Limit Points of Endogenous Misspecified Learning

59 Pages Posted: 3 Apr 2020 Last revised: 26 May 2020

See all articles by Drew Fudenberg

Drew Fudenberg

Massachusetts Institute of Technology (MIT)

Giacomo Lanzani

Massachusetts Institute of Technology (MIT) - Department of Economics

Philipp Strack

Yale, Department of Economics

Date Written: March 12, 2020

Abstract

We study how a misspecified agent learns from endogenous data when their prior belief does not impose restrictions on the distribution of outcomes, but can assign probability 0 to a neighborhood of the true model. We characterize the stable actions, which have a very high probability of being the long-run outcome for some initial beliefs, and the positively attracting actions, which have a positive probability of being the long-run outcome for any initial full support belief. A Berk-Nash equilibrium is uniformly strict if the equilibrium action is a strict best response to all the outcome distributions that minimize the Kullback-Leibler divergence from the truth, and uniform if the action is a best response to all those distributions. Uniform Berk-Nash equilibria are the unique possible limit actions under a myopic policy. All uniformly strict Berk-Nash equilibria are stable. They are positively attractive under causation neglect, where the agent believes that their action does not influence the outcome, and under correlation neglect, where the agent believes that the outcome distribution associated with one action does not convey information about the outcomes associated with others. We generalize these results to settings where the agent observes a signal before acting.

Keywords: Misspecified Learning, Berk-Nash Equilibrium

Suggested Citation

Fudenberg, Drew and Lanzani, Giacomo and Strack, Philipp, Limit Points of Endogenous Misspecified Learning (March 12, 2020). Available at SSRN: https://ssrn.com/abstract=3553363 or http://dx.doi.org/10.2139/ssrn.3553363

Drew Fudenberg

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Giacomo Lanzani

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

50 Memorial Drive
E52-391
Cambridge, MA 02142
United States

Philipp Strack (Contact Author)

Yale, Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States

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