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Bayesian Updating for General Maxmin Expected Utility Preferences

  • Marciano Siniscalchi

A characterization of “generalized Bayesian updating” in a maxmin expected utility setting is provided. The key axioms are consequentialism and constant-act dynamic consistency. The latter requires that, if an arbitrary act f is preferred (inferior) to a constant act y conditional upon E, and if f dominates (is dominated by) y pointwise on the complementary event Ec, then f is unconditionally preferred (inferior) to y. The result provides a basis for a model of dynamic choice that accommodates arbitrary unconditional maxmin EU preferences, and allows for deviations from full dynamic consistency related to ambiguity. Standard Expected Utility (EU) preferences are separable across events. In a static setting, the notion of separability is formalized by Savage’s Postulate P2 (the “Sure-Thing Principle”). In a dynamic framework, separability corresponds to dynamic consistency: if the decision maker would prefer some course of action to another if she learned that some event has obtained, and also if she learned that the same event has not obtained, then she should prefer it even prior to learning whether or not the event in question has obtained. As is well-known, P2 and dynamic consistency are closely related (see e.g. Ghirardato, 2001). In a static setting, Ellsberg (1961) demonstrates that separability may fail if the decision maker perceives some ambiguity in the relative likelihood of events. Thus, in a dynamic setting, it is at least plausible to expect some tension between ambiguity and dynamic consistency. Recent experimental evidence (Cohen et al., 2000) based on a dynamic version of the single-urn Ellsberg example seems to indicate that ambiguity may indeed lead to violations of dynamic consistency.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1366.

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Date of creation: Sep 2001
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Handle: RePEc:nwu:cmsems:1366
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  1. Epstein, L.G. & Zhang, J., 1998. "Subjective Probabilities on Subjectivity Unambiguous Event," RCER Working Papers 456, University of Rochester - Center for Economic Research (RCER).
  2. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
  3. Peter Klibanoff, 2001. "Stochastically independent randomization and uncertainty aversion," Economic Theory, Springer, vol. 18(3), pages 605-620.
  4. Roger B. Myerson, 1984. "Multistage Games with Communication," Discussion Papers 590, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
  6. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  7. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  8. 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.
  9. Cohen, M. & Gilboa, I. & Jaffray, J.Y. & Schmeidler, D., 2000. "An experimental study of updating ambiguous beliefs," Risk, Decision and Policy, Cambridge University Press, vol. 5(02), pages 123-133, June.
  10. Larry G. Epstein & Jiankang Zhang, 1999. "Subjective Probabilities on Subjectively Unambiguous Events," Carleton Economic Papers 99-18, Carleton University, Department of Economics.
  11. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer, vol. 20(1), pages 83-92.
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