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 problem which requires optimization over the infinite dimensional set, we consider the equivalent dual problem which entails optimization over only a finite-dimensional Euclidean space. 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. (2014) to characterize the identified region of marginal costs.