In this paper, we study the optimal number of active firms in a
coalition and in a merger. We consider two kinds of game : a merger game
and a coalition game, both in the context of price competition with horizontal
product differentiation. These are two-stage games. The first stage consists
of determining the number of active firms; the second stage is price competition
between active firms. Firms belonging to the same owner or to the
same coalition play cooperatively between themselves but face competition
between 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 coalition
case we obtain a similar result in which the number of active firms in the
second stage is less than the initial number of firms.
Moreover we show that if competitive pressure is high enough then the
initial number of firms in the industry is the same as the number of active
firms in the last stage for each kind of game.