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 modifications and extensions. We first introduce market share attraction games where the dynamics are driven by a generalization of the gradient adjustment process introduced in Chaps. 1 and 1. We carry out both a local and global analysis of the stability of this game. 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 properties 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.