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On stochastic independence under ambiguity

Author

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  • Federica Ceron

    (University of Paris 1 Panthéon-Sorbonne)

  • Vassili Vergopoulos

    (University of Paris 1 Panthéon-Sorbonne)

Abstract

We provide behavioral characterizations of notions of stochastic independence between two sources of uncertainty for agents with ambiguity-sensitive preferences. These notions, inspired from the literature on imprecise probabilities, include the independent product of two sets of marginal beliefs proposed by Gilboa and Schmeidler (J Math Econ 18(2): 141–153, 1989) in their seminal paper. Our analysis draws a clear relationship between the property of dynamic consistency of preferences and some form of stochastic independence between the relevant events.

Suggested Citation

  • Federica Ceron & Vassili Vergopoulos, 2021. "On stochastic independence under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 925-960, April.
    • Handle: RePEc:spr:joecth:v:71:y:2021:i:3:d:10.1007_s00199-020-01267-z
    DOI: 10.1007/s00199-020-01267-z
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    References listed on IDEAS

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    1. 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.
    2. Sujoy Mukerji & Jean-Marc Tallon, 2005. "Ambiguity aversion and the absence of indexed debt," Studies in Economic Theory, in: Alessandro Citanna & John Donaldson & Herakles Polemarchakis & Paolo Siconolfi & Stephan E. Spear (ed.), Essays in Dynamic General Equilibrium Theory, pages 143-179, Springer.
    3. Lawrence Blume & Adam Brandenburger & Eddie Dekel, 2014. "Lexicographic Probabilities and Choice Under Uncertainty," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 6, pages 137-160, World Scientific Publishing Co. Pte. Ltd..
    4. Alain Chateauneuf & Jürgen Eichberger & Simon Grant, 2003. "A simple axiomatization and constructive representation proof for choquet expected utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(4), pages 907-915, November.
    5. 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.
    6. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    7. ,, 2011. "Dynamic choice under ambiguity," Theoretical Economics, Econometric Society, vol. 6(3), September.
    8. Alain Chateauneuf & Fabio Maccheroni & Massimo Marinacci & Jean-Marc Tallon, 2005. "Monotone continuous multiple priors," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 973-982, November.
    9. Leonardo Pejsachowicz, 2016. "Stochastic Independence under Knightian Uncertainty," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01753323, HAL.
    10. Mark Machina, 2011. "Event-Separability in the Ellsberg urn," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 425-436, October.
    11. Epstein Larry G. & Le Breton Michel, 1993. "Dynamically Consistent Beliefs Must Be Bayesian," Journal of Economic Theory, Elsevier, vol. 61(1), pages 1-22, October.
    12. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    13. De Castro, Luciano & Yannelis, Nicholas C., 2018. "Uncertainty, efficiency and incentive compatibility: Ambiguity solves the conflict between efficiency and incentive compatibility," Journal of Economic Theory, Elsevier, vol. 177(C), pages 678-707.
    14. de Castro, Luciano I. & Liu, Zhiwei & Yannelis, Nicholas C., 2017. "Implementation under ambiguity," Games and Economic Behavior, Elsevier, vol. 101(C), pages 20-33.
    15. Mongin, Philippe & Pivato, Marcus, 2015. "Ranking multidimensional alternatives and uncertain prospects," Journal of Economic Theory, Elsevier, vol. 157(C), pages 146-171.
    16. Leonardo Pejsachowicz, 2016. "Stochastic Independence under Knightian Uncertainty," Revue d'économie politique, Dalloz, vol. 126(3), pages 379-398.
    17. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    18. Matthew J. Ryan, 2002. "What do uncertainty-averse decision-makers believe?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 47-65.
    19. Benoit Decerf & Frank Riedel, 2020. "Purification and disambiguation of Ellsberg equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(3), pages 595-636, April.
    20. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, vol. 71(2), pages 443-484, November.
    21. 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.
    22. Kota Saito, 2015. "Preferences for Flexibility and Randomization under Uncertainty," American Economic Review, American Economic Association, vol. 105(3), pages 1246-1271, March.
    23. Cesaltina Pacheco Pires, 2002. "A Rule For Updating Ambiguous Beliefs," Theory and Decision, Springer, vol. 53(2), pages 137-152, September.
    24. Alon, Shiri & Schmeidler, David, 2014. "Purely subjective Maxmin Expected Utility," Journal of Economic Theory, Elsevier, vol. 152(C), pages 382-412.
    25. Mark J. Machina, 2014. "Ambiguity Aversion with Three or More Outcomes," American Economic Review, American Economic Association, vol. 104(12), pages 3814-3840, December.
    26. Tatjana Chudjakow & Frank Riedel, 2013. "The best choice problem under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 77-97, September.
    27. Leonardo Pejsachowicz, 2016. "Stochastic Independence under Knightian Uncertainty," Post-Print hal-01753323, HAL.
    28. Marciano Siniscalchi, 2001. "Bayesian Updating for General Maxmin Expected Utility Preferences," Discussion Papers 1366, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    Cited by:

    1. Michel Grabisch & Benjamin Monet & Vassili Vergopoulos, 2023. "Subjective expected utility through stochastic independence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(3), pages 723-757, October.

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    More about this item

    Keywords

    Stochastic independence; Ambiguity; MaxMin expected utility; Bewley expected utility; Imprecise probability;
    All these keywords.

    JEL classification:

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

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