Nonlinear Oligopolies: Stability and Bifurcations - Softcover

Bischi, Gian Italo; Chiarella, Carl; Kopel, Michael; Szidarovszky, Ferenc

Softcover

ISBN 10: 3642424600 ISBN 13: 9783642424601

Publisher: Springer, 2014

Synopsis

Oligopoly theory is one of the most intensively studied areas of mathematical economics. On the basis of the pioneering works of Cournot (1838), many res- rchers have developed and extensively examined the different variants of oligopoly models. Initially, the existence and uniqueness of the equilibrium of the different types of oligopolies was the main concern, and later the dynamic extensions of these models became the focus. The classical result of Theocharis (1960) asserts that under discrete time scales and static expectations, the equilibrium of a sing- product oligopoly without product differentiation and with linear price and cost functions is asymptotically stable if and only if it is a duopoly. In the continuous time case, asymptotic stability is guaranteed for any number of ?rms. In these cases the resulting dynamical systems are also linear, where local and global asymptotic stability are equivalent to each other. The classical book of Okuguchi (1976) gives a comprehensive summary of the earlier results and developments. The multipr- uct extensionshave been discussed in Okuguchiand Szidarovszky(1999);however, nonlinear features were barely touched upon in these contributions. WiththedevelopmentofthecriticalcurvemethodbyGumowskiandMira(1980) (see also Mira et al. (1996))fordiscrete time systemsand the introductionof cont- uously distributed information lags by Invernizzi and Medio (1991) in continuous time systems, increasing attention has been given to the global dynamics of n- linear oligopolies. The authors of this book have devoted a great deal of research effort to this area.

About this title

Review:

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)

From the Back Cover:

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.

 

About this edition

• Publisher: Springer
• Publication date: 2014
• ISBN 10: 3642424600
• ISBN 13: 9783642424601
• Binding: Paperback
• Number of pages: 349