We investigate the dynamics of a cobweb model with heterogeneous beliefs. 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. Conditions that generate stable cycles are specified in two cases.

Firstly, we generalize the examples of Brock and Hommes (1997). We assume that the measure of welfare is equal to realized net profits in the past two periods. The cycle conditions then depend on a set of parameters that includes the intensity of switching between beliefs and the adaption parameter. As in Lasselle et al (2005) and unlike Brock and Hommes (1997), we show that both the Flip bifurcation and Neimark-Sacker bifurcation can occur as primary bifurcation when the steady state is unstable.

Secondly, following Waters (2007), we introduce the learning dynamic of Brown, von Neuman and Nash (1950) into our model. In our case, the steady state may not be a saddle but cycles occur. Conditions depend on the adaption parameter. They can be easily related to those developed in the first part of the paper. However, unlike Lasselle et al (2005) and as in Waters (2007), when the agents are sufficiently aggressive in switching between performing strategies, there is minimal variation in the price.

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