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Abraham Wald's complete class theorem and Knightian uncertainty

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  • Kuzmics, Christoph

Abstract

I study the implications of Wald's (1947) complete class theorem for decision making under Knightian uncertainty (or ambiguity). Suppose we call someone who uses Wald's approach to statistical decision making a Waldian. A Waldian may then have preferences over acts that are not in agreement with subjective expected utility but always chooses as if she was a subjective expected utility maximizer. In particular, even Wald's (1945) minmax decision rule is consistent with subjective expected utility.

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  • Kuzmics, Christoph, 2017. "Abraham Wald's complete class theorem and Knightian uncertainty," Games and Economic Behavior, Elsevier, vol. 104(C), pages 666-673.
    • Handle: RePEc:eee:gamebe:v:104:y:2017:i:c:p:666-673
    DOI: 10.1016/j.geb.2017.06.012
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    1. Stoye, Jörg, 2015. "Choice theory when agents can randomize," Journal of Economic Theory, Elsevier, vol. 155(C), pages 131-151.
    2. Peter Klibanoff, 2001. "Stochastically independent randomization and uncertainty aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(3), pages 605-620.
    3. Reny, Philip J. & Robson, Arthur J., 2004. "Reinterpreting mixed strategy equilibria: a unification of the classical and Bayesian views," Games and Economic Behavior, Elsevier, vol. 48(2), pages 355-384, August.
    4. Zambrano, Eduardo, 2005. "Testable implications of subjective expected utility theory," Games and Economic Behavior, Elsevier, vol. 53(2), pages 262-268, November.
    5. Eran Shmaya & Leeat Yariv, 2016. "Experiments on Decisions under Uncertainty: A Theoretical Framework," American Economic Review, American Economic Association, vol. 106(7), pages 1775-1801, July.
    6. R. J. Aumann & M. Maschler, 1972. "Some Thoughts on the Minimax Principle," Management Science, INFORMS, vol. 18(5-Part-2), pages 54-63, January.
    7. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136, World Scientific Publishing Co. Pte. Ltd..
    8. P. Battigalli & S. Cerreia‐Vioglio & F. Maccheroni & M. Marinacci, 2016. "A Note on Comparative Ambiguity Aversion and Justifiability," Econometrica, Econometric Society, vol. 84, pages 1903-1916, September.
    9. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-1668, December.
    10. Kota Saito, 2015. "Preferences for Flexibility and Randomization under Uncertainty," American Economic Review, American Economic Association, vol. 105(3), pages 1246-1271, March.
    11. Jürgen Eichberger & Simon Grant & David Kelsey, 2016. "Randomization and dynamic consistency," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(3), pages 547-566, August.
    12. Pierpaolo Battigalli & Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2017. "Mixed extensions of decision problems under uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(4), pages 827-866, April.
    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. Camerer, Colin & Weber, Martin, 1992. "Recent Developments in Modeling Preferences: Uncertainty and Ambiguity," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 325-370, October.
    15. Kyoungwon Seo, 2009. "Ambiguity and Second-Order Belief," Econometrica, Econometric Society, vol. 77(5), pages 1575-1605, September.
    16. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    17. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    18. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    19. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, April.
    20. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo & Montrucchio, Luigi, 2013. "Ambiguity and robust statistics," Journal of Economic Theory, Elsevier, vol. 148(3), pages 974-1049.
      • Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2011. "Ambiguity and Robust Statistics," Working Papers 382, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    21. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    22. Bade, Sophie, 2015. "Randomization devices and the elicitation of ambiguity-averse preferences," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 221-235.
    23. Howard Raiffa, 1961. "Risk, Ambiguity, and the Savage Axioms: Comment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 690-694.
    24. Yoram Halevy, 2007. "Ellsberg Revisited: An Experimental Study," Econometrica, Econometric Society, vol. 75(2), pages 503-536, March.
    25. Segal, Uzi, 1988. "Does the Preference Reversal Phenomenon Necessarily Contradict the Independence Axiom?," American Economic Review, American Economic Association, vol. 78(1), pages 233-236, March.
    26. Holt, Charles A, 1986. "Preference Reversals and the Independence Axiom," American Economic Review, American Economic Association, vol. 76(3), pages 508-515, June.
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    Cited by:

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    3. Aurélien Baillon & Yoram Halevy & Chen Li, 2022. "Randomize at Your Own Risk: On the Observability of Ambiguity Aversion," Econometrica, Econometric Society, vol. 90(3), pages 1085-1107, May.
    4. Oechssler, Jörg & Rau, Hannes & Roomets, Alex, 2019. "Hedging, ambiguity, and the reversal of order axiom," Games and Economic Behavior, Elsevier, vol. 117(C), pages 380-387.
    5. Roxane Bricet, 2018. "Preferences for information precision under ambiguity," THEMA Working Papers 2018-09, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    6. Christoph Kuzmics & Brian W. Rogers & Xiannong Zhang, 2019. "Is Ellsberg behavior evidence of ambiguity aversion?," Graz Economics Papers 2019-07, University of Graz, Department of Economics.
    7. Eran Hanany & Peter Klibanoff & Sujoy Mukerji, 2020. "Incomplete Information Games with Ambiguity Averse Players," American Economic Journal: Microeconomics, American Economic Association, vol. 12(2), pages 135-187, May.
    8. Bade, Sophie, 2022. "Dynamic semi-consistency," Games and Economic Behavior, Elsevier, vol. 134(C), pages 117-126.
    9. Brown, Alexander L. & Healy, Paul J., 2018. "Separated decisions," European Economic Review, Elsevier, vol. 101(C), pages 20-34.

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    More about this item

    Keywords

    Ambiguity; Decision theory; Knightian uncertainty; Experimental design;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • C90 - Mathematical and Quantitative Methods - - Design of Experiments - - - General
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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