论文标题
关于广义总体游戏中平衡的鲁棒性
On the robustness of equilibria in generalized aggregative games
论文作者
论文摘要
我们解决了评估不确定的多代理游戏中平衡的鲁棒性的问题。具体而言，我们专注于汇总形式中普遍的NASH平衡问题，但受到不确定性影响的线性耦合约束，可能是未知的概率分布。在数据驱动的上下文中，我们应用方案方法范式为整个游戏中的整个NASH平衡提供了A-tosteriori的可行性证书。然后，我们表明，评估这种集合的违规概率仅需要列举``形状''的约束。对于总体游戏类别，这会导致解决可行性区域每个活跃方面的可行性问题，我们建议使用半分解的算法。我们通过学术示例来证明我们的理论结果。
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.
