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 equalibria (MPNE) for these games. These conditions result in an auxilary 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.

Markov-perfect Nash equilibria in models with a single capital stock (Revised version, August 2008)

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 characterise Markov perfect Nash equilibria for these games. These conditions result in an auxiliary system of ordinary differential equations that helps us to explore stability, continuity and differentiability of these equilibria. The techniques are used to derive detailed properties of Markov-perfect Nash equilibria 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.

Dynamic R&D competition with memory

We consider a differential game of R&D competition and explore the impact of rivalry on the firms' investment behavior over time. Using closed-loop strategies and hence allowing for strategic interactions among rival firms we show that R&D spending by the individual competitor is increased due to competition in the race for priority. This leads us to argue that competitive encounters enhance R&D activities at the same time as increasing efficiency in the race for a technological breakthrough

Dynamic capital structure choice and investment timing

The paper considers the problem of an investor that has the option to acquire a firm. Initially this firm is run as to maximize shareholder value, where the shareholders are risk averse. To do so it has to decide each time on investment and dividend levels. The firm’s capital stock can be financed by equity and debt, where less solvable firms pay a higher interest rate on debt. Revenue is stochastic. We find that the firm is run such that capital stock and dividends develop in a fixed proportion to the equity. In particular, it turns out that more dividends are paid if the economic environment is more uncertain. We also derive that the relationship between the levels of risk aversion of the current shareholders and the potential investor is a significant determinant in establishing whether the firm is a profitable takeover target for the investor