Heterogeneous Learning in Bertrand Competition with Differentiated Goods

Abstract

This paper stresses that the coexistence of different learning methods can have a substantial effect on the convergence properties of these methods. We consider a Bertrand oligopoly with differentiated goods in which firms either use least squares learning or gradient learning for determining the price for a given period. These methods are well-established in oligopoly models but, up till now, are used mainly in homogeneous setups. We illustrate that the stability of gradient learning depends on the distribution of learning methods over firms: as the number of gradient learners increases, the method may lose stability and become less profitable. We introduce competition between the learning methods and show that a cyclical switching between the methods may occur.