线性收敛速率的算法A：纳什均衡解的有效性分析

Theorem 1 demonstrates that Algorithm A, designed by appropriately selecting a fixed step size A and adjusting parameter B, will enjoy a linear convergence rate. In addition, in S and D, sufficient conditions for choosing effective A and B to ensure a spectral radius C less than 1 are provided. Moreover, the impact of topological-related parameter E, problem-related parameter W, and the number of players Q on parameter selection is revealed. The results indicate that although the presence of uncertainty hinders the search for Nash equilibrium solutions, when the growth of the number of sampled pseudo-gradients satisfies A, the error sequence S will converge to 0 in expectation.