Coexisting stable equilibria under least squares learning

This paper illustrates that least squares learning may lead to sub-optimal outcomes even when firms observe all the variables that affect their demand and they use a locally correct functional form in the estimation. We consider the Salop model with three firms and two types of consumers that face different transportation costs. Firms do not know the demand structure and they apply least squares learning to learn the demand function. In each period, firms estimate a linear perceived demand function and they play the perceived best response to the previous-period price of the other firms. This learning rule can lead to three different outcomes: a self-sustaining equilibrium, the Nash equilibrium or an asymmetric learning-equilibrium in which one firm focuses only on the consumers with high transportation costs. The latter equilibria are locally stable therefore the model has coexisting stable equilibria. We analyze the conditions under which the different outcomes are reached.