Stability and Cycles in a Cobweb Model with Heterogeneous Expectations

We investigate the dynamics of a cobweb model with heterogeneous beliefs, generalising the example of Brock and Hommes (1997). We examine situations where the agents form expectations by using either perfect foresight, or a form 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 proportion of rational agents, 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.