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...

In games with strict strategic complementarities, properly mixed Nash equilibria--equilibria that are not in pure strategies--are unstable for a broad class of learning dynamics.