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
Annals of Operations Research – Springer Journals
Published: Jun 4, 2018
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