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Published February 2004 | Accepted Version
Journal Article Open

A characterization of strategic complementarities


I characterize games for which there is an order on strategies such that the game has strategic complementarities. I prove that, with some qualifications, games with a unique equilibrium have complementarities if and only if Cournot best-response dynamics has no cycles; and that all games with multiple equilibria have complementarities. As applications of my results, I show that: (1) generic 2×2 games either have no pure-strategy equilibria, or have complementarities; (2) generic two-player finite ordinal potential games have complementarities.

Additional Information

© 2003 Elsevier Inc. Received 1 April 2002. Available online 21 November 2003. I thank an associate editor and a referee for their comments. I also thank Elvio Accinelli, Bob Anderson, Juan Dubra, Paul Milgrom, StephenMorris, Charles Púgh, Ilya Segal, Chris Shannon, Satoru Takahashi, Xavier Vives, and seminar participants at Arizona State and Stanford Universities. A conversation with Ted O'Donoghue and Clara Wang prompted me to work on the research presented here. The nonstandard proof of Theorem 3 owes a great deal to Bob Anderson; I am deeply grateful for his help. I worked out the results in Section 8 in response to Stephen Morris's very stimulating questions. Finally, part of this paper was written while I visited UC Berkeley's Economics Department, I appreciate Berkeley's hospitality. Any errors are my responsibility.

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