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Published October 2002 | Submitted
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A Characterization of Strategic Complementarities

Echenique, Federico ORCID icon
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Abstract

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: 1. That generic 2X2 games either have no pure-strategy equilibria, or have complementarities. 2. That generic two-player infinite ordinal potential games have complementarities.

Additional Information

I thank an associate editor and a referee for their comments. I also thank Elvio Accinelli, Bob Anderson, Juan Dubra, Paul Milgrom, Stephen Morris, Charles Púugh, Ilya Segal, Chris Shannon, 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 non-standard 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. Published as Echenique, F. (2004). A characterization of strategic complementarities. Games and Economic Behavior, 46(2), 325-347.

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