The Monopolist's Market with Discrete Choices and Network Externality Revisited: Small-Worlds, Phase Transition and Avalanches in an ACE Framework

In this paper, we explore the effects of the introduction of localised externalities through interaction structures upon local and global properties of the simplest market model: the discrete choice model with a single homogeneous prod- uct and a single seller (the monopoly case). Following Kirman, the resulting mar- ket is viewed as a complex interactive system with a communication network be- tween entities. We use an ACE (Agent based Computational Economics) approach to investigate corresponding market mechanisms and underline in what way the knowledge of generic properties of complex adaptive system dynamics can enhance our perception of the market mechanism in the numerous cases where individual decisions are inter-related. More specifically, we discuss analogies between simu- lated market mechanisms and classical phenomena in the physics of disordered systems such as phase transition, symmetry breaking, avalanches and long range dependence. Various network structures are taken into account: as regular network (lattices) and random networks represent two limiting cases of localised interaction structures, the so-called "small-world" networks are an intermediate form between these two extremes. The first and second sections are devoted to the local and global dimension of the related dynamics, while the third section is dedicated to first investigations into the incidence of externalties and network structure upon the optimal asymptotic price for a monopolist.