In this paper I develop a new approach for identi…cation and estimation of the parameters of an oligopoly model, without relying on a potentially unveri…able equilibrium assumption. Rather, I consider inference on model parameters when the researcher does not know precisely what decision rule …rms use, but is willing to consider a set of possibilities. In contrast to traditional approaches in the literature, the proposed methodology allows …rm behavior to vary ‡exibly across observations, in a manner consistent with many Nash Equilibria. I derive identi…cation results for both homogeneous product and di¤erentiated product markets. Due to the ‡exibility a¤orded to …rm behavior, the parameters of …rms' marginal cost functions may only be set identi…ed rather than point identi…ed. The restrictions of the model are, however, still informative. I …nd that the size of the identi…ed set for marginal cost parameters depends on the elasticity of market demand, the set of decision rules considered, and the functional form assumptions imposed. I formulate how to compute consistent set estimates for marginal cost parameters and demonstrate the proposed methodology with price and quantity data on the Joint Executive Committee, a 19th century railway cartel. To perform statistical inference I implement the methodology of Rosen (2005) to construct asymptotically valid con…dence regions for the partially identi…ed marginal cost parameters. The application illustrates how