Markov perfect equilibria for a class of capital accumulation games

We formulate a class of dynamic games which consists of so-called capital accumulation games. In such games, rival firms invest strategically in a stock of physical capital. The capital stocks of all firms in the industry are the state variables of the game and firms use the rate of change of the capital stocks as their control variables. It is assumed that current profits of a firm are not only dependent on the firm's own capital stock, but also on the stock of capital of the rival firm. We prove existence of multiple Markov Perfect Equilibria and study their qualitative characteristics. It turns out that there exist two different types of equilibria: a strict equilibrium that is degenerate and coincides with the unique open-loop one and so-called indifferent equilibria that are non-strict. For both types, we study the equilibrium dynamics. While the strict equilibrium is characterized by simple equilibrium dynamics, the indifferent equilibria may exhibit complex dynamic behaviour.