Collective bounded rationality: theory and experiments

Abstract

This paper introduces an endogenous cognitive hierarchy model in which players are assumed to best-reply holding heterogeneous beliefs on the other players' cognitive levels. Contrary to the previous models, players are allowed to consider presence of opponents at their own cognitive level. This extension is shown to eradicate the incompatibility of standard cognitive hierarchy models in the games where the best-reply function is an expansion mapping. We employ the model to explain asymptotic voting behavior in information aggregation problems of the Condorcet Jury Theorem. Behavioral assumption of the strategic thinking turns out to be a crucial factor in whether the asymptotic efficiency is obtained or not. We conducted laboratory experiments and obtained evidences that the endogenous cognitive hierarchy model provides significant improvements upon standard cognitive hierarchy models and symmetric Bayesian Nash equilibrium in explaining observed behavior of voters. With Ali Ihsan Ozkes.