  Estimating structural models is an essential tool for economists. However,
existing methods are often inefficient either computationally or statistically,
depending on how equilibrium conditions are imposed. We propose a class of
penalized sieve estimators that are consistent, asymptotic normal, and
asymptotically efficient. Instead of solving the model repeatedly, we
approximate the solution with a linear combination of basis functions and
impose equilibrium conditions as a penalty in searching for the best fitting
coefficients. We apply our method to an entry game between Walmart and Kmart.
