In this note, we investigate the robustness of Nash equilibria (NE) in multi-player aggregative games with coupling constraints. There are many algorithms for computing an NE of an aggregative game given a known aggregator. When the coupling parameters are affected by uncertainty, robust NE need to be computed. We consider a scenario where players' weight in the aggregator is unknown, making the aggregator kind of "a black box". We pursue a suitable learning approach to estimate the unknown aggregator by proposing an inverse variational inequality-based relationship. We then utilize the counterpart to reconstruct the game and obtain first-order conditions for robust NE in the worst case. Furthermore, we characterize the generalization property of the learning methodology via an upper bound on the violation probability. Simulation experiments show the effectiveness of the proposed inverse learning approach.

翻译：本文研究了带有耦合约束的多参与者聚合博弈中纳什均衡的鲁棒性问题。在已知聚合器的情况下，已有多种算法可用于计算聚合博弈的纳什均衡。当耦合参数受到不确定性影响时，需计算鲁棒纳什均衡。我们考虑一种场景：参与者权重在聚合器中未知，导致聚合器呈现"黑箱"特性。通过提出基于逆变分不等式的关系，我们探索了一种合适的学习方法来估计未知聚合器。随后利用该对应关系重构博弈，并推导出最坏情况下鲁棒纳什均衡的一阶条件。此外，我们通过违例概率的上界刻画了学习方法的泛化性能。仿真实验验证了所提逆向学习方法的有效性。