Thursday, May 6, 2021
We study potential alliance formation among three competing firms with asymmetric capacity: One large firm has ample capacity, and two small firms have limited capacity. Each firm can either operate independently or form an alliance with another firm. Due to antitrust laws, an alliance of all three firms is not permitted. When a two-firm alliance is formed, the alliance and the remaining independent firm use prices and the resulting capacity to capture their own “loyal buyers” and compete for price-sensitive “disloyal switchers”. We first derive and compare equilibrium profits under different alliance structures in the base model where the size of loyal buyers for different firms is symmetric. By considering a standard equilibrium concept, we find that either no alliance will be formed or the large firm will form a “mixed” alliance with a small firm under conditions pertaining to the sizes of each firm’s capacity and loyal buyers. We explain how the equilibrium alliance structure is driven by the “price effect” and the “demand effect”. Specifically, the mixed alliance structure dominates when the price effect overshadows the demand effect, and no alliance will be formed when the demand effect outweighs the price effect. We also extend our base model to the case when the large firm has more loyal buyers than the small ones, and show that a “small” alliance consisting of two small firms can emerge as the dominant alliance structure on some occasions.