We develop a revealed preference characterization of those data sets which are consistent with the agent obeying single crossing differences and the interval dominance order.  This characterization can be extended to test for strategic complementarity in games and to make out-of-sample predictions of Nash equilibria. In keeping with the literature on axiomatic or revealed preference characterizations, these results require repeated observations of the same agent or group of agents. To facilitate the empirical application of these tests, we formulate stochastic versions that are applicable to cross sectional data.  Lastly, to illustrate how our results could be used, we apply them to model spousal and regulatory influence on smoking behavior.