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Nonlinear Oligopolies - Stability and Bifurcations (Hardcover, 2010 ed.)
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Nonlinear Oligopolies - Stability and Bifurcations (Hardcover, 2010 ed.)
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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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