Smart or stupid depends on who is your counterpart: a cobweb model with heterogeneous expectations

We investigate the dynamics of a cobweb model with heterogeneous expectations, generalizing the famous model of Brock and Hommes (Brock, W. A., and C. H. Hommes. 1997. “A Rational Route to Randomness.” Econometrica 65 (5): 1059–1095) by adding a new predictor – periodical expectation – which predicts that the price will revert to its level two periods previously. We show that under the periodical expectation, when the agents are homogeneous, they will always make wrong predictions, whereas when the agents are heterogeneous, they may be either smart or stupid depending on their counterparts’ types. Moreover, in the cobweb framework, the periodical predictor may be a destabilizer in some cases, but a stabilizer in other cases. We also find that in the cobweb model with rational, naive and periodical expectations, under certain refined conditions, the rational predictor may be endogenously dominated by naive and periodical predictors.