Confidence Regions for Parameters in Discrete Games with Multiple Equilibria, with an Application to Discount Chain Store Location

In this paper, we consider the empirical problem of estimating the underlying profit function of firms from “revealed choice” data on entry in a cross-section of oligopoly markets. One problem faced in the earlier literature is the problem of multiple equilibrium, which makes traditional maximum likelihood estimation (MLE) techniques difficult to implement. The problem of multiple equilibria is serious enough that Sutton (2000), for example, suggests giving up on parameter estimation in the case of realistic entry models. However, Manski and co-authors (e.g. Manski and Tamer (2002)) encourage work on a related class of “incomplete” parametric models. In this paper, we combine the two ideas and consider the estimation of complicated entry models that exhibit multiple equilibria, without attempting to resolve the equilibrium selection problem.