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Random Expected Utility

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  • F. Gul
  • W. Pesendorfer

Abstract

We develop and analyze a model of random choice and random expected utility. A decision problem is a finite set of lotteries that describe the feasible choices. A random choice rule associates with each decision problem a probability measure over choices. A random utility function is a probability measure over von Neumann-Morgenstern utility functions. We show that a random choice rule maximizes some random utility function if and only if it is mixture continuous, monotone (the probability that a lottery is chosen does not increase when other lotteries are added to the decision problem), extreme (lotteries that are not extreme points of the decision problem are chosen with probability 0), and linear (satisfies the independence axiom). Copyright The Econometric Society 2006.
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Suggested Citation

  • F. Gul & W. Pesendorfer, 2002. "Random Expected Utility," Princeton Economic Theory Working Papers 497768e9b9fc18361ac0810b3, David K. Levine.
    • Handle: RePEc:cla:princt:497768e9b9fc18361ac0810b33ef8396
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    1. Gil Kalai & Ariel Rubinstein & Ran Spiegler, 2002. "Rationalizing Choice Functions By Multiple Rationales," Econometrica, Econometric Society, vol. 70(6), pages 2481-2488, November.
    2. Barbera, Salvador & Pattanaik, Prasanta K, 1986. "Falmagne and the Rationalizability of Stochastic Choices in Terms of Random Orderings," Econometrica, Econometric Society, vol. 54(3), pages 707-715, May.
    3. Stephen A. Clark, 1995. "The random utility model with an infinite choice space," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 179-189.
    4. Fishburn, Peter C., 1992. "Induced binary probabilities and the linear ordering polytope: a status report," Mathematical Social Sciences, Elsevier, vol. 23(1), pages 67-80, February.
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