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The Use of Distribution Functions to Represent Utility Functions

Author

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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
    DOI: 10.1287/mnsc.19.7.825
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    Citations

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    Cited by:

    1. 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.
    2. Robert Bordley & Marco Licalzi & Luisa Tibiletti, 2017. "A Target-Based Foundation for the “Hard-Easy Effect” Bias," Eurasian Studies in Business and Economics, in: Mehmet Huseyin Bilgin & Hakan Danis & Ender Demir & Ugur Can (ed.), Country Experiences in Economic Development, Management and Entrepreneurship, pages 659-671, Springer.
    3. Denuit, Michel M., 2018. "Risk apportionment and multiply monotone targets," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 74-77.
    4. LiCalzi, Marco & Sorato, Annamaria, 2006. "The Pearson system of utility functions," European Journal of Operational Research, Elsevier, vol. 172(2), pages 560-573, July.
    5. Jeffrey M. Keisler & Robert F. Bordley, 2015. "Project Management Decisions with Uncertain Targets," Decision Analysis, INFORMS, vol. 12(1), pages 15-28, March.
    6. Xinwei Zhang & Qiong Feng & Shurong Tong & Hakki Eres, 2022. "Multilinear target-based decision analysis with hybrid-information targets and performance levels," Fuzzy Optimization and Decision Making, Springer, vol. 21(4), pages 605-647, December.
    7. Ilia Tsetlin & Robert L. Winkler, 2006. "On Equivalent Target-Oriented Formulations for Multiattribute Utility," Decision Analysis, INFORMS, vol. 3(2), pages 94-99, June.
    8. 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.
    9. Marco LiCalzi, 2005. "A language for the construction of preferences under uncertainty," Game Theory and Information 0509002, University Library of Munich, Germany.
    10. Ali E. Abbas, 2006. "Maximum Entropy Utility," Operations Research, INFORMS, vol. 54(2), pages 277-290, April.
    11. Ali Abbas, 2004. "Maximum Entropy Utility," Game Theory and Information 0403002, University Library of Munich, Germany.
    12. 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.
    13. Denuit, Michel, 2016. "Risk Apportionment and Multiply Monotone Targets," LIDAM Discussion Papers ISBA 2016044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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