29 / 2024-04-15 14:32:47

Horizontal Merger Decisions with Asymmetric Capacity and Heterogenous Customers

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

This paper examines voluntary merger decisions among three firms engaged in price competition, two large firms and one small firm that differ in capacity and have either symmetric or asymmetric loyal buyer segments. The large firms may or may not be capacity-constrained. Depending on the firms' merger decisions, three market structures are possible: The initial independent structure where firms operate independently, the “mega merger” structure where two large firms merge, and the “mixed merger” structure where one large firm merges with the small firm. We investigate how the degree of firms' asymmetry affects their merger incentives and the equilibrium market structure. When the large firms have much more capacities than the small firm, the mega merger is preferred because it can significantly dampen competition between the large firms. However, as capacity asymmetry between the large and small firms decreases, the benefit of the mega merger decreases and the mixed merger can emerge in equilibrium due to its advantage of reducing unsatisfied loyal buyers. Furthermore, when all firms operate at relatively low capacity levels, the mega merger may even reduce the merging firms' profits, and hence the firms opt to remain independent. Conversely, when the large firms' advantage in capacity over the small firm is lower than their advantage in loyal segment, the independent structure never emerges as an equilibrium, the mega merger structure is always an equilibrium, and the mixed merger structure emerges as an equilibrium when the small firm's capacity is intermediate. Finally, we compare social welfare across different market structures to analyze the welfare effect of horizontal mergers. Our findings suggest that at least one type of merger can enhance social welfare when all firms have constrained capacities. This underscores the importance for regulatory agencies to take into account capacities when assessing the welfare effects of mergers.

Technically, when involving mixed-strategy equilibrium, the literature focuses on two firms or multiple symmetric firms, mostly because it is challenging to solve the mixed-strategy equilibrium among three or more than three asymmetric firms whose price supports may differ and present many possible patterns. We contribute to the literature by solving the mixed-strategy equilibrium of a pricing game with three capacity constrained firms for the first time and identifying the effects of capacity and loyal buyer size on the pricing equilibrium.