Before revision:  Furthermore, EPL iterations are stable and locally convergent to the finite-sample maximum likelihood estimator at a nearly-quadratic rate for all regular Markov perfect equilibria, including unstable equilibria where NPL encounters convergence problems.
After revision:  Furthermore, EPL iterations are stable and locally convergent to the finite-sample maximum likelihood estimator with iteration and that the sequence of estimators converges almost surely to the maximum likelihood estimator at a nearly-superlinear rate when the data are generated by any regular Markov perfect equilibria, including unstable equilibria where NPL encounters convergence problems.