2022/12/09 by Qing Tang, Jiahao Song, Tang, Qing +1
Economics, Econometrics and Finance · Engineering · Materials Science · #Economic Policies and Impacts #FOS: Mathematics #Frequency Control in Power Systems #Magnetic and transport properties of perovskites and related materials #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2212.04791
openalex publication_date 2022/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce two Smoothed Policy Iteration algorithms (SPIs) as rules for learning policies and methods for computing Nash equilibria in second order potential Mean Field Games (MFGs). Global convergence is proved if the coupling term in the MFG system satisfy the Lasry Lions monotonicity condition. Local convergence to a stable solution is proved for system which may have multiple solutions. The convergence analysis shows close connections between SPIs and the Fictitious Play algorithm, which has been widely studied in the MFG literature. Numerical simulation results based on finite difference schemes are presented to supplement the theoretical analysis.