Horizontal Merger Decisions with Asymmetric Capacity and Loyal Buyers

Abstract

Capacity constraint and customer structure are key factors influencing firms' competitive strategies and merger decisions. This paper investigates voluntary merger decisions in a market with two dominant firms and one small firm. We use two parameters to measure capacity asymmetry and loyal buyer asymmetry respectively between large and small firms. The relative magnitude of these two dimensions of asymmetry has a significant impact on firms' merger incentives, the resulting market structure, and the impact of different mergers on social welfare. We find that capacity asymmetry promotes a "mega merger" between large firms due to its significant reduction in competitive pressure. However, as capacity asymmetry declines, this benefit wanes, and a "mixed merger" between a large firm and the small firm may arise in equilibrium by reducing unmet demand among loyal customers. When the small firm refrains from price competition in the independent structure, mergers may even reduce profits, encouraging firms to remain independent. If firms' asymmetry in the loyal segment outweighs their capacity asymmetry, the small firm consistently engages in price competition, and the independent structure never emerges in equilibrium. From a regulatory perspective, at least one merger type can enhance social welfare when all firms face capacity constraints: When capacity asymmetry is more significant, a mixed merger maximizes social welfare; when loyal segment asymmetry prevails, a mega merger may result in the highest social welfare. Technically, this study contributes to the literature on mixed-strategy equilibria by demonstrating that the small firm may exhibit a discontinuous equilibrium price support, a notable departure from the continuous price support typically found in the existing literature.

Keywords: Endogenous merger decisions, mixed-strategy equilibrium, capacity constraint, loyal buyers, price competition