Price Setting with Strategic Complementarities as a Mean Field Game

We study the propagation of monetary shocks in a sticky-price general-equilibrium economy where firms set prices subject to strategic complementarities with the decision of other firms. In the dynamic equilibrium the firm’s price-setting decisions depend on aggregates, which in turn depend on firms’ decisions. We cast this fixed-point problem as a Mean Field Game (MFG) and establish several analytic results. We study existence and uniqueness of the equilibrium and analytically characterize the impulse response function (IRF) of output following an aggregate “MIT†shock. We prove that strategic complementarities make the IRF larger at each horizon, in a convex fashion. We establish that complementarities may give rise to a non-monotone IRF, with a hump-shaped profile. As the complementarity becomes large enough the IRF diverges and at a critical point there is no equilibrium. Finally, we show that the amplification effect of the strategic interactions is similar across models. For instance, the Calvo model and the Golosov-Lucas model display a comparable amplification, in spite of the fact that the non-neutrality in Calvo is much larger.