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Ambiguity from the Differential Viewpoint

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Author Info
Paolo Ghirardato ()
Fabio Maccheroni ()
Massimo Marinacci ()

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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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Publisher Info
Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 17-2002.

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Length: 76 pages
Date of creation: Apr 2002
Date of revision:
Handle: RePEc:icr:wpmath:17-2002

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo & Siniscalchi, Marciano, 2001. "A Subjective Spin on Roulette Wheels," Working Papers 1127, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
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  2. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March. [Downloadable!] (restricted)
  3. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April. [Downloadable!] (restricted)
  4. Larry G. Epstein & Martin Schneider, 2001. "Recursive Multiple-Priors," RCER Working Papers 485, University of Rochester - Center for Economic Research (RCER). [Downloadable!]
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  5. Larry G. Epstein & Jiankang Zhang, 1999. "Subjective Probabilities on Subjectively Unambiguous Events," Carleton Economic Papers 99-18, Carleton University, Department of Economics. [Downloadable!]
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  6. Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity and the Separation of Utility and Beliefs," Econometric Society World Congress 2000 Contributed Papers 1143, Econometric Society. [Downloadable!]
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  7. Marinacci, Massimo & Montrucchio, Luigi, 2004. "A characterization of the core of convex games through Gateaux derivatives," Journal of Economic Theory, Elsevier, vol. 116(2), pages 229-248, June. [Downloadable!] (restricted)
  8. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May. [Downloadable!] (restricted)
  9. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February. [Downloadable!] (restricted)
  10. 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. [Downloadable!]
  11. Fox, Craig R & Tversky, Amos, 1995. "Ambiguity Aversion and Comparative Ignorance," The Quarterly Journal of Economics, MIT Press, vol. 110(3), pages 585-603, August. [Downloadable!] (restricted)
  12. Heath, Chip & Tversky, Amos, 1991. " Preference and Belief: Ambiguity and Competence in Choice under Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 4(1), pages 5-28, January.
  13. Truman F. Bewley, 1986. "Knightian Decision Theory: Part 1," Cowles Foundation Discussion Papers 807, Cowles Foundation, Yale University. [Downloadable!]
  14. Ghirardato, Paolo & Katz, Jonathan N., 2000. "Indecision Theory: Explaining Selective Abstention in Multiple Elections," Working Papers 1106, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Marciano Siniscalchi, 2003. "A Behavioral Characterization of Plausible Priors," Levine's Bibliography 234936000000000064, UCLA Department of Economics. [Downloadable!]
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  2. Ghirardato, Paolo & Katz, Jonathan N., 2000. "Indecision Theory: Explaining Selective Abstention in Multiple Elections," Working Papers 1106, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  3. 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. [Downloadable!]
  4. Thibault Gajdos & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2002. "Decision Making with Imprecise Probabilistic Information," ICER Working Papers - Applied Mathematics Series 18-2003, ICER - International Centre for Economic Research, revised May 2003. [Downloadable!]
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  5. Massimiliano Amarante, 2003. "Ambiguity, Measurability and Multiple Priors," Discussion Papers 0203-23, Columbia University, Department of Economics. [Downloadable!]
  6. Thibault Gajdos & Eric Maurin, 2002. "Unequal uncertainties and uncertain inequalities: an axiomatic approach," ICER Working Papers - Applied Mathematics Series 15-2003, ICER - International Centre for Economic Research, revised Mar 2003. [Downloadable!]
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  7. Bruno Girotto & Silvano Holzer, 2003. "Representing complete and incomplete subjective linear preferences on random numbers," Decisions in Economics and Finance, Springer, vol. 26(2), pages 129-144, November. [Downloadable!] (restricted)
  8. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Dynamic Variational Preferences," Carlo Alberto Notebooks 1, Collegio Carlo Alberto. [Downloadable!]
    Other versions:
  9. 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. [Downloadable!]
  10. Erio Castagnoli & Fabio Maccheroni & Massimo Marinacci, 2002. "Insurance Premia Consistent with the Market," ICER Working Papers - Applied Mathematics Series 24-2002, ICER - International Centre for Economic Research. [Downloadable!]
    Other versions:
  11. Massimiliano Amarante, 2003. "Ambiguous Events," Discussion Papers 0304-04, Columbia University, Department of Economics. [Downloadable!]
  12. Alfred Müller & Marco Scarsini, 2003. "Archimedean Copulae and Positive Dependence," ICER Working Papers - Applied Mathematics Series 25-2003, ICER - International Centre for Economic Research. [Downloadable!]
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  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. [Downloadable!]
  14. 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. [Downloadable!]
  15. 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. [Downloadable!]
  16. Chateauneuf, Alain & Eichberger, Jürgen & Grant, Simon, 2003. "Choice under Uncertainty with the Best and Worst in Mind: Neo-additive Capacities," Sonderforschungsbereich 504 Publications 03-10, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim. [Downloadable!]
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  17. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2002. "A smooth model of decision making under ambiguity," ICER Working Papers - Applied Mathematics Series 11-2003, ICER - International Centre for Economic Research, revised Apr 2003. [Downloadable!]
    Other versions:
  18. Sujoy Mukerji, 2003. "Ambiguity Aversion and Cost-Plus Procurement Contracts," Economics Series Working Papers 171, University of Oxford, Department of Economics. [Downloadable!]
    Other versions:
  19. Jerome Renault & Sergio Scarlatti & Marco Scarsini, 2003. "A folk theorem for minority games," ICER Working Papers - Applied Mathematics Series 10-2003, ICER - International Centre for Economic Research. [Downloadable!]
    Other versions:
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