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The Use of Distribution Functions to Represent Utility Functions

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  • Marvin H. Berhold

    (Georgia State University)

Abstract

This paper considers the decision maker whose evaluation and consequent choice of actions is accomplished through the use of the expected utility hypothesis. In cases where the utility function is increasing with upper and lower bounds then the utility function can be characterized by a distribution function, and we can take advantage of the various properties of such functions as well as existing results with respect to such functions. Using these properties and results we can determine the certainty equivalents as a function of the parameters of the distribution function (utility function) and the parameters of the probability distribution on the uncertain payoff. The following cases are considered: (1) Gaussian distribution function and Gaussian probability distribution, (2) Exponential distribution function and exponential distribution and (3) Exponential distribution function and Gaussian probability distribution.

Suggested Citation

  • Marvin H. Berhold, 1973. "The Use of Distribution Functions to Represent Utility Functions," Management Science, INFORMS, vol. 19(7), pages 825-829, March.
  • Handle: RePEc:inm:ormnsc:v:19:y:1973:i:7:p:825-829
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    File URL: http://dx.doi.org/10.1287/mnsc.19.7.825
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    Cited by:

    1. Wim Linden, 1981. "Using aptitude measurements for the optimal assignment of subjects to treatments with and without mastery scores," Psychometrika, Springer;The Psychometric Society, vol. 46(3), pages 257-274, September.
    2. Denis Conniffe, 2007. "The Generalised Extreme Value Distribution as Utility Function," The Economic and Social Review, Economic and Social Studies, vol. 38(3), pages 275-288.
    3. Robert Bordley & Marco LiCalzi & Luisa Tibiletti, 2014. "A target-based foundation for the "hard-easy effect" bias," Working Papers 23, Department of Management, Università Ca' Foscari Venezia.
    4. Marco LiCalzi, 2005. "A language for the construction of preferences under uncertainty," Game Theory and Information 0509002, EconWPA.
    5. Ali Abbas, 2004. "Maximum Entropy Utility," Game Theory and Information 0403002, EconWPA.
    6. repec:eee:matsoc:v:92:y:2018:i:c:p:74-77 is not listed on IDEAS
    7. LiCalzi, Marco & Sorato, Annamaria, 2006. "The Pearson system of utility functions," European Journal of Operational Research, Elsevier, vol. 172(2), pages 560-573, July.
    8. Wynn C. Stirling & Teppo Felin, 2016. "Satisficing, preferences, and social interaction: a new perspective," Theory and Decision, Springer, vol. 81(2), pages 279-308, August.

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