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Price Setting with Strategic Complementarities as a Mean Field Game

Author

Listed:
  • Alvarez, Fernando
  • Lippi, Francesco
  • Souganidis, Panagiotis
Abstract
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.

Suggested Citation

  • Alvarez, Fernando & Lippi, Francesco & Souganidis, Panagiotis, 2022. "Price Setting with Strategic Complementarities as a Mean Field Game," CEPR Discussion Papers 16998, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:16998
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    1. Boppart, Timo & Krusell, Per & Mitman, Kurt, 2018. "Exploiting MIT shocks in heterogeneous-agent economies: the impulse response as a numerical derivative," Journal of Economic Dynamics and Control, Elsevier, vol. 89(C), pages 68-92.
    2. Fernando Alvarez & Francesco Lippi, 2022. "The Analytic Theory of a Monetary Shock," Econometrica, Econometric Society, vol. 90(4), pages 1655-1680, July.
    3. Olivier Wang & Iván Werning, 2022. "Dynamic Oligopoly and Price Stickiness," American Economic Review, American Economic Association, vol. 112(8), pages 2815-2849, August.
    4. Mary Amiti & Oleg Itskhoki & Jozef Konings, 2019. "International Shocks, Variable Markups, and Domestic Prices," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(6), pages 2356-2402.
    5. Adrien Auclert & Rodolfo Rigato & Matthew Rognlie & Ludwig Straub, 2024. "New Pricing Models, Same Old Phillips Curves?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 139(1), pages 121-186.
    6. SeHyoun Ahn & Greg Kaplan & Benjamin Moll & Thomas Winberry & Christian Wolf, 2018. "When Inequality Matters for Macro and Macro Matters for Inequality," NBER Macroeconomics Annual, University of Chicago Press, vol. 32(1), pages 1-75.
    7. Fernando Alvarez & Hervé Le Bihan & Francesco Lippi, 2016. "The Real Effects of Monetary Shocks in Sticky Price Models: A Sufficient Statistic Approach," American Economic Review, American Economic Association, vol. 106(10), pages 2817-2851, October.
    8. Calvo, Guillermo A., 1983. "Staggered prices in a utility-maximizing framework," Journal of Monetary Economics, Elsevier, vol. 12(3), pages 383-398, September.
    9. Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lionse & Benjamin Moll, 2022. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(1), pages 45-86.
    10. Kimball, Miles S, 1995. "The Quantitative Analytics of the Basic Neomonetarist Model," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 27(4), pages 1241-1277, November.
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    Citations

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    Cited by:

    1. Cannerozzi, Federico & Ferrari, Giorgio, 2024. "Cooperation, Correlation and Competition in Ergodic $N$-Player Games and Mean-Field Games of Singular Controls: A Case Study," Center for Mathematical Economics Working Papers 691, Center for Mathematical Economics, Bielefeld University.
    2. Krueger, Dirk & Uhlig, Harald, 2022. "Neoclassical Growth with Limited Commitment," CEPR Discussion Papers 17757, C.E.P.R. Discussion Papers.
    3. Yves Achdou & Guillaume Carlier & Quentin Petit & Daniela Tonon, 2024. "A mean field model for the interactions between firms on the markets of their inputs," Mathematics and Financial Economics, Springer, volume 18, number 2, December.
    4. Hassan Afrouzi & Saroj Bhattarai, 2023. "Inflation and GDP Dynamics in Production Networks: A Sufficient Statistics Approach," CESifo Working Paper Series 10416, CESifo.
    5. Fernando Alvarez & Francesco Lippi & Panagiotis Souganidis, 2024. "Caballero–Engel meet Lasry–Lions: A uniqueness result," Mathematics and Financial Economics, Springer, volume 18, number 13, December.
    6. Federico Cannerozzi & Giorgio Ferrari, 2024. "Cooperation, Correlation and Competition in Ergodic $N$-player Games and Mean-field Games of Singular Controls: A Case Study," Papers 2404.15079, arXiv.org.
    7. Dirk Krueger & Harald Uhlig, 2024. "Neoclassical Growth with Limited Commitment," PIER Working Paper Archive 24-021, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    8. Eric Qian, 2023. "Heterogeneity-robust granular instruments," Papers 2304.01273, arXiv.org, revised Jun 2024.
    9. Isaac Baley & Andrés Blanco, 2022. "The Macroeconomics of Partial Irreversibility," Working Papers 1312, Barcelona School of Economics.
    10. Lambert Dong, 2024. "Strategic complementarities as stochastic control under sticky price," Papers 2403.19847, arXiv.org.

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    More about this item

    Keywords

    Monetary economics; Sticky prices; Strategic complementarities; Dynamic equilibria; Mean field games; Singular stochastic control;
    All these keywords.

    JEL classification:

    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
    • E5 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit

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