Active Learning with Misspecified Beliefs
35 Pages Posted: 9 Feb 2016 Last revised: 28 Feb 2016
Date Written: February 11, 2016
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.
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