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Ambiguity from the Differential Viewpoint

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  • Paolo Ghirardato

    ()

  • Fabio Maccheroni

    ()

  • Massimo Marinacci

    ()

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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Bibliographic 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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  1. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
  2. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
  3. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2003. "A Subjective Spin on Roulette Wheels," Econometrica, Econometric Society, vol. 71(6), pages 1897-1908, November.
  4. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  5. 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.
  6. Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Levine's Working Paper Archive 7616, David K. Levine.
  7. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
  8. 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.
  9. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer, vol. 20(1), pages 83-92.
  10. 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.
  11. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  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.
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