Cars Hommes proposed many models based on agents having heterogeneous expectations. Agents switch between a fixed set of prediction rules depending on their forecast error history. However, it seems that the predictions of these models can differ but qualitatively and quantitatively (convergence might happen, economy might also keep oscillating or not, with declining amplitudes, or not, ...) because of path dependence en dependence on initial conditions.
So, do these models still have equilibria? Are they determinate? Are they still usefull for prediction?
Hommes, C. (2013). Behavioral Rationality and Heterogeneous Expectations in Complex Economic Systems. In Behavioral Rationality and Heterogeneous Expectations in Complex Economic Systems. https://doi.org/10.1017/cbo9781139094276