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Journal of Economic Theory
Volume 124, Issue 2, October 2005, Pages 258-301
Learning and Bounded Rationality
 
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doi:10.1016/j.jet.2005.06.006    
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Copyright © 2005 Published by Elsevier Inc.

Robust estimation and control under commitment

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Lars Peter Hansena, E-mail The Corresponding Author and Thomas J. Sargentb, Corresponding Author Contact Information, E-mail The Corresponding Author

aUniversity of Chicago, Chicago, USA

bNew York University, Hoover Institution, New York, NY 10003, USA


Received 4 January 2005; 
revised 28 June 2005. 
Available online 28 September 2005.

Abstract

In a Markov decision problem with hidden state variables, a decision maker expresses fear that his model is misspecified by surrounding it with a set of alternatives that are nearby as measured by their expected log likelihood ratios (entropies). Sets of martingales represent alternative models. Within a two-player zero-sum game under commitment, a minimizing player chooses a martingale at time 0. Probability distributions that solve distorted filtering problems serve as state variables, much like the posterior in problems without concerns about misspecification. We state conditions under which an equilibrium of the zero-sum game with commitment has a recursive representation that can be cast in terms of two risk-sensitivity operators. We apply our results to a linear quadratic example that makes contact with findings of T. Başar and P. Bernhard [H-Optimal Control and Related Minimax Design Problems, second ed., Birkhauser, Basel, 1995] and P. Whittle [Risk-sensitive Optimal Control, Wiley, New York, 1990].

Keywords: Learning; Model uncertainty; Bayes’ law; Entropy; Robustness; Risk-sensitivity; Commitment; Time inconsistency

JEL classification: C32; C52; D81; D83; D84


Corresponding Author Contact InformationCorresponding author.
1 This epigraph is quoted by Georgii [12, p. 37].

Journal of Economic Theory
Volume 124, Issue 2, October 2005, Pages 258-301
Learning and Bounded Rationality
 
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