Learning Cycles in Bertrand Competition with Differentiated Commodities and Competing Learning Rules

This paper stresses the importance of heterogeneity in learning rules. We introduce an evolutionary competition between different learning rules and demonstrate that, though these rules can coexist, their convergence properties are strongly affected by heterogeneity. We consider a Bertrand oligopoly with differentiated goods. Firms do not have full information about the demand structure and they want to maximize their perceived one-period profit by applying one of two different learning rules: OLS learning and gradient learning. We analytically show that the stability of gradient learning depends on the distribution of learning rules over firms. In particular, as the number of gradient learners increases, gradient learning may become unstable. We study evolutionary competition between the learning rules by means of computer simulations and illustrate that this change in stability for gradient learning may lead to cyclical switching between the rules. Stable gradient learning typically gives higher average profit than OLS learning, making firms switch to gradient learning. This however, destabilizes gradient learning which, because of decreasing profits, makes firms switch back to OLS learning. This cycle may repeat itself indefinitely.