Competing Complements

In Cournot's model of complements, the producers of A and B are bothmonopolists. This paper extends Cournot's model to allow for competitionbetween complements on one side of the market. Consider two complements,A and B, where the A + B bundle is valuable only when purchasedtogether. Good A is supplied by a monopolist (e.g., Microsoft) and thereis competition in the B goods from vertically differentiated suppliers(e.g., Intel and AMD). In this simple game, there may not be apure-strategy equilibria. In the standard case where marginal costs areweakly positive, there is no pure strategy where the lower quality Bfirm obtains positive market share. We also consider the case where Ahas negative marginal costs, as would arise when A can expect to makeupgrade sales to an installed base. When profits from the installed baseare sufficiently large, a pure strategy equilibrium exists with two Bfirms active in the market. Although there is competition in thecomplement market, the monopoly Firm A may earn lower profits in thisenvironment. Consequently, A may prefer to accept lower future profitsin order to interact with a monopolist complement in B.