Learning to Believe in Sunspots

An adaptive learning rule is exhibited for the Azariadis (1981) overlapping generations model of a monetary economy with multiple equilibria, under which the economy may converge to a stationary sunspot equilibrium, even if agents do not initially believe that outcomes are significantly different in different "sunspot" states. The type of learning rule studied is of the "stochastic approximation" form studied by Robbins and Monro (1951); methods for analyzing the convergence of this form of algorithm are presented that may be of use in many other contexts as well. Conditions are given under which convergence to a sunspot equilibrium occurs with probability one