We address the problem of assessing the robustness of the equilibria in uncertain, multi-agent games. Specifically, we focus on generalized Nash equilibrium problems in aggregative form subject to linear coupling constraints affected by uncertainty with a possibly unknown probability distribution. Within a data-driven context, we apply the scenario approach paradigm to provide a-posteriori feasibility certificates for the entire set of generalized Nash equilibria of the game. Then, we show that assessing the violation probability of such set merely requires to enumerate the constraints that ``shape'' it. For the class of aggregative games, this results in solving a feasibility problem on each active facet of the feasibility region, for which we propose a semi-decentralized algorithm. We demonstrate our theoretical results by means of an academic example.

中文翻译：

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广义聚合博弈中均衡的鲁棒性

我们解决了在不确定的多智能体博弈中评估均衡稳健性的问题。具体来说，我们专注于受线性耦合约束的聚合形式的广义纳什均衡问题，该约束受不确定性影响，概率分布可能未知。在数据驱动的上下文中，我们应用场景方法范式为游戏的整个广义纳什均衡集提供后验可行性证明。然后，我们表明评估此类集合的违规概率仅需要枚举“塑造”它的约束。对于聚合游戏类，这导致解决可行性区域的每个活动方面的可行性问题，为此我们提出了一种半去中心化算法。