Random expected utility theory with a continuum of prizes

Random expected utility theory with a continuum of prizes Ann Oper Res https://doi.org/10.1007/s10479-018-2914-z ORIGINAL RESEARCH Random expected utility theory with a continuum of prizes 1,2 Wei Ma © Springer Science+Business Media, LLC, part of Springer Nature 2018 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, 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, 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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Operations Research Springer Journals

Random expected utility theory with a continuum of prizes

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Publisher
Springer US
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Business and Management; Operations Research/Decision Theory; Combinatorics; Theory of Computation
ISSN
0254-5330
eISSN
1572-9338
D.O.I.
10.1007/s10479-018-2914-z
Publisher site
See Article on Publisher Site

Abstract

Ann Oper Res https://doi.org/10.1007/s10479-018-2914-z ORIGINAL RESEARCH Random expected utility theory with a continuum of prizes 1,2 Wei Ma © Springer Science+Business Media, LLC, part of Springer Nature 2018 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, 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, 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

Journal

Annals of Operations ResearchSpringer Journals

Published: Jun 4, 2018

References

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