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Ambiguity from the Differential Viewpoint

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  • Ghirardato, Paolo
  • Maccheroni, Fabio
  • Marinacci, Massimo

Abstract

The objective of this paper is to show how ambiguity, and a decision maker (DM)'s response to it, can be modelled formally in the context of a very general decision model. In the first part of the paper we introduce an "unambiguous preference" relation derived from the DM's preferences, and show that it can be represented by a set of probability measures. We provide such set with a simple differential interpretation and argue that it represents the DM's perception of the "ambiguity" present in the decision problem. Given the notion of ambiguity, we show that preferences can be represented so as to provide an intuitive representation of ambiguity attitudes. In the second part of the paper we provide some extensions and "applications" of these ideas. We present an axiomatic characterization of the "alfa"-MEU decision rule. We also consider a simple dynamic choice setting and show the characterization of the updating rule that revises every prior in the afore-mentioned set by Bayes's rule; i.e., the generalized Bayesian updating rule.
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Suggested Citation

  • Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2002. "Ambiguity from the Differential Viewpoint," Working Papers 1130, California Institute of Technology, Division of the Humanities and Social Sciences.
    • Handle: RePEc:clt:sswopa:1130
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    File URL: http://www.hss.caltech.edu/SSPapers/wp1130.pdf
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    2. Maccheroni, Fabio & Marinacci, Massimo & Rustichini, Aldo, 2006. "Dynamic variational preferences," Journal of Economic Theory, Elsevier, vol. 128(1), pages 4-44, May.
    3. Salvatore Modica & Marco Scarsini, 2003. "The convexity-cone approach to comparative risk and downside risk," ICER Working Papers - Applied Mathematics Series 01-2003, ICER - International Centre for Economic Research.
    4. Taizhong Hu & Alfred Müller & Marco Scarsini, 2002. "Some Counterexamples in Positive Dependence," ICER Working Papers - Applied Mathematics Series 28-2003, ICER - International Centre for Economic Research, revised Jul 2003.
    5. Ken Binmore, 2016. "A minimal extension of Bayesian decision theory," Theory and Decision, Springer, vol. 80(3), pages 341-362, March.
    6. Daniele Pennesi, 2013. "Endogenous Status Quo," Carlo Alberto Notebooks 314, Collegio Carlo Alberto.
    7. Gajdos, Thibault & Maurin, Eric, 2004. "Unequal uncertainties and uncertain inequalities: an axiomatic approach," Journal of Economic Theory, Elsevier, vol. 116(1), pages 93-118, May.
    8. Bruno Girotto & Silvano Holzer, 2003. "Representing complete and incomplete subjective linear preferences on random numbers," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 26(2), pages 129-144, November.
    9. Müller, Alfred & Scarsini, Marco, 2005. "Archimedean copulæ and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 434-445, April.
    10. Gajdos, Thibault & Tallon, Jean-Marc & Vergnaud, Jean-Christophe, 2004. "Decision making with imprecise probabilistic information," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 647-681, September.
    11. Erin Baker & Valentina Bosetti & Ahti Salo, 2017. "Finding common ground when experts disagree: Robust portfolio decision analysis," Working Papers 2017/11, Institut d'Economia de Barcelona (IEB).
    12. Siniscalchi, Marciano, 2006. "A behavioral characterization of plausible priors," Journal of Economic Theory, Elsevier, vol. 128(1), pages 91-135, May.
    13. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On consistency of nonparametric normal mixtures for Bayesian density estimation," ICER Working Papers - Applied Mathematics Series 23-2004, ICER - International Centre for Economic Research.
    14. Renault, Jerome & Scarlatti, Sergio & Scarsini, Marco, 2005. "A folk theorem for minority games," Games and Economic Behavior, Elsevier, vol. 53(2), pages 208-230, November.
    15. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On rates of convergence for posterior distributions in infinite–dimensional models," ICER Working Papers - Applied Mathematics Series 24-2004, ICER - International Centre for Economic Research.
    16. Claude Henry, 2005. "Du risque à l'incertitude dans les modèles de décisions," Working Papers hal-00242967, HAL.
    17. Baker, Erin & Bosetti, Valentina & Salo, Ahti, 2020. "Robust portfolio decision analysis: An application to the energy research and development portfolio problem," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1107-1120.
    18. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "Contributions to the understanding of Bayesian consistency," ICER Working Papers - Applied Mathematics Series 13-2004, ICER - International Centre for Economic Research.
    19. Henry, Marc, 2007. "A representation of decision by analogy," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 771-794, September.
    20. Castagnoli, Erio & Maccheroni, Fabio & Marinacci, Massimo, 2002. "Insurance premia consistent with the market," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 267-284, October.
    21. Hartmann, Lorenz, 2023. "Strength of preference over complementary pairs axiomatizes alpha-MEU preferences," Journal of Economic Theory, Elsevier, vol. 213(C).

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