Convergence to Rational Expectations in a Stationary Linear Game

Abstract

This paper describes several learning processes which converge, with probability one, to the rational expectations (Bayesian-Nash) equilibrium of a stationary linear game. The learning processes include a test for convergence to equilibrium, and a method for changing the parameters of the process when nonconvergence is indicated. This self-stabilization property eliminates the need to impose stability conditions on the economic environment. Convergence to equilibrium is proved for two types of self-stabilizing learning mechanisms: a centralized forecasting mechanism and a decentralized strategy adjustment process. For a version of the decentralized process it is also shown that the publicly observable information, on which learning is based, does not necessarily reveal anything about the economic environment except the equilibrium.