Overview

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.

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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 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. Muresan, Mathematical Reviews, Issue 2011 e)

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