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An Impulse-Regime Switching Game Model of Vertical Competition

Aïd, René; Campi, Luciano; Li, Liangchen; Ludkovski, Mike (2021), An Impulse-Regime Switching Game Model of Vertical Competition, Dynamic Games and Applications. 10.1007/s13235-021-00381-4

Type
Article accepté pour publication ou publié
Date
2021
Journal name
Dynamic Games and Applications
Publisher
Springer
Publication identifier
10.1007/s13235-021-00381-4
Metadata
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Author(s)
Aïd, René
Laboratoire d'Economie de Dauphine [LEDa]
Campi, Luciano

Li, Liangchen
Department of Statistics and Applied Probability, University of California, Santa Barbara [USCB]
Ludkovski, Mike
Department of Statistics and Applied Probability, University of California, Santa Barbara [USCB]
Abstract (EN)
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.
Subjects / Keywords
Stochastic differential games; Impulse controls; Optimal switching; Quasi-variational inequalities; Nash equilibrium; Commodity markets
JEL
Q43 - Energy and the Macroeconomy
C73 - Stochastic and Dynamic Games; Evolutionary Games; Repeated Games

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