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Great Expectations. Part I: On the Customizability of Generalized Expected Utility

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  • Francis Chu
  • Joseph Halpern

Abstract

Many different rules for decision making have been introduced in the literature. We present a single framework in which to study and compare these rules. This is done by defining expected utility with respect to general expectation structures, where a decision maker's beliefs are represented by plausibility measures and the decision maker's tastes are represented by general (i.e., not necessarily real-valued) utility functions. We call the resulting notion of expected utility generalized EU (GEU) and show that we can represent arbitrary preference relations on acts using GEU. We then show that each of Savage's postulates corresponds to an axiom on GEU. Thus, GEU can be customized to capture postulates of interest.
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  • Francis Chu & Joseph Halpern, 2008. "Great Expectations. Part I: On the Customizability of Generalized Expected Utility," Theory and Decision, Springer, vol. 64(1), pages 1-36, February.
    • Handle: RePEc:kap:theord:v:64:y:2008:i:1:p:1-36
    DOI: 10.1007/s11238-007-9044-4
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    References listed on IDEAS

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    1. Francis C. Chu & Joseph Y. Halpern, 2004. "Great expectations. Part II: Generalized expected utility as a universal decision rule," Game Theory and Information 0411004, University Library of Munich, Germany.
    2. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    3. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-686, May.
    4. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    5. Francis Chu & Joseph Halpern, 2008. "Great Expectations. Part I: On the Customizability of Generalized Expected Utility," Theory and Decision, Springer, vol. 64(1), pages 1-36, February.
    6. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    7. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    8. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    9. Wakker, Peter & Tversky, Amos, 1993. "An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-175, October.
    10. Fishburn, Peter C, 1987. "Reconsiderations in the Foundations of Decision under Uncertainty," Economic Journal, Royal Economic Society, vol. 97(388), pages 825-841, December.
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    Cited by:

    1. Chollete, Loran & Schmeidler, David, 2014. "Demand-Theoretic Approach to Choice of Priors," UiS Working Papers in Economics and Finance 2014/14, University of Stavanger.
    2. Francis Chu & Joseph Halpern, 2008. "Great Expectations. Part I: On the Customizability of Generalized Expected Utility," Theory and Decision, Springer, vol. 64(1), pages 1-36, February.
    3. Z Hua & S Li & Z Tao, 2006. "A rule-based risk decision-making approach and its application in China's customs inspection decision," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(11), pages 1313-1322, November.

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    More about this item

    Keywords

    generalized expected utility; representation theorem; plausibility measure; Savage’s Postulates;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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