Models of Subjective Learning

39 Pages Posted: 13 Dec 2011

See all articles by David Dillenberger

David Dillenberger

University of Pennsylvania - Department of Economics

Philipp Sadowski

Duke University - Department of Economics

Date Written: December 12, 2011

Abstract

We study a decision maker who faces a dynamic decision problem in which the process of information arrival is subjective. By studying preferences over menus of acts, we derive a sequence of utility representations that captures the decision maker’s uncertainty about the beliefs he will hold when choosing from a menu. In the most general model of second-order beliefs, we characterize a notion of "more preference for flexibility" via a subjective analogue of Blackwell’s (1951, 1953) comparisons of experiments. We proceed to analyze a model in which signals are subsets of the state space. The corresponding representation enables us to compare the behavior of two decision makers who expect to learn differently, even if they do not agree on their prior beliefs. The class of information systems that can support such a representation generalizes the notion of modeling information as a partition of the state space. We apply the model to study a decision maker who anticipates subjective uncertainty to be resolved gradually over time. We derive a representation that uniquely identifies both the filtration, which is the timing of information arrival with the sequence of partitions it induces, and the decision maker’s prior beliefs.

Keywords: Resolution of uncertainty, second-order beliefs, preference for flexibility, valuing binary bets more, generalized partition

JEL Classification: D80, D81

Suggested Citation

Dillenberger, David and Sadowski, Philipp, Models of Subjective Learning (December 12, 2011). PIER Working Paper No. 11-042. Available at SSRN: https://ssrn.com/abstract=1971259 or http://dx.doi.org/10.2139/ssrn.1971259

David Dillenberger (Contact Author)

University of Pennsylvania - Department of Economics ( email )

Ronald O. Perelman Center for Political Science
133 South 36th Street
Philadelphia, PA 19104-6297
United States
215-898-1503 (Phone)

Philipp Sadowski

Duke University - Department of Economics ( email )

213 Social Sciences Building
Box 90097
Durham, NC 27708-0204
United States
919-660-1800 (Phone)

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