Endogenous Merger Decisions Among Competitors: Impact of Limited Capacity and Loyal Segments

Abstract

We study endogenous merger decisions 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 merge with another firm. Because of antitrust laws, all three firms merging is not permitted. When two firms merge, the merged entity and the remaining independent firm use the resulting capacity to capture their own “loyal buyers” and compete in price for price-sensitive “disloyal switchers.” We first consider a base model in which the size of loyal buyers for different firms is symmetric. We find that, in equilibrium, either there is no merger or the large firm will merge with a small firm as a “mixed merger.” We explain how this equilibrium structure is driven by the mergers’ impacts on market competition and firms’ pricing aggressiveness. Specifically, the mixed merger that can most effectively reduce price competition is the equilibrium under relatively competitive market conditions (i.e., the size of loyal buyers is small and capacity is large but limited). We also extend to the case with asymmetric size of loyal segments and show that two small firms merging (“small merger” structure) can be the equilibrium structure when the large firm has a much larger loyal segment than the small firms and the small firms’ capacity is sufficiently large. The impacts of mergers on social welfare and consumer surplus provide practical implications from the antitrust perspective. The antitrust agencies can approve a mixed merger to improve social welfare under certain conditions, but if the agencies pay more attention to consumer surplus, then mixed mergers should not be permitted. Small mergers, though sometimes not the equilibrium structures, can improve social welfare and consumer surplus. In such cases, the government can appropriately promote mergers that are beneficial for society and/or consumers by adopting some restrictive measures or offering incentives. This paper was accepted by Jeannette Song, operations management. Funding: The work of D. Wang was supported by the National Natural Science Foundation of China [Grant 72401275]; the work of X. Wu was supported by the National Natural Science Foundation of China [Grants 72025102, 72293560/72293565]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2022.01943 .