Markov-perfect Nash equilibria in models with a single capital stock

Many economic problems can be formulated as dynamic games in which strategically interacting agents choose actions that determine the current and future levels of a single capital stock. We study necessary conditions that allow us to characterize Markov perfect Nash equilibria (MPNE) for these games. These conditions result in an auxiliary system of ordinary differential equations that helps us to explore stability, continuity and differentiability of MPNE. The techniques are used to derive detailed properties of MPNE for several games including the exploitation of a finite resource, the voluntary investment in a public capital stock, and the inter-temporal consumption of a reproductive asset.