An Impulse-Regime Switching Game Model of Vertical Competition

René Aïd, Luciano Campi, Liangchen Li and Mike Ludkovski
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René Aïd: LEDa - Laboratoire d'Economie de Dauphine - IRD - Institut de Recherche pour le Développement - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique
Luciano Campi: Department of Mathematics "Federigo Enriques" - UNIMI - Università degli Studi di Milano = University of Milan
Liangchen Li: UC Santa Barbara - University of California [Santa Barbara] - UC - University of California
Mike Ludkovski: UC Santa Barbara - University of California [Santa Barbara] - UC - University of California

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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.

Keywords: Stochastic differential games; Impulse controls; Optimal switching; Quasi-variational inequalities; Nash equilibrium; Commodity markets (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

Published in Dynamic Games and Applications, 2021, ⟨10.1007/s13235-021-00381-4⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03215811

DOI: 10.1007/s13235-021-00381-4

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