DP16998 Price Setting with Strategic Complementarities as a Mean Field Game

Author(s): Fernando Alvarez, Francesco Lippi, Panagiotis Souganidis
Publication Date: February 2022
Keyword(s): dynamic equilibria, mean field games, Monetary Economics, singular stochastic control, sticky prices, strategic complementarities
JEL(s): E3, E5
Programme Areas: International Macroeconomics and Finance, Monetary Economics and Fluctuations
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=16998

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.