Stable Market Structure and Sufficient Conditions for Horizontal Mergers

Consider the four possible mergers in a market with three firms: 12, 13, 23, and 123. Which one, if any, will take place? Although the question seems fairly simple, it has not yet been fully answered. The existing literature provides two necessary conditions for a merger: profitability and a non-empty core (i.e., a merger will not be formed if it is unprofitable or if its core is empty). This paper shows that a stable partition of the firms, which is immune to breakups and new mergers, is sufficient for mergers in the partition to take place. The paper provides a tractable condition for checking stability. By applying the condition, the paper completely characterizes stability in all three firm linear markets, and it partially characterizes stability in n-firm markets. JEL Classification Number: C62, C71, C72, D43, L10