This paper analyzes dynamic oligopoly models where investment is the principal strategic variable of interest, there are a large number of investment choices, and there are privately observed shocks to the marginal cost of investment. We show that simulation methods to compute these models can result in non-existence of pure strategy equilibrium. We provide a computationally efficient method to calculate optimal investment probabilities and show how to apply our methods to the recent dynamic empirical literature. The method iteratively finds the investment choices chosen with positive probability and cutoff values of the private information shocks across options in this set.