We consider the stochastic generalized Nash equilibrium problem (SGNEP) with joint feasibility constraints and expected-value cost functions. We propose a distributed stochastic projected reflected gradient algorithm and show its almost sure convergence when the pseudogradient mapping is monotone and the solution is unique. The algorithm is based on monotone operator splitting methods tailored for SGNEPs when the expected-value pseudogradient mapping is approximated at each iteration via an increasing number of samples of the random variable. Finally, we show that a preconditioned variant of our proposed algorithm has convergence guarantees when the pseudogradient mapping is cocoercive.

翻译：我们考虑了带有联合可行性限制和预期价值成本功能的随机普遍纳什平衡问题(SGNEP ) 。 我们提出一个分布式随机预测梯度算法,并在假梯度映射为单质且解决方案独特时显示其几乎肯定的趋同性。 该算法基于单质操作器分离方法,当预期值伪梯度映射通过随机变量的越来越多的样本在每次迭代时接近于预期值的单质操作器绘制。 最后,我们表明,我们拟议算法的一个先决条件变量在伪梯度映射为可凝固性时具有趋同性保证。