Bayesian Updating for General Maxmin Expected Utility Preferences
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.
|Date of creation:||Sep 2001|
|Contact details of provider:|| Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014|
Web page: http://www.kellogg.northwestern.edu/research/math/
More information through EDIRC
|Order Information:|| Email: |
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.:
- Peter Klibanoff, 2001. "Stochastically independent randomization and uncertainty aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(3), pages 605-620.
- Itzhak Gilboa & David Scheidler, 1993.
"Updating Ambiguous Beliefs,"
- Larry G. Epstein & Martin Schneider, 2001.
RCER Working Papers
485, University of Rochester - Center for Economic Research (RCER).
- Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 83-92.
- Gilboa, Itzhak & Schmeidler, David, 1989.
"Maxmin expected utility with non-unique prior,"
Journal of Mathematical Economics,
Elsevier, vol. 18(2), pages 141-153, April.
- Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2003.
"A Subjective Spin on Roulette Wheels,"
Econometric Society, vol. 71(6), pages 1897-1908, November.
- Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2001. "A subjective spin on roulette wheels," ICER Working Papers - Applied Mathematics Series 17-2001, ICER - International Centre for Economic Research, revised Aug 2001.
- 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.
- Roger B. Myerson, 1984.
"Multistage Games with Communication,"
590, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- 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.
- Epstein, Larry G & Zhang, Jiankang, 2001.
"Subjective Probabilities on Subjectively Unambiguous Events,"
Econometric Society, vol. 69(2), pages 265-306, March.
- Larry G. Epstein & Jiankang Zhang, 1999. "Subjective Probabilities on Subjectively Unambiguous Events," Carleton Economic Papers 99-18, Carleton University, Department of Economics.
- Schmeidler, David, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Econometric Society, vol. 57(3), pages 571-587, May.
- David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
- Epstein, L.G. & Zhang, J., 1998. "Subjective Probabilities on Subjectivity Unambiguous Event," RCER Working Papers 456, University of Rochester - Center for Economic Research (RCER).
When requesting a correction, please mention this item's handle: RePEc:nwu:cmsems:1366. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Fran Walker)
If references are entirely missing, you can add them using this form.