In this paper we introduce a new computationally tractable framework for Ericson and Pakes (1995)-style dynamic oligopoly models that overcomes the computational complexity involved in computing Markov perfect equilibrium (MPE). First, we define a new equilibrium concept that we call moment-based Markov equilibrium (MME), in which firms keep track of their own state, the detailed state of dominant firms, and few moments of the distribution of fringe firms’ states. Second, we provide guidelines to use MME in applied work and illustrate with an application how it can endogenize the market structure in a dynamic industry model even with hundreds of firms. Third, we develop a series of results that provide support for using MME as an approximation. We present numerical experiments showing that MME approximates MPE for important classes of models. Then, we introduce novel unilateral deviation error bounds that can be used to test the accuracy of MME as an approximation in large-scale settings. Overall, our new framework opens the door to study novel issues in industry dynamics.