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An Impulse-Regime Switching Game Model of Vertical Competition

Author

Listed:
  • 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)

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.

Suggested Citation

  • René Aïd & Luciano Campi & Liangchen Li & Mike Ludkovski, 2021. "An Impulse-Regime Switching Game Model of Vertical Competition," Post-Print hal-03215811, HAL.
    • Handle: RePEc:hal:journl:hal-03215811
    DOI: 10.1007/s13235-021-00381-4
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    Cited by:

    1. Utsav Sadana & Puduru Viswanadha Reddy & Tamer Başar & Georges Zaccour, 2021. "Sampled-Data Nash Equilibria in Differential Games with Impulse Controls," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 999-1022, September.

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