Learning In Mis-Specified Models And The Possibility Of Cycles

Abstract I study the problem of a monopolist maximizing a sum of discounted profits facing a linear demand curve whose slope and intercept are unknown. I show that if the monopolist has a mis-specified model, i.e., if the true slope and intercept lie outside of the support of the monopolist's prior beliefs, then actions and beliefs may cycle on every sample path. This behavior is shown to be robust to perturbations in the prior, true parameter, and actions. Such behavior is not possible if the agent's model is correctly specified; instead actions and beliefs necessarily converge.

[1]  L. J. Savage,et al.  The Foundations of Statistics , 1955 .

[2]  M. Rothschild A two-armed bandit theory of market pricing , 1974 .

[3]  David M. Kreps,et al.  Rational Learning and Rational Expectations , 1987 .

[4]  L. Blume,et al.  Learning to be rational , 1982 .

[5]  N. Kiefer,et al.  Optimal Control of an Unknown Linear Process with Learning , 1989 .

[6]  Keigo Yamada Asymptotic behavior of posterior distributions for random processes under incorrect models , 1976 .

[7]  Kazuo Nishimura,et al.  Competitive equilibrium cycles , 1985 .

[8]  E. Prescott THE MULTI-PERIOD CONTROL PROBLEM UNDER UNCERTAINTY , 1972 .

[9]  John B. Taylor Asymptotic Properties of Multiperiod Control Rules in the Linear Regression Model , 1974 .

[10]  Mark Feldman An Example of Convergence to Rational Expectations with Heterogeneous Beliefs , 1987 .

[11]  A. McLennan Price dispersion and incomplete learning in the long run , 1984 .

[12]  Roman Frydman,et al.  Towards an Understanding of Market Processes: Individual Expectations, Market Behavior and Convergence to Rational Expectations Equilibrium , 1981 .

[13]  Diversity of Information, Least Squares Learning Rules, and Market Behavior , 1988 .

[14]  Michael Frierman,et al.  Learning Rational Expectations: Classical Conditions Ensure Uniqueness And Global Stability , 1990 .

[15]  R. Radner Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices , 1979 .

[16]  T. Sargent,et al.  Convergence of Least Squares Learning Mechanisms in Self- Referential Linear Stochastic Models* , 1989 .

[17]  Yaw Nyarko On the convergence of Bayesian posterior processes in linear economic models Counting equations and unknowns , 1991 .

[18]  M. Bray Learning, estimation, and the stability of rational expectations , 1982 .

[19]  D. Freedman On the Asymptotic Behavior of Bayes' Estimates in the Discrete Case , 1963 .

[20]  D. Blackwell Discounted Dynamic Programming , 1965 .

[21]  Mark Feldman,et al.  On the generic nonconvergence of Bayesian actions and beliefs , 1990 .

[22]  L. Blume,et al.  Rational expectations equilibrium: An alternative approach , 1984 .

[23]  N. Kiefer,et al.  Controlling a Stochastic Process with Unknown Parameters , 1988 .

[24]  M. Woodford Learning to Believe in Sunspots , 1990 .