One of the driving forces in a market economy is the growth of firms and industries. While traditionally economists have analysed firm and industry growth under the assumption of perfectly competitive product markets (i.e., firms are assumed to be price takers in the output market) more recent research has focused on game theoretic models of growth and capital accumulation. Therefore the aim of this chapter is to present a number of differential games in which two or more firms invest strategically in a physical capital stock and the output market is organized by oligopolistic competition. In such a setting the dynamic evolution of a firm and that of an industry differ substantially from the predictions of perfectly competitive firm models. In particular, the strategic interactions among rival firms give rise to a number of interesting conclusions, such as overaccumulation of capital, preemption, and entry (mobility) deterrence.

We begin with the description of a general Cournot model in which two firms invest in their capital stocks. If they face capacity constraints, oligopolistic product market competition allows us to derive a reduced form profit function for each firm that is dependent on the firm's own capital stock as well as on the capital stock of the rival. Investment is costly and can give rise to internal adjustment costs. In this setting we study two alternative games, one in which firms employ open-loop strategies and one in which strategic interactions are explicitly taken into account through state dependent (nondegenerate) Markovian strategies.