An Impulse-Regime Switching Game Model of Vertical Competition

TL;DR

This paper models a strategic game between upstream and downstream firms in commodity markets, using impulse and regime switching controls to analyze equilibrium behaviors and diversification effects, especially in crude oil markets.

Contribution

It introduces a novel impulse-regime switching game framework with explicit threshold equilibria, revealing multiple Nash equilibria and diversification benefits in vertical integration.

Findings

Multiple Nash equilibria depend on the number of downstream switches.

Diversification gains are influenced by pass-through rates from crude to gasoline prices.

Explicit threshold-type equilibria are derived for the game.

Abstract

We study a new kind of non-zero-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 Nash equilibria, which we obtain via a verification based approach. We exhibit three 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.