  We propose a new sequential Efficient Pseudo-Likelihood (k-EPL) estimator for
dynamic discrete choice games of incomplete information. k-EPL considers the
joint behavior of multiple players simultaneously, as opposed to individual
responses to other agents' equilibrium play. This, in addition to reframing the
problem from conditional choice probability (CCP) space to value function
space, yields a computationally tractable, stable, and efficient estimator. We
show that each iteration in the k-EPL sequence is consistent and asymptotically
efficient, so the first-order asymptotic properties do not vary across
iterations. Furthermore, we show the sequence achieves higher-order equivalence
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 equilibrium, including equilibria that lead to
inconsistency of other sequential estimators. When utility is linear in
parameters, k-EPL iterations are computationally simple, only requiring that
the researcher solve linear systems of equations to generate pseudo-regressors
which are used in a static logit/probit regression. Monte Carlo simulations
demonstrate the theoretical results and show k-EPL's good performance in finite
samples in both small- and large-scale games, even when the game admits
spurious equilibria in addition to one that generated the data. We apply the
estimator to study the role of competition in the U.S. wholesale club industry.
