We investigate the stability properties of Muth's model of price movements when agents choose a production level using replicator dynamic learning. It turns out that when there is a discrete set of possible production levels, possible stable states and stability conditions differ between adaptive learning and replicator dynamic learning.

This paper explores the equilibrium properties of boundedly rational heterogeneous agents under adaptive learning. In a modified cobweb model with a Stackelberg framework, there is an asymmetric information diffusion process from leading to following firms. It turns out that the conditions for at least one learnable equilibrium are similar to those under homogeneous expectations. However, the introduction of information diffusion leads to the possibility of multiple equilibria and can expand the parameter space of potential learnable equilibria. In addition, the inability to correctly interpret expectations will cause a “boomerang effect” on the forecasts and forecast efficiency of the leading firms. The leading firms' mean square forecast error can be larger than that of following firms if the proportion of following firms is sufficiently large.

We investigate the dynamics of a cobweb model with heterogeneous beliefs, generalizing the example of Brock and Hommes (1997). We examine situations where the agents form expectations by using either rational expectations, or a type of adaptive expectations with limited memory defined from the last two prices. We specify conditions that generate cycles. These conditions depend on a set of factors that includes the intensity of switching between beliefs and the adaption parameter. We show that both Flip bifurcation and Neimark–Sacker bifurcation can occur as primary bifurcation when the steady state is unstable.