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Random expected utility theory with a continuum of prizes

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  • Wei Ma

    (Xi’an Jiaotong-Liverpool University
    University of Pretoria)

Abstract

This note generalizes Gul and Pesendorfer’s random expected utility theory, a stochastic reformulation of von Neumann–Morgenstern expected utility theory for lotteries over a finite set of prizes, to the circumstances with a continuum of prizes. Let [0, M] denote this continuum of prizes; assume that each utility function is continuous, let $$C_0[0,M]$$ C 0 [ 0 , M ] be the set of all utility functions which vanish at the origin, and define a random utility function to be a finitely additive probability measure on $$C_0[0,M]$$ C 0 [ 0 , M ] (associated with an appropriate algebra). It is shown here that a random choice rule is mixture continuous, monotone, linear, and extreme if, and only if, the random choice rule maximizes some regular random utility function. To obtain countable additivity of the random utility function, we further restrict our consideration to those utility functions that are continuously differentiable on [0, M] and vanish at zero. With this restriction, it is shown that a random choice rule is continuous, monotone, linear, and extreme if, and only if, it maximizes some regular, countably additive random utility function. This generalization enables us to make a discussion of risk aversion in the framework of random expected utility theory.

Suggested Citation

  • Wei Ma, 2018. "Random expected utility theory with a continuum of prizes," Annals of Operations Research, Springer, vol. 271(2), pages 787-809, December.
  • Handle: RePEc:spr:annopr:v:271:y:2018:i:2:d:10.1007_s10479-018-2914-z
    DOI: 10.1007/s10479-018-2914-z
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    References listed on IDEAS

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    1. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
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    Cited by:

    1. Wei Ma, 2023. "Random dual expected utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(2), pages 293-315, February.
    2. Mira Frick & Ryota Iijima & Tomasz Strzalecki, 2019. "Dynamic Random Utility," Econometrica, Econometric Society, vol. 87(6), pages 1941-2002, November.

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