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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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An Impulse-Regime Switching Game Model of Vertical Competition
Abstract We study a new kind of nonzero-sum stochastic differential game with mixed impulse/switching controls, motivated by strategic competition in commodity markets. A representative upstream firm produces a commodity that is used by a representative downstream firm to produce a final consumption good. Both firms can influence the price of the commodity. By shutting down or increasing generation capacities, the upstream firm influences the price with impulses. By switching (or not) to a substitute, the downstream firm influences the drift of the commodity price process. We study the resulting impulse-regime switching game between the two firms, focusing on explicit threshold-type equilibria. Remarkably, this class of games naturally gives rise to multiple potential Nash equilibria, which we obtain thanks to a verification-based approach. We exhibit three candidate types of equilibria depending on the ultimate number of switches by the downstream firm (zero, one or an infinite number of switches). We illustrate the diversification effect provided by vertical integration in the specific case of the crude oil market. Our analysis shows that the diversification gains strongly depend on the pass-through from the crude price to the gasoline price.
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- Award ID(s):
- 1736439
- PAR ID:
- 10296116
- Date Published:
- Journal Name:
- Dynamic Games and Applications
- ISSN:
- 2153-0785
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s13235-021-00381-4
