Rational expectations and differentiated information costs for heterogeneous fundamentalists in an evolutive Muthian cobweb model

We extend the evolutionary cobweb setting proposed in Hommes and Wagener [J. Econ. Behav. Organ. 75, 25-39 (2010)] in which the share updating mechanism is based on a comparison among the profits realized by the different kinds of agents, by assuming that the market is populated by rational producers, endowed with perfect foresight expectations about prices, in addition to biased and unbiased fundamentalists. Moreover, we suppose that agents face heterogeneous information costs, which are proportional to their rationality degree. Since we found in Naimzada and Pireddu [Econ. Lett. 186, 108513 (2020a)] that considering diversified information costs for fundamentalists shrinks the stability region of the steady state, while we discovered in Naimzada and Pireddu [J. Econ. Behav. Organ. 177, 415-432 (2020b)] that introducing rational agents enlarges it, we analyze whether one of the two aspects always prevails over the other one when they are jointly taken into account. We also investigate if the chaotic phenomena detected in Naimzada and Pireddu [J. Econ. Behav. Organ. 177, 415-432 (2020b)] emerging when enriching the original framework in Hommes and Wagener [J. Econ. Behav. Organ. 75, 25-39 (2010)] with rational agents, persist or are inhibited by the introduction of information costs for all agent types. We complete our analysis by studying the network of the relationships among the four settings obtained possibly considering information costs for biased and unbiased fundamentalists and possibly introducing rational agents.