An ordinal approach to the empirical analysis of games with monotone best responses

We develop a nonparametric and ordinal approach for testing pure strategy Nash equilibrium play in games with monotone best responses, such as those with strategic complements/substitutes. The approach makes minimal assumptions on unobserved heterogeneity, requires no parametric assumptions on payoff functions, and no restriction on equilibrium selection from multiple equilibria. The approach can also be extended in order to make inferences and predictions. Both model-testing and inference can be implemented by a tractable computation procedure based on column generation. To illustrate how our approach works, we include an application to an IO entry game.