Dynamics of a minimal consumer network with uni-directional influence

Abstract

In a model of interdependent consumer behavior due to (Econ Lett 27(2):145–150 1988, J Econ Behav Organ 21(2):223–231 1993) an individual adjusts his preferences in response to his own past consumption decisions and the observable past consumption of another individual. The resulting 2D non-invertible demand system exhibits a rich dynamics. We focus on two special cases: The baseline case of two independent consumers and a situation in which the autonomous individual 1 is viewed as a representative member of a group that serves as a normative reference group for individual 2. The consumption behavior of individual 2 is determined by his own past consumption experience as well as by the observable consumption behavior of individual 1, who is in turn not influenced by individual 2. The associated map belongs to the class of triangular maps. Our analysis focuses on the coexistence of attractors and the mechanisms underlying qualitative transformations of attractors. Relying on a mix of analytical, numerical, and graphical methodology, we demonstrate how various bifurcations occur as the importance of the individuals’ own past consumption as well as the strength of influence of individual 1 on 2 varies. Economic interpretations of the observed dynamic phenomena are emphasized.