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Variational Bewley Preferences

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  • Faro, José Heleno

Abstract

This paper characterizes variational Bewley preferences over Anscombe and Aumann acts, a class of binary relations that may fail completeness or transitivity vis à vis independence. The main result gives an axiomatization of preference relations ≿ represented as follows:f≿g⇔∫u(f)dp+η(p)≥∫u(g)dp for all p∈Δ, where u is an affine utility index over a convex set X of consequences, η:Δ→[0,∞] is an ambiguity index, and Δ is the set of priors over the state space S. This representation has a natural interpretation as a weighted unanimity rule, with the function η reflecting the weight given to a prior and higher values of η corresponding to priors given less weight. Bewley's incomplete preferences can be identified precisely with the addition of transitivity or independence, and a prior receives weight either 0 if plausible or ∞ when discarded. Also, by adding only completeness, we recover subjective expected utility, i.e., the lack of transitivity implies incompleteness. Finally, we find a strong connection of our model with the class of variational preferences.
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Suggested Citation

  • Faro, José Heleno, 2011. "Variational Bewley Preferences," Insper Working Papers wpe_258, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
  • Handle: RePEc:ibm:ibmecp:wpe_258
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Minardi, Stefania & Savochkin, Andrei, 2015. "Preferences with grades of indecisiveness," Journal of Economic Theory, Elsevier, vol. 155(C), pages 300-331.
    2. Dana, Rose-Anne & Riedel, Frank, 2013. "Intertemporal equilibria with Knightian uncertainty," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1582-1605.
    3. Hill, Brian, 2011. "Deferral, incomplete preferences and confidence," Les Cahiers de Recherche 940, HEC Paris.
    4. Beißner, Patrick & Riedel, Frank, 2016. "Knight-Walras equilibria," Center for Mathematical Economics Working Papers 558, Center for Mathematical Economics, Bielefeld University.
    5. Beißner, Patrick, 2016. "Radner Equilibria under Ambiguous Volatility," Center for Mathematical Economics Working Papers 493, Center for Mathematical Economics, Bielefeld University.
    6. repec:ipg:wpaper:2013-016 is not listed on IDEAS
    7. repec:dau:papers:123456789/11268 is not listed on IDEAS
    8. Riella, Gil & Teper, Roee, 2014. "Probabilistic dominance and status quo bias," Games and Economic Behavior, Elsevier, vol. 87(C), pages 288-304.
    9. repec:dau:papers:123456789/5375 is not listed on IDEAS
    10. repec:ipg:wpaper:16 is not listed on IDEAS
    11. repec:spr:joecth:v:64:y:2017:i:2:d:10.1007_s00199-016-0979-y is not listed on IDEAS
    12. Hill, Brian, 2016. "Incomplete preferences and confidence," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 83-103.
    13. S. Cerreia-Vioglio & A. Giarlotta & S. Greco & F. Maccheroni & M. Marinacci, 2016. "Rational Preference and Rationalizable Choice," Working Papers 589, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    14. Georgios Gerasimou, 2016. "On the Indifference Relation in Bewley Preferences," Discussion Paper Series, Department of Economics 201609, Department of Economics, University of St. Andrews, revised 11 Dec 2017.

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    JEL classification:

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

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