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Optimism and Pessimism with Expected Utility, Third Version

Author

Listed:
  • David Dillenberger

    (Department of Economics, University of Pennsylvania)

  • Andrew Postlewaite

    (Department of Economics, University of Pennsylvania)

  • Kareen Rozen

    (Department of Economics, Yale University)

Abstract

Savage (1954) provides axioms on preferences over acts that are equivalent to the existence of a subjective expected utility representation. We show that there is a continuum of other \expected utility" representations in which for any act, the probability distribution over states depends on the corresponding outcomes and is first-order stochastically dominated by (dominates) the Savage distribution. We suggest that pessimism (optimism) can be captured by the stake-dependent probabilities in these alternate representations. We then extend the DM's preferences to be defined over both subjective acts and objective lotteries. Our result permits modeling ambiguity aversion in Ellsberg's two-urn experiment using pessimistic probability assessments, the same utility over prizes for lotteries and acts, and without relaxing Savage's axioms. An implication of our results is that the large body of existing research based on expected utility can, with a simple reinterpretation, be understood as modeling the behavior of optimistic or pessimistic decision makers.

Suggested Citation

  • David Dillenberger & Andrew Postlewaite & Kareen Rozen, 2011. "Optimism and Pessimism with Expected Utility, Third Version," PIER Working Paper Archive 13-001, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 26 Dec 2012.
    • Handle: RePEc:pen:papers:13-001
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    References listed on IDEAS

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    1. Wakker, Peter P, 2001. "Testing and Characterizing Properties of Nonadditive Measures through Violations of the Sure-Thing Principle," Econometrica, Econometric Society, vol. 69(4), pages 1039-1059, July.
    2. Itzhak Gilboa & Massimo Marinacci, 2011. "Ambiguity and the Bayesian Paradigm," Working Papers 379, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    3. Chew, Soo Hong & Sagi, Jacob S., 2008. "Small worlds: Modeling attitudes toward sources of uncertainty," Journal of Economic Theory, Elsevier, vol. 139(1), pages 1-24, March.
    4. Simon Grant & Edi Karni, 2005. "Why Does It Matter That Beliefs And Valuations Be Correctly Represented?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(3), pages 917-934, August.
    5. Eddie Dekel & Barton L. Lipman, 2012. "Costly Self‐Control and Random Self‐Indulgence," Econometrica, Econometric Society, vol. 80(3), pages 1271-1302, May.
    6. Wolfgang Pesendorfer, 2006. "Behavioral Economics Comes of Age: A Review Essay on Advances in Behavioral Economics," Journal of Economic Literature, American Economic Association, vol. 44(3), pages 712-721, September.
    7. Gilboa, Itzhak & Postlewaite, Andrew & Schmeidler, David, 2009. "Is It Always Rational To Satisfy Savage'S Axioms?," Economics and Philosophy, Cambridge University Press, vol. 25(3), pages 285-296, November.
    8. Wakker, Peter, 1990. "Characterizing optimism and pessimism directly through comonotonicity," Journal of Economic Theory, Elsevier, vol. 52(2), pages 453-463, December.
    9. Peter P. Wakker, 2008. "Lessons Learned by (from?) an Economist Working in Medical Decision Making," Medical Decision Making, , vol. 28(5), pages 690-698, September.
    10. Wakker,Peter P., 2010. "Prospect Theory," Cambridge Books, Cambridge University Press, number 9780521765015, September.
    11. Simon Grant & Ben Polak & Tomasz Strzalecki, "undated". "Second-Order Expected Utility," Working Paper 8340, Harvard University OpenScholar.
    12. Eva Kislingerová, 2012. "Recenze publikace Stanislawa Sudola Řízení vědy. Hlavní problémy a diskuse," Ekonomika a Management, Prague University of Economics and Business, vol. 2012(2), pages 1-65.
    13. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    14. Dean, Mark & Ortoleva, Pietro, 2017. "Allais, Ellsberg, and preferences for hedging," Theoretical Economics, Econometric Society, vol. 12(1), January.
    15. Eddie Dekel & Barton L. Lipman, 2010. "How (Not) to Do Decision Theory," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 257-282, September.
    16. Edi Karni, 2011. "Subjective Probabilities on a State Space," American Economic Journal: Microeconomics, American Economic Association, vol. 3(4), pages 172-185, November.
    17. Edi Karni, 2009. "A theory of medical decision making under uncertainty," Journal of Risk and Uncertainty, Springer, vol. 39(1), pages 1-16, August.
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    Cited by:

    1. Weinstock, Eyal & Sonsino, Doron, 2014. "Are risk-seekers more optimistic? Non-parametric approach," Journal of Economic Behavior & Organization, Elsevier, vol. 108(C), pages 236-251.
    2. Paola Manzini & Marco Mariotti, 2015. "Modelling Imperfect Attention," Working Papers 744, Queen Mary University of London, School of Economics and Finance.
    3. Paola Manzini & Marco Mariotti, 2015. "Modelling Imperfect Attention," Working Papers 744, Queen Mary University of London, School of Economics and Finance.

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    More about this item

    Keywords

    Subjective expected utility; optimism; pessimism; stake-dependent probability;
    All these keywords.

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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