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 non-convergence 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.