Active firms in horizontal mergers and cartel stability

In this paper, we study the optimal number of active firms in acoalition and in a merger. We consider two kinds of game : a merger gameand a coalition game, both in the context of price competition with horizontalproduct differentiation. These are two-stage games. The first stage consistsof determining the number of active firms; the second stage is price competitionbetween active firms. Firms belonging to the same owner or to thesame coalition play cooperatively between themselves but face competitionbetween other firms.We show that when there is no competitive pressure (i.e. no outside firm)then only merged equilibria can occur in the merger case. In the coalitioncase we obtain a similar result in which the number of active firms in thesecond stage is less than the initial number of firms.Moreover we show that if competitive pressure is high enough then theinitial number of firms in the industry is the same as the number of activefirms in the last stage for each kind of game.