We develop a robust algorithm for computing the nested full solution maximum likelihood estimator for a class of directional dynamic stochastic games with multiple equilibria.

We show how the computational burden of the full solution approach can be substantially reduced in large datasets, making it computationally feasible.

The proposed estimator is remarkably robust to multiplicity of equilibria in the theoretical model, and reliably delivers efficient maximum likelihood estimates of the structural parameters while identifying the equilibria played in the data.