Markov Perfect Equilibria for a classof capital accumulation games

Abstract

We formulate a class of dynamic games which consists of so‐called capital accumulationgames. In such games, rival firms invest strategically in a stock of physical capital. Thecapital stocks of all firms in the industry are the state variables of the game and firms usethe rate of change of the capital stocks as their control variables. It is assumed that currentprofits of a firm are not only dependent on the firm's own capital stock, but also on thestock of capital of the rival firm. We prove existence of multiple Markov Perfect Equilibria(MPE) and study their qualitative characteristics. It turns out that there exist two differenttypes of equilibria: a strict equilibrium that is degenerate and coincides with the uniqueopen‐loop one and so‐called indifferent equilibria that are non‐strict. For both types, westudy the equilibrium dynamics. While the strict equilibrium is characterized by simpleequilibrium dynamics, the indifferent equilibria may exhibit complex dynamic behaviour.