We study econometric models of complete information games with ordered action spaces, such as the number of store fronts operated in a market by a rm, or the daily number of flights on a city-pair off ered by an airline. The model generalizes single agent models such as ordered probit and logit to a simultaneous equations model of ordered response, allowing for multiple equilibria and set identication. We characterize identifed sets for model parameters under mild shape restrictions on agents’ payo functions. We then propose a novel inference method for a parametric version of our model based on a test statistic that embeds conditional moment inequalities implied by equilibrium behavior. Using maximal inequalities for U-processes, we show that an asymptotically valid condence set is attained by employing an easy to compute fixed critical value, namely the appropriate quantile of a chi-square random variable. We apply our method to study capacity decisions measured as the number of stores operated by Lowe’s and Home Depot in geographic markets. We demonstrate how our condence sets for model parameters can be used to perform inference on other quantities of economic interest, such as the probability that any given outcome is an equilibrium and the propensity with which any particular outcome is selected when it is one of multiple equilibria, and we perform a counterfactual analysis of store congurations under both collusive and monopolistic regimes.