Stability analysis of an adjustment process for oligopolistic market equilibrium modeld as a projected dynamical system

This paper presents an analysis of the stability for the continuous time adjustment processes proposed for the spatial oligopolistic market equilibrium problem by Nagurney, Dupuis, and Zhang [13] and for the classical (aspatial) oligopoly problem by Dupuis and Nagurney [6], modeled as projected dynamicalsystems. Here two distinct approaches are presented, a monotonicity approach and a regularity approach. The monotonicity approach utilizes monotonicity conditions on the underlying functions, whereas the regularity approach utilizes the regularity concept of oligopolistic market equilibrium, adapted from Zhang and Nagurney [20], which enables us to explore the stability of the adjustment process—a nonstandard dynamical system, via its minimal face flow—a standard dynamical system. These approaches to stability analysis are shown to generalize some of the results in the existing literature