Horizontal mergers: a solution of the insiders' dilemma

We show that in a three-firm infinitely repeated Cournot game, there exists a stick and carrot strategy equilibrium in which an exogenous bilateral horizontal merger is profitable and the incentive to remain out of the merger disappears. In this sub-game perfect equilibrium, the merged entity produces the duopoly quantity and the outsider limits its production to half the duopoly quantity. Our stick and carrot strategy entails that the merged entity threatens to produce twice the triopoly quantity for two periods if the outsider does not produce half the duopoly quantity. In this equilibrium, the aggregate price remains high enough to make the merger profitable for the insiders. Also, the quantity produced by the outsider is sufficiently low to eliminate the difference between the profit of the outsider and the merging firm.