Active Learning with Misspecified Beliefs

35 Pages Posted: 9 Feb 2016 Last revised: 28 Feb 2016

Drew Fudenberg

Harvard University - Department of Economics

Gleb Romanyuk

Harvard University

Philipp Strack

University of California, Berkeley - Department of Economics

Date Written: February 11, 2016

Abstract

We study learning and information acquisition by a Bayesian agent who is misspecified in the sense that his prior belief assigns probability zero to the true state of the world. In our model, at each instant the agent takes an action and observes the corresponding payoff, which is the sum of the payoff generated by a fixed but unknown function and an additive error term. We provide a complete characterization of asymptotic actions and beliefs when the agent's subjective state space is a doubleton. A simple example with three actions shows that in a misspecified environment a myopic agent's beliefs converge while a sufficiently patient agent's beliefs do not. This shows that examples of myopic agents with non-converging beliefs in the prior literature require all myopically optimal actions to be informative, and illustrates a novel interaction between misspecification and the agent's subjective interest rate.

Suggested Citation

Fudenberg , Drew and Romanyuk, Gleb and Strack, Philipp, Active Learning with Misspecified Beliefs (February 11, 2016). Available at SSRN: https://ssrn.com/abstract=2729537 or http://dx.doi.org/10.2139/ssrn.2729537

Drew Fudenberg

Harvard University - Department of Economics ( email )

Littauer Center
Room 310
Cambridge, MA 02138
United States
617-496-5895 (Phone)
617-495-7730 (Fax)

Gleb Romanyuk (Contact Author)

Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

Philipp Strack

University of California, Berkeley - Department of Economics ( email )

549 Evans Hall #3880
Berkeley, CA 94720-3880
United States

HOME PAGE: http://philippstrack.com

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