Eductive Stability, Heterogeneous Information Costs and Period-Two Cycle Multiplicity

Starting from a Muthian cobweb model, we here extend the profit-based evolutionary settings in Hommes and Wagener (2010) and in Naimzada and Pireddu (2020a) by assuming that unbiased fundamentalists and several groups of biased fundamentalists face information costs that are inversely proportional to their bias. Like in those works, we deal with the case in which the model is globally eductively stable, being globally stable under naive expectations. Similarly to Naimzada and Pireddu (2020a), we find that the stability of the unique steady state, which coincides with the fundamental, holds either for every value of the bias, like in Hommes and Wagener (2010), or just for suitably small and large values of the bias. On the other hand, introducing into the economy new couples of symmetrically biased groups of fundamentalists with a sufficiently high bias, multiple coexisting locally stable period-two cycles emerge. While in Hommes and Wagener (2010) such phenomenon occurs only when the steady state is locally stable, we observe the coexistence of multiple locally stable period-two cycles also when the equilibrium is unstable, thanks to information costs. Moreover, we show that the relative position of the newly arisen period-two cycles may not coincide with and without information costs.