Electronic copy available at: http://ssrn.com/abstract=1032461
NET Institute*
www.NETinst.org
Working Paper #07-44
November 2007
Competing Complements
Ramon Casadesus-Masanell
Harvard Business School
Barry Nalebuff
SOM Yale University
David Yoffie
Harvard Business School
* The Networks, Electronic Commerce, and Telecommunications (“NET”) Institute,
http://www.NETinst.org, is a non-profit institution devoted to research on network
industries, electronic commerce, telecommunications, the Internet, “virtual networks”
comprised of computers that share the same technical standard or operating system, and
on network issues in general.
Electronic copy available at: http://ssrn.com/abstract=1032461
Competing Complements∗
Ramon Casadesus-Masanell†
Barry Nalebuff‡
David Yoffie§
November 21, 2007
Abstract
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
equilibria. In the standard case where marginal costs are weakly positive, there is no
pure strategy where the lower quality B firm obtains positive market share. We also
consider the case where A has negative marginal costs, as would arise when A can
expect to make upgrade sales to an installed base. When profits from the installed
base are sufficiently large, a pure strategy equilibrium exists with two B firms 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.
Keyword