Bayesian Updating for General Maxmin Expected Utility Preferences
AbstractA 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1366.
Date of creation: Sep 2001
Date of revision:
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
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.:
- Epstein, Larry G. & Schneider, Martin, 2003.
Journal of Economic Theory,
Elsevier, vol. 113(1), pages 1-31, November.
- Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
- Gilboa Itzhak & Schmeidler David, 1993.
"Updating Ambiguous Beliefs,"
Journal of Economic Theory,
Elsevier, vol. 59(1), pages 33-49, February.
- Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer, vol. 20(1), pages 83-92.
- Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo & Siniscalchi, Marciano, 2001.
"A Subjective Spin on Roulette Wheels,"
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.
- 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.
- David Schmeidler, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Levine's Working Paper Archive
7662, David K. Levine.
- Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
- Epstein, L.G. & Zhang, J., 1998. "Subjective Probabilities on Subjectivity Unambiguous Event," RCER Working Papers 456, University of Rochester - Center for Economic Research (RCER).
- 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.
- Chambers, Robert G. & Melkonyan, Tigran, 2009. "Smoothing preference kinks with information," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 173-189, September.
- Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2002.
"Ambiguity from the Differential Viewpoint,"
1130, California Institute of Technology, Division of the Humanities and Social Sciences.
- Marciano Siniscalchi, 2003.
"A Behavioral Characterization of Plausible Priors,"
1365, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Marciano Siniscalchi, 2006.
"Dynamic Choice Under Ambiguity,"
1430, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Alexander Zimper & Alexander Ludwig, 2007.
MEA discussion paper series
07155, Munich Center for the Economics of Aging (MEA) at the Max Planck Institute for Social Law and Social Policy.
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.