Adaptive Learning and Complex Dynamics

In this paper, we explore the dynamic properties of a group of simple deterministic difference equation systems in which the conventional perfect foresight assumption gives place to a mechanism of adaptive learning. These systems have a common feature: under perfect foresight (or rational expectations) they all possess a unique fixed point steady-state. This long term outcome is obtained also under learning if the quality underlying the learning process is high. Otherwise, when the innefficiency of the learning process is relatively strong, nonlinear dynamics (periodic and aperiodic cycles) arise. The specific properties of each one of the proposed systems is explored both in terms of local and global dynamics. Two macroeconomic models are used to illustrate how the formation of expectations through learning may eventually lead to awkward long term outcomes.