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.
