Estimation of (static or dynamic) games under equilibrium multiplicity

We propose a multiplicity-robust estimation method for static or dynamic games. The method allows for distinct behaviors and strategies across markets by treating market-specific behaviors as correlated latent variables, with their conditional probability measure treated as an infinite-dimensional nuisance parameter. Instead of solving the intermediate infinite-dimensional optimization problem, we consider the equivalent finite-dimensional dual problem. This property allows for a practically feasible characterization of the identified region for the structural parameters. We apply the estimation method to newspaper market previously studied in Gentzkow et al. (American Economic Review 104 (2014), 3073–114) to characterize the identified region of marginal costs.