Leveraging Uniformization and Sparsity for Computation of Continuous Time Dynamic Discrete Choice Games

• Main Author: Blevins, Jason R
• Format: Journal Article
• Language: English
• Published: 20-07-2024
• DOI: 10.48550/arxiv.2407.14914

Continuous-time formulations of dynamic discrete choice games offer notable
computational advantages, particularly in modeling strategic interactions in
oligopolistic markets. This paper extends these benefits by addressing
computational challenges in order to improve model solution and estimation. We
first establish new results on the rates of convergence of the value iteration,
policy evaluation, and relative value iteration operators in the model, holding
fixed player beliefs. Next, we introduce a new representation of the value
function in the model based on uniformization -- a technique used in the
analysis of continuous time Markov chains -- which allows us to draw a direct
analogy to discrete time models. Furthermore, we show that uniformization also
leads to a stable method to compute the matrix exponential, an operator
appearing in the model's log likelihood function when only discrete time
"snapshot" data are available. We also develop a new algorithm that
concurrently computes the matrix exponential and its derivatives with respect
to model parameters, enhancing computational efficiency. By leveraging the
inherent sparsity of the model's intensity matrix, combined with sparse matrix
techniques and precomputed addresses, we show how to significantly speed up
computations. These strategies allow researchers to estimate more sophisticated
and realistic models of strategic interactions and policy impacts in empirical
industrial organization.