This paper presents a two-step algorithm for estimating dynamic games under the assumption that behavior is consistent with Markov Perfect Equilibrium. The first step estimates policy functions and the law of motion for state variables. The second step estimates remaining structural parameters using optimality conditions for equilibrium. The second step estimator is a simple simulated minimum distance estimator. The algorithm applies to a broad class of models, including I.O. models with both discrete and continuous controls. The authors test the algorithm on dynamic discrete choice models with normally distributed errors and dynamic oligopoly models similar to Pakes and McGuire (1994). The paper also discusses computational efficiency, identification issues, and the use of bounds in non-identified models. The algorithm is shown to be computationally efficient and effective in recovering parameters even with small data sets. The authors provide asymptotic theory and discuss the implications of their estimation method for policy analysis.This paper presents a two-step algorithm for estimating dynamic games under the assumption that behavior is consistent with Markov Perfect Equilibrium. The first step estimates policy functions and the law of motion for state variables. The second step estimates remaining structural parameters using optimality conditions for equilibrium. The second step estimator is a simple simulated minimum distance estimator. The algorithm applies to a broad class of models, including I.O. models with both discrete and continuous controls. The authors test the algorithm on dynamic discrete choice models with normally distributed errors and dynamic oligopoly models similar to Pakes and McGuire (1994). The paper also discusses computational efficiency, identification issues, and the use of bounds in non-identified models. The algorithm is shown to be computationally efficient and effective in recovering parameters even with small data sets. The authors provide asymptotic theory and discuss the implications of their estimation method for policy analysis.