Modified and Extended Oligopolies - Nonlinear Oligopolies: Stability and Bifurcations - page 138

Chapter 4
Modified and Extended Oligopolies

The previous chapters have introduced and analyzed the classical Cournot model
under a number of assumptions. In this chapter we discuss some important modifi-
cations and extensions. We first introduce market share attraction games where the
dynamics are driven by a generalization of the gradient adjustment process intro-
duced in Chaps. 1 and 2. We carry out both a local and global analysis of the
stability of these games. In Sect. 4.2 we consider labor-managed oligopolies with
best response dynamics. We give a detailed discussion of the local stability in the
discrete time case and via an example show the type of global dynamical behavior
that is possible in this model type. The section concludes with a brief discussion of
the local stability of a continuous time version of the labor-managed oligopoly. In
Sect. 4.3 we introduce intertemporal demand interaction effects, brought about for
example by habit formation, into dynamic oligopolies with best response dynamics.
We give a local and global stability analysis of the model in discrete time. For the
continuous time version we study the local stability of the dynamics, including also
the case when there are information lags. In Sect. 4.4 we analyze oligopolies with
production adjustment costs. For the case of best reply dynamics in discrete time
we give local stability conditions. In the final section we consider oligopolies where
there is partial cooperation amongst the firms of the industry. We show various prop-
erties of the best response function, give local stability for best reply dynamics in
continuous time, and analyze the global dynamics of a particular example under
discrete time best response dynamics.

4.1 Market Share Attraction Games

Market share attraction models have been used in a variety of contexts to describe
the behavior of competitors in a market. Not only have they been employed fre-
quently in empirical applications, they are also prevalent in the economics, game
theory and operations research literature. In the marketing literature, market share
attraction models are often used to describe the competition between several brands
of a product in the market (see for example, Hanssens et al. (1990) and Cooper and
Nakanishi (1988)). The models are then sometimes referred to as brand competition