Stability analysis of horizontal mergers in a market with asymmetric substitutability

• Published in: Mathematical social sciences 2018-11, Vol.96, p.73-84
• Main Authors: Takeda, Kohei, Hosoe, Toyoki, Watanabe, Takayuki, Matsubayashi, Nobuo
• Format: Article
• Language: English
• Subjects: Acquisitions & mergers; Asymmetry; Companies; Markets; Mergers; Monopolies; Oligopoly
• ISSN: 0165-4896; 1879-3118
• DOI: 10.1016/j.mathsocsci.2018.09.004

This study analyzes the stability of horizontal mergers in a Cournot oligopoly market. Although many researchers have addressed this issue, most previous studies assume symmetric firms in terms of demand and cost structures due to analytical tractability. We attempt to find a stable merger in a general n-firm oligopoly in which we allow for asymmetric substitutability between firms. To ensure analytical tractability, we follow the related literature and employ a simple core allocation for a monopoly merger as a stability concept. We analyze several typical markets with asymmetric substitutability and show that although γ-core is always nonempty in every setting that we examine, the δ-core is very likely to be empty—it is always empty in a market with three or more symmetric firms. Nevertheless, we present an example of a market with a nonempty δ-core, regardless of the number of firms in a market. The market has at most two symmetric firms in terms of substitutability (e.g., a linear city). Furthermore, substitutability is so low across the market that each firm competes with only two neighboring firms. Therefore, contrary to the conventional view suggested in previous studies, we show that a monopoly merger can be stable in a Cournot oligopoly market, even if there are many firms in the market. •We find a stable merger in a Cournot-oligopoly with asymmetric substitutability.•The γ-core is always nonempty in every setting we examine.•For the δ-core existence, the degree of differentiation must be low over firms.•The δ-core is always empty in a market with three or more symmetric firms.•We present an example of a market with a nonempty δ-core regardless of the number of firms.