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The structure of variational preferences

Author

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  • Cerreia-Vioglio, S.
  • Maccheroni, F.
  • Marinacci, M.
  • Rustichini, A.

Abstract

Maccheroni, Marinacci, and Rustichini (2006), in an Anscombe–Aumann framework, axiomatically characterize preferences that are represented by the variational utility functional V(f)=minp∈Δ{∫u(f)dp+c(p)}∀f∈F, where u is a utility function on outcomes and c is an index of uncertainty aversion. In this paper, for a given variational preference, we study the class C of functions c that represent V. Inter alia, we show that this set is fully characterized by a minimal and a maximal element, c⋆ and d⋆. The function c⋆, also identified by Maccheroni, Marinacci, and Rustichini (2006), fully characterizes the decision maker’s attitude toward uncertainty, while the novel function d⋆ characterizes the uncertainty perceived by the decision maker.

Suggested Citation

  • Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M. & Rustichini, A., 2015. "The structure of variational preferences," Journal of Mathematical Economics, Elsevier, vol. 57(C), pages 12-19.
    • Handle: RePEc:eee:mateco:v:57:y:2015:i:c:p:12-19
    DOI: 10.1016/j.jmateco.2015.01.002
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    References listed on IDEAS

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    1. Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M. & Montrucchio, L., 2011. "Uncertainty averse preferences," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1275-1330, July.
    2. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
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    4. 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.
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    6. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    7. 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.
    8. Hanany Eran & Klibanoff Peter, 2009. "Updating Ambiguity Averse Preferences," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-53, November.
    9. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, November.
    10. Luca Rigotti & Chris Shannon & Tomasz Strzalecki, 2008. "Subjective Beliefs and ex ante Trade," Econometrica, Econometric Society, vol. 76(5), pages 1167-1190, September.
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    Cited by:

    1. Matthias Lang, 2017. "First-Order and Second-Order Ambiguity Aversion," Management Science, INFORMS, vol. 63(4), pages 1254-1269, April.
    2. Simone Cerreia-Vioglio & Alfio Giarlotta & Salvatore Greco & Fabio Maccheroni & Massimo Marinacci, 2020. "Rational preference and rationalizable choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(1), pages 61-105, February.
    3. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2015. "On the equality of Clarke-Rockafellar and Greenberg-Pierskalla differentials for monotone and quasiconcave functionals," Working Papers 561, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.

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