We consider quadratic, nonmonotone generalized Nash equilibrium problems with symmetric interactions among the agents, which are known to be potential. As may happen in practical cases, we envision a scenario in which an explicit expression of the underlying potential function is not available, and we design a two-layer Nash equilibrium seeking algorithm. In the proposed scheme, a coordinator iteratively integrates the noisy agents' feedback to learn the pseudo-gradients of the agents, and then design personalized incentives for them. On their side, the agents receive those personalized incentives, compute a solution to an extended game, and then return feedback measures to the coordinator. We show that our algorithm returns an equilibrium in case the coordinator is endowed with standard learning policies, and corroborate our results on a numerical instance of a hypomonotone game.
翻译:我们认为,在代理人之间对称性互动中存在着四面性、非摩诺普遍纳什均衡问题,已知这种互动是潜在的。在实际情况下,我们设想一种可能无法明确表达潜在功能的情景,我们设计了一种双层纳什均衡的算法。在拟议的办法中,一位协调员将噪音代理人的反馈反复整合在一起,以学习代理人的假等级,然后为他们设计个性化激励。在他们一边,代理人得到那些个性化激励,计算一个延长游戏的解决方案,然后将反馈措施归还给协调员。我们表明,如果协调员具备标准的学习政策,我们的算法返回了一种平衡,并在一个低调游戏的数字实例中证实了我们的结果。