A Robust Semi-parametric Inference of Dynamic Discrete Games1

Zhengyuan Gao This paper considers the dynamic discrete game model with fixed points in the worst case and with incomplete beliefs. In the worst case, an -approximation to a fixed point does not lead to the consistent second step estimator of the parametric structural parameters. Given certain structures of the value function, we propose an alternative two-step inference algorithm. The first step is to control the complexity of the nonparametric approximation and to estimated value and policy functions under the worst case. The second step is to select a pseudo parameter that can give a -fitting and can generate an empirical log-likelihood test statistic. The hypothesis testing should accept the estimated values of structural parameters. The objective functions in both steps can reduce to linear-quadratic equations and are robust to outliers.