Eductive Stability May not Imply Evolutionary Stability in the Presence of Information Costs

Starting from a Muthian cobweb model, we extend the profit-based evolutionary setting in Hommes and Wagener (2010) populated by pessimistic, optimistic and unbiased fundamentalists, by assuming that agents face heterogeneous information costs, inversely proportional to the entity of their bias. Hommes and Wagener (2010) proved that, when the unique steady state of their model is globally eductively stable in the sense of Guesnerie (2002), the equilibrium under evolutionary learning may be just locally, but not globally, stable, due to the presence of a period-two cycle. Thanks to the introduction of information costs, we find that the equilibrium, when globally eductively stable, may be not even locally stable under evolutionary learning. More precisely, we analyze our setting by measuring the influence of agents' heterogeneity through the parameter describing the degree of optimism and pessimism. According to the considered parameter configuration, the unique steady state, which coincides with the fundamental, may be (locally or globally) stable for every value of the bias, like in Hommes and Wagener (2010), or it may be stable just for suitably small and for suitably large values of the bias. Hence, increasing beliefs' heterogeneity can be stabilizing when information costs are taken into account. We give an interpretation of such counterintuitive result in terms of profits, on which the share updating rule is based