📝 SummarXiv

Abstract

Continuous-time empirical dynamic discrete choice games offer notable computational advantages over discrete-time models. This paper addresses remaining computational challenges to further improve both model solution and maximum likelihood estimation. We establish convergence rates for value iteration and policy evaluation with fixed beliefs, and develop Newton-Kantorovich methods that exploit analytical Jacobians and sparse matrix structure. We apply uniformization both to derive a new representation of the value function that draws direct analogies to discrete-time models and to enable stable computation of the matrix exponential and its parameter derivatives for likelihood-based estimation with snapshot data. Critically, these methods provide a complete chain of analytical derivatives from the equilibrium value function through the log likelihood function, eliminating numerical approximations in both model solution and estimation and improving finite-sample statistical properties. Monte Carlo experiments demonstrate substantial gains in computational time and estimator accuracy, enabling estimation of richer models of strategic interaction.