DSGE Nash: Solving Nash games in macro models

This paper presents DSGE Nash, a toolkit to solve for pure strategy Nash equilibria of global games in macro models. Nash equilibria are computed with a decentralized approach: each player controls only its own policy function while other agents in the economy act independently. Although primarily designed to solve for Nash equilibria in DSGE models, the toolkit encompasses a broad range of settings, including the possibility of matching empirical data. Importantly, it allows to solve for the equilibrium in the presence of non-linearities or conditionally on shocks. When only one player is selected, the problem is re-framed as a standard optimal policy problem. We apply the algorithm to a standard two-country open-economy model, where central banks compete for rate setting. In the Nash equilibrium, central banks symmetrically trade-off inflation for output stabilization, in the presence of a zero lower bound constraint, the equilibrium becomes asymmetric: the central bank in the shock-originating economy implements a tighter policy, to reduce the zero lower bound duration, while the central bank in the other country opts for a more lenient rate setting strategy.