Endogenous choice of price or quantity contract with partial vertical ownership

We study a supply chain that consists of an upstream firm and two downstream firms. The downstream firms are assumed to have partial ownership in the upstream firm but lack control rights. We explore how these downstream firms decide whether to compete on quantity or price. Our findings show that the outcomes vary based on the degree of partial vertical ownership and the level of product substitutability, with possible equilibria including Cournot, Bertrand, and Cournot-Bertrand competition. This contradicts the conventional wisdom that firms typically prefer Cournot competition as their primary strategy.understanding that firms tend to engage in Cournot competition as their dominant strategy.