Variable-sample method for the computation of stochastic Nash equilibrium
提出一种变样本方法计算随机稳定纳什均衡，每轮迭代用不同样本量近似目标函数，证明算法收敛到一阶均衡条件，数值测试验证了有效性。
This article proposes a variable-sample method for the computation of stochastic stable Nash equilibrium, in which the objective functions are approximated, in each iteration, by the sample average approximation with different sample sizes. We start by investigating the contraction mapping properties under the variable-sample framework. Under some moderate conditions, it is shown that the accumulation points attained from the algorithm satisfy the first-order equilibrium conditions with probability one. Moreover, we use the asymptotic unbiasedness condition to prove the convergence of the accumulation points of the algorithm into the set of fixed points and prove the finite termination property of the algorithm. We also verify that the algorithm converges to the equilibrium even if the optimization problems in each iteration are solved inexactly. In the numerical tests, we comparatively analyze the accuracy error and the precision error of the estimators with different sample size schedules with respect to the sampling loads and the computational times. The results validate the effectiveness of the algorithm.