Active learning with a misspecified prior
Author(s)Fudenberg, Drew; Romanyuk, Gleb; Strack, Philipp
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We study learning and information acquisition by a Bayesian agent whose prior belief is misspecified in the sense that it assigns probability 0 to the true state of the world. At each instant, the agent takes an action and observes the corresponding payoff, which is the sum of a fixed but unknown function of the action 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 illustrates a novel interaction between misspecification and the agent's subjective discount rate.
DepartmentMassachusetts Institute of Technology. Department of Economics
The Econometric Society
Fudenberg, Drew, Gleb Romanyuk, and Philipp Strack. “Active Learning with a Misspecified Prior.” Theoretical Economics 12, no. 3 (September 2017): 1155–1189.
Final published version