Asymptotic Properties of Static Output Feedback for Large-Scale Stochastic Mean Field Games

In this paper, we consider large-scale mean-field stochastic systems. After defining a stabilization problem based on a static output feedback strategy, we apply Nash equilibrium strategies to the problem. Note that the initial condition assumption is extended to the general case compared to existing results. The problem of minimizing the cost function is solved using the Lagrange multiplier technique. However, as the number of players increases, computational challenges arise in determining solutions. To address this problem, we develop a decentralized design and the numerical algorithm to obtain the suboptimal solution set. As a result, the parameter-independent strategy and the associated function are investigated. The Pareto strategy is also considered as another cooperative game. Numerical examples validate the practicality and effectiveness of the decentralized numerical algorithm.