Open AccessActive learning with a misspecified prior
Author(s) -
Fudenberg Drew,
Romanyuk Gleb,
Strack Philipp
Publication year - 2017
Publication title -
theoretical economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.404
H-Index - 32
eISSN - 1555-7561
pISSN - 1933-6837
DOI - 10.3982/te2480
Subject(s) - stochastic game , action (physics) , computer science , simple (philosophy) , mathematical economics , state space , bayesian probability , space (punctuation) , term (time) , artificial intelligence , econometrics , mathematics , statistics , philosophy , physics , epistemology , quantum mechanics , operating system
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.