Adaptive Expectations Coordination in an Economy with Heterogeneous Agents

In this paper I study expectations coordination on the stationary state in a one-dimensional economy. I allow for two sources of heterogeneity: the first concerns the "fundamentals", the second concerns the adaptive learning rules. Specifically, I consider heterogeneous adaptive learning algorithm within a class of constant gain learning algorithm, where the parameter of gain differ across agents. We show that the interaction of these two sources of heterogeneity create difficulty to coordination. Our first result says that the condition for convergence of dynamics with learning in an economy with heterogeneity is equivalent to the condition for convergence in an economy with identical agents if and only if the partial derivative of the temporary equilibrium map with respect to agents' expectations are all of the same sign. Our second results say that when the signs of these partial derivatives are different across agents, there exist some regions in the parameters space in which convergence of dynamics with learning obtains under a kind of "corridor of stability". This means that, given the reaction coefficient of type 2 agents, coordination on the stationary state obtains if and only if the reaction coefficient of type 1 agents is neither too small nor too large. We give two examples concerning a cobweb and an overlapping generations economy.