Working Paper | HBS Working Paper Series | 2010

Competing Complements

by Ramon Casadesus-Masanell, Barry Nalebuff and David B. Yoffie


In Cournot's model of complements, the producers of A and B are both monopolists. This paper extends Cournot's model to allow for competition between complements on one side of the market. Consider two complements, A and B, where the A + B bundle is valuable only when purchased together. Good A is supplied by a monopolist (e.g., Microsoft) and there is competition in the B goods from vertically differentiated suppliers (e.g., Intel and AMD). In this simple game, there may not be a pure-strategy equilibrium. With constant marginal costs, there is never a pure-strategy solution where the lower-quality B firm obtains positive market share. We also consider the case where A obtains revenue from follow-on sales, as might arise when A expects to make upgrade sales to an installed base. If profits from the installed base are sufficiently large, a pure-strategy equilibrium exists where both B firms are active in the market. Although there is competition in the complement market, the monopoly Firm A may earn lower profits in this environment. Consequently, A may prefer to accept lower future profits in order to interact with a monopolist complement in B.

Keywords: Profit; Revenue; Monopoly; Game Theory; Competition;


Casadesus-Masanell, Ramon, Barry Nalebuff, and David B. Yoffie. "Competing Complements." Harvard Business School Working Paper, No. 09-009, July 2008. (Revised March 2010.)