A Caltech Library Service

The Rational Expectations-n(ϵ)ϵ-Equilibrium

El-Gamal, Mahmoud (1992) The Rational Expectations-n(ϵ)ϵ-Equilibrium. Social Science Working Paper, 823. California Institute of Technology , Pasadena, CA. (Unpublished)

[img] PDF (sswp 823 - Dec. 1992) - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


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)
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:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80856
Deposited By: Jacquelyn Bussone
Deposited On:28 Aug 2017 21:06
Last Modified:03 Oct 2019 18:35

Repository Staff Only: item control page