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Maximum Entropy Utility

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  • Ali E. Abbas

    (School of Engineering, University of Illinois at Urbana-Champaign, 104 S. Mathews Avenue, Urbana, Illinois 61801)

Abstract

This paper presents a method to assign utility values when only partial information is available about the decision maker’s preferences. We introduce the notion of a utility density function and a maximum entropy principle for utility assignment. The maximum entropy utility solution embeds a large family of utility functions that includes the most commonly used functional forms. We discuss the implications of maximum entropy utility on the preference behavior of the decision maker and present an application to competitive bidding situations where only previous decisions are observed by each party. We also present minimum cross entropy utility, which incorporates additional knowledge about the shape of the utility function into the maximum entropy formulation, and work through several examples to illustrate the approach.

Suggested Citation

  • Ali E. Abbas, 2006. "Maximum Entropy Utility," Operations Research, INFORMS, vol. 54(2), pages 277-290, April.
    • Handle: RePEc:inm:oropre:v:54:y:2006:i:2:p:277-290
    DOI: 10.1287/opre.1040.0204
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Abbas, Ali E., 2007. "Moments of utility functions and their applications," European Journal of Operational Research, Elsevier, vol. 180(1), pages 378-395, July.
    2. Nathan Lassance & Frédéric Vrins, 2021. "Minimum Rényi entropy portfolios," Annals of Operations Research, Springer, vol. 299(1), pages 23-46, April.
    3. Zhou, Wei & Zhang, Cheng & Wang, Qiangqiang, 2018. "Concealment measurement and flow distribution of military supply transportation: A double-entropy model," European Journal of Operational Research, Elsevier, vol. 264(2), pages 570-581.
    4. Ali E. Abbas & Ronald A. Howard, 2005. "Attribute Dominance Utility," Decision Analysis, INFORMS, vol. 2(4), pages 185-206, December.
    5. Charles-Cadogan, G., 2018. "Probability interference in expected utility theory," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 163-175.
    6. A. B. Leoneti & G. A. Prataviera, 2020. "Entropy-Norm space for geometric selection of strict Nash equilibria in n-person games," Papers 2003.09225, arXiv.org.
    7. Payandeh Najafabadi, Amir T. & Hatami, Hamid & Omidi Najafabadi, Maryam, 2012. "A maximum-entropy approach to the linear credibility formula," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 216-221.
    8. Sean M. Murphy & Dan L. Friesner & Robert Rosenman, 2012. "Patients' perceptions and treatment effectiveness: a reassessment using generalized maximum entropy," Applied Economics Letters, Taylor & Francis Journals, vol. 19(13), pages 1243-1248, September.
    9. Samuel Kotz & Johan René van Dorp, 2010. "Generalized Diagonal Band Copulas with Two-Sided Generating Densities," Decision Analysis, INFORMS, vol. 7(2), pages 196-214, June.
    10. Chen Wang & Vicki M. Bier, 2013. "Expert Elicitation of Adversary Preferences Using Ordinal Judgments," Operations Research, INFORMS, vol. 61(2), pages 372-385, April.
    11. Leoneti, A.B. & Prataviera, G.A., 2020. "Entropy-norm space for geometric selection of strict Nash equilibria in n-person games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 546(C).
    12. Ali E. Abbas & James E. Matheson & Robert F. Bordley, 2009. "Effective utility functions induced by organizational target-based incentives," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 30(4), pages 235-251.
    13. Chao Fu & Dong-Ling Xu, 2016. "Determining attribute weights to improve solution reliability and its application to selecting leading industries," Annals of Operations Research, Springer, vol. 245(1), pages 401-426, October.
    14. Johannes G. Jaspersen & Gilberto Montibeller, 2015. "Probability Elicitation Under Severe Time Pressure: A Rank‐Based Method," Risk Analysis, John Wiley & Sons, vol. 35(7), pages 1317-1335, July.
    15. Tervonen, Tommi & Figueira, José Rui & Lahdelma, Risto & Dias, Juscelino Almeida & Salminen, Pekka, 2009. "A stochastic method for robustness analysis in sorting problems," European Journal of Operational Research, Elsevier, vol. 192(1), pages 236-242, January.
    16. Jeffrey M. Keisler & Robert F. Bordley, 2015. "Project Management Decisions with Uncertain Targets," Decision Analysis, INFORMS, vol. 12(1), pages 15-28, March.
    17. Zhengwei Sun & Ali E. Abbas, 2014. "On the sensitivity of the value of information to risk aversion in two-action decision problems," Environment Systems and Decisions, Springer, vol. 34(1), pages 24-37, March.

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