vol. 0, pages 1-23.

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