Econometrica

Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Nov, 2023, Volume 91, Issue 6

Price Setting with Strategic Complementarities as a Mean Field Game

https://doi.org/10.3982/ECTA20797
p. 2005-2039

Fernando Alvarez, Francesco Lippi, Panagiotis Souganidis

We study the propagation of monetary shocks in a sticky‐price general equilibrium economy where the firms' pricing strategy features a complementarity with the decisions of other firms. In a dynamic equilibrium, the firm's price‐setting decisions depend on aggregates, which in turn depend on the firms' decisions. We cast this fixed‐point problem as a Mean Field Game and prove several analytic results. We establish existence and uniqueness of the equilibrium and characterize the impulse response function (IRF) of output following an aggregate shock. We prove that strategic complementarities make the IRF larger at each horizon. We establish that complementarities may give rise to an 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: 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.


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Supplemental Material

Supplement to "Price Setting with Strategic Complementarities as a Mean Field Game"

Fernando Alvarez, Francesco Lippi and Panagiotis Souganidis

This online appendix contains material not found within the manuscript.

Supplement to "Price Setting with Strategic Complementarities as a Mean Field Game"

Fernando Alvarez, Francesco Lippi and Panagiotis Souganidis

The replication package for this paper is available at https://doi.org/10.5281/zenodo.8200032. The Journal checked the data and codes included in the package for their ability to reproduce the results in the paper and approved online appendices.

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