Nonlinear Oligopolies: Stability and Bifurcations

The Classical Cournot Model.- Concave Oligopolies.- General Oligopolies.- Modified and Extended Oligopolies.- Oligopolies with Misspecified and Uncertain Price Functions, and Learning.- Overview and Directions for Future Research.

From the reviews:
“This excellent book is a continuation of the work of K. Okuguchi and F. Szidarovszky … and it focuses on the nonlinearity of oligopoly models. It consists of 6 chapters and 6 appendices. … gives a brief overview of the very large and complex field covered in this book, as well as an outline of future research directions. … large collection of references is cited and listed in the bibliography. … the authors of this book have obtained many and important results in this area.” (Anton S. Mureşan, Mathematical Reviews, Issue 2011 e)

The book focuses on the dynamics of nonlinear oligopoly models. It discusses the classical Cournot model with a large variety of demand and cost functions that illustrate the many different types of possible best response functions and it shows the existence of unique and multiple equilibria. Particular emphasis is placed on the influence of nonnegativity and capacity constraints. Dynamics are introduced under various assumptions for the adjustment process. An introduction to the analysis of global dynamics is given through some specific examples. The book also considers concave and general oligopolies and gives conditions for the local asymptotic stability of their equilibria, and it investigates global dynamics in some special cases. Other oligopolies examined include market share attraction games, labor-managed oligopolies, partially cooperating firms and models with intertemporal demand attraction. Local/global stability analyses are carried out for these models and the impact of constraints is discussed. The book contains a number of technical appendices that summarize techniques of global dynamics not easily accessible elsewhere.
 

Presents latest trends, methods and results in nonlinear dynamics with a special focus on oligopolies