Downstream mergers in vertically related markets with capacity constraints

Motivated by a recent merger proposal in the French outdoor advertising market, we develop a model in which firms are initially endowed with some advertising capacities and compete on two fronts. First, firms compete to acquire additional advertising capacities on an upstream market; a first stage modeled as a second-price auction with externalities. Second, those firms, privately informed on their own costs, use their capacities on the downstream market to supply advertisers whose demand is random; a second stage modeled by means of mechanism design techniques. We study the linkages between the equilibrium outcomes on both markets. When a firm is endowed with more initial capacity, through the acquisition of a competitor for instance, whether it becomes more or less eager to acquire extra capacity on the upstream market depends a priori on fine details of the downstream market. Under reasonable choices of functional forms, we demonstrate that a downstream merger does not create any bias in the upstream market towards the already dominant firm.