A Markov analysis of social learning and adaptation

Abstract

A number of recent contributions to the literature have modelled social learning and adaptation in an economic context. Understanding the processes driving these models is important in order to explain and predict the behaviour of the economy. In this paper, we analyze the economic applications for a class of adaptive learning models with bounded rational agents. The dynamics of these economies can be thought of as arising from discrete-time Markov chains. In particular, conditions for uniqueness of equilibria, convergence and stability in the economic systems follow from the accessibility and communication structures of these Markov chains. We establish a correspondence between absorbing states of the Markov chains and economic equilibria, whether stable or unstable, and develop theorems giving conditions for absorption and recurrence. Furthermore, we develop practical applications of these theorems using a cobweb model. We use a genetic algorithm, operating under election, as an example of a well known adaptive learning process.