We consider for the first time a stochastic generalized Nash equilibrium problem, i.e., with expected-value cost functions and joint feasibility constraints, under partial-decision information, meaning that the agents communicate only with some trusted neighbours. We propose several distributed algorithms for network games and aggregative games that we show being special instances of a preconditioned forward-backward splitting method. We prove that the algorithms converge to a generalized Nash equilibrium when the forward operator is restricted cocoercive by using the stochastic approximation scheme with variance reduction to estimate the expected value of the pseudogradient.

中文翻译：

---

部分决策信息下的随机广义纳什均衡寻求

我们第一次考虑随机广义纳什均衡问题，即在部分决策信息下具有期望值成本函数和联合可行性约束，这意味着代理仅与一些受信任的邻居进行通信。我们为网络游戏和聚合游戏提出了几种分布式算法，我们展示了它们是预处理前向后向分裂方法的特殊实例。我们通过使用方差减少的随机逼近方案来估计伪梯度的期望值，证明了当前向算子被限制cocoercive 时，算法收敛到广义纳什均衡。