El-Gamal, Mahmoud (1992) The Rational Expectations-n(ϵ)ϵ-Equilibrium. Social Science Working Paper, 823. California Institute of Technology , Pasadena, CA. (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20170828-135832080
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Abstract
In the rational expectations paradigm, one solves models of a large number of agents who optimize subject to a stochastic law of motion by assuming that all agents know that law of motion. If the agents do not know that law of motion perfectly, one needs a learning model. This paper follows the optimal learning literature by assuming that each agent constructs priors about the unknowns of the problem, and then updates those priors using the Bayes updating rule. The agents need to construct priors on the distribution of other agents' priors, and then on the distribution of priors on the distribution of priors, and so on, leading to an infinite hierarchy of beliefs. The existence of an optimal response given the current state vector and hierarchy of beliefs is proved. It is then shown that the resulting equilibrium, labeled the Rational Expectations-∞ equilibrium can be approximated by an ϵ-equilibrium where the infinite hierarchy is truncated at some level n(ϵ), and each agent believes that all of his higher level beliefs are concentrated at their true values.
Item Type: | Report or Paper (Working Paper) |
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Additional Information: | This paper was motivated in part by lengthy discussions with Peter Bossaerts about equilibrium asset pricing without rational expectations. I am grateful to Kim Border for enlightening technical discussions. All errors are, of course, my own. |
Group: | Social Science Working Papers |
Subject Keywords: | Rational expectations, Bayesian learning, bounded rationality |
Series Name: | Social Science Working Paper |
Issue or Number: | 823 |
Record Number: | CaltechAUTHORS:20170828-135832080 |
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170828-135832080 |
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
ID Code: | 80856 |
Collection: | CaltechAUTHORS |
Deposited By: | Jacquelyn Bussone |
Deposited On: | 28 Aug 2017 21:06 |
Last Modified: | 03 Oct 2019 18:35 |
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