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Foundations of ambiguity models under symmetry: α-MEU and smooth ambiguity

Author

Listed:
  • Peter Klibanoff

    (Northwestern University)

  • Sujoy Mukerji

    (Queen Mary University of London)

  • Kyoungwon Seo

    (Seoul National University)

  • Lorenzo Staca

    (Northwestern University)

Abstract

The α-MEU model and the smooth ambiguity model are two popular models in decision making under ambiguity. However, the axiomatic foundations of these two models are not completely understood. We provide axiomatic foundations of these models in a symmetric setting with a product state space . This setting allows marginals over S to be linked behaviorally with (limiting frequency) events. Bets on such events are shown to reveal the i.i.d. measures that are relevant for the decision maker's preferences and appear in the representations. By characterizing both models within a common framework, it becomes possible to better compare and relate them.

Suggested Citation

  • Peter Klibanoff & Sujoy Mukerji & Kyoungwon Seo & Lorenzo Staca, 2021. "Foundations of ambiguity models under symmetry: α-MEU and smooth ambiguity," Working Papers 922, Queen Mary University of London, School of Economics and Finance.
    • Handle: RePEc:qmw:qmwecw:922
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    1. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2011. "Definitions of ambiguous events and the smooth ambiguity model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 399-424, October.
    2. Larry G. Epstein, 2010. "A Paradox for the “Smooth Ambiguity” Model of Preference," Econometrica, Econometric Society, vol. 78(6), pages 2085-2099, November.
    3. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2012. "On the Smooth Ambiguity Model: A Reply," Econometrica, Econometric Society, vol. 80(3), pages 1303-1321, May.
    4. Grant, Simon & Polak, Ben, 2013. "Mean-dispersion preferences and constant absolute uncertainty aversion," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1361-1398.
    5. Cohen, Michele & Jaffray, Jean-Yves, 1980. "Rational Behavior under Complete Ignorance," Econometrica, Econometric Society, vol. 48(5), pages 1281-1299, July.
    6. Klibanoff, Peter & Marinacci, Massimo & Mukerji, Sujoy, 2009. "Recursive smooth ambiguity preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 930-976, May.
    7. Mohammed Abdellaoui & Aurelien Baillon & Laetitia Placido & Peter P. Wakker, 2011. "The Rich Domain of Uncertainty: Source Functions and Their Experimental Implementation," American Economic Review, American Economic Association, vol. 101(2), pages 695-723, April.
    8. Yan Chen & Robert Gazzale, 2004. "When Does Learning in Games Generate Convergence to Nash Equilibria? The Role of Supermodularity in an Experimental Setting," American Economic Review, American Economic Association, vol. 94(5), pages 1505-1535, December.
    9. 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.
    10. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    11. Epstein Larry G & Seo Kyoungwon, 2011. "Symmetry or Dynamic Consistency?," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-14, June.
    12. Peter Klibanoff & Sujoy Mukerji & Kyoungwon Seo, 2014. "Perceived Ambiguity and Relevant Measures," Econometrica, Econometric Society, vol. 82, pages 1945-1978, September.
    13. Kyoungwon Seo, 2009. "Ambiguity and Second-Order Belief," Econometrica, Econometric Society, vol. 77(5), pages 1575-1605, September.
    14. Paolo Ghirardato & Marciano Siniscalchi, 2012. "Ambiguity in the Small and in the Large," Econometrica, Econometric Society, vol. 80(6), pages 2827-2847, November.
    15. 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.
    16. Gul, Faruk & Pesendorfer, Wolfgang, 2015. "Hurwicz expected utility and subjective sources," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 465-488.
    17. Jürgen Eichberger & Simon Grant & David Kelsey, 2008. "Differentiating ambiguity: an expository note," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(2), pages 327-336, August.
    18. 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.
    19. Berger, Loïc & Bosetti, Valentina, 2020. "Characterizing ambiguity attitudes using model uncertainty," Journal of Economic Behavior & Organization, Elsevier, vol. 180(C), pages 621-637.
    20. Chateauneuf, Alain & Eichberger, Jurgen & Grant, Simon, 2007. "Choice under uncertainty with the best and worst in mind: Neo-additive capacities," Journal of Economic Theory, Elsevier, vol. 137(1), pages 538-567, November.
    21. Stefania Minardi & Andrei Savochkin, 2017. "Characterizations of Smooth Ambiguity Based on Continuous and Discrete Data," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 167-178, January.
    22. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    23. Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2011. "Rational preferences under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 341-375, October.
    24. Amarante, Massimiliano, 2009. "Foundations of neo-Bayesian statistics," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2146-2173, September.
    25. Robin Cubitt & Gijs van de Kuilen & Sujoy Mukerji, 2020. "Discriminating Between Models of Ambiguity Attitude: a Qualitative Test," Journal of the European Economic Association, European Economic Association, vol. 18(2), pages 708-749.
    26. repec:hal:wpaper:hal-02428398 is not listed on IDEAS
    27. Stanca, Lorenzo, 2020. "A simplified approach to subjective expected utility," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 151-160.
    28. Al-Najjar, Nabil I. & De Castro, Luciano, 2014. "Parametric representation of preferences," Journal of Economic Theory, Elsevier, vol. 150(C), pages 642-667.
    29. , G. & ,, 2010. "Symmetry of evidence without evidence of symmetry," Theoretical Economics, Econometric Society, vol. 5(3), September.
    30. Aurélien Baillon & Han Bleichrodt, 2015. "Testing Ambiguity Models through the Measurement of Probabilities for Gains and Losses," American Economic Journal: Microeconomics, American Economic Association, vol. 7(2), pages 77-100, May.
    31. Baillon, Aurélien & Placido, Lætitia, 2019. "Testing constant absolute and relative ambiguity aversion," Journal of Economic Theory, Elsevier, vol. 181(C), pages 309-332.
    32. Paolo Ghirardato & Marciano Siniscalchi, 2010. "A more robust definition of multiple priors," Carlo Alberto Notebooks 144, Collegio Carlo Alberto.
    33. Weg, Eythan & Rapoport, Amnon & Felsenthal, Dan S., 1990. "Two-person bargaining behavior in fixed discounting factors games with infinite horizon," Games and Economic Behavior, Elsevier, vol. 2(1), pages 76-95, March.
    34. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, January.
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    More about this item

    Keywords

    Symmetry; beliefs; ambiguity; multiple priors; smooth ambiguity;
    All these keywords.

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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