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We study a new kind of non-zero-sum stochastic differential game with mixedimpulse/switching controls, motivated by strategic competition in commoditymarkets. A representative upstream firm produces a commodity that is used by arepresentative downstream firm to produce a final consumption good. Both firmscan influence the price of the commodity. By shutting down or increasinggeneration capacities, the upstream firm influences the price with impulses. Byswitching (or not) to a substitute, the downstream firm influences the drift ofthe commodity price process. We study the resulting impulse--regime switchinggame between the two firms, focusing on explicit threshold-type equilibria.Remarkably, this class of games naturally gives rise to multiple Nashequilibria, which we obtain via a verification based approach. We exhibit threetypes of equilibria depending on the ultimate number of switches by thedownstream firm (zero, one or an infinite number of switches). We illustratethe diversification effect provided by vertical integration in the specificcase of the crude oil market. Our analysis shows that the diversification gainsstrongly depend on the pass-through from the crude price to the gasoline price.

An Impulse-Regime Switching Game Model of Vertical Competition