Cross sales in supply chains: An equilibrium analysis

Consider a supply chain system with two manufacturers, each producing a single substitutable product. The products are sold through two retailers, each to be privately owned or owned by the manufacturer. A manufacturer is free to use a single retailer or both. We define cross sales to be the situation where at least one retailer sells both products and analyze the cross sales in channels with different degree of vertical integration. We show that cross sale will happen in quantity competition or in a capacity constrained price competition. However, cross sales may never happen in a pure Bertrand price competition.