DSGE Nash : Solving Nash Games in Macro Models with an application to optimal monetary policy under monopolistic commodity pricing

This paper presents DSGE Nash, a toolkit to solve for pure strategy Nash equilibria of global games in general equilibrium macroeconomic models. Although primarily designed to solve for Nash equilibria in DSGE models, the toolkit encompasses a broad range of options including solutions up to the third order, multiple players/strategies, the use of user-defined objective functions and the possibility of matching empirical moments and IRFs. When only one player is selected, the problem is re-framed as a standard optimal policy problem. We apply the algorithm to an open-economy model where a commodity importing country and a monopolistic commodity producer compete on the commodities market with barriers to entry. If the commodity price becomes relevant in production, the central bank in the commodity importing economy deviates from the first best policy to act strategically. In particular, the monetary authority tolerates relatively higher commodity price volatility to ease barriers to entry in commodity production and to limit the market power of the dominant exporter