论文标题
在不确定的多代理游戏中，纳什均衡的后验概率可行性保证
A posteriori probabilistic feasibility guarantees for Nash equilibria in uncertain multi-agent games
论文作者
论文摘要
在本文中，提出了一种无分配方法，以提供多代理游戏的NASH Equilibria（NE）的鲁棒性保证。利用了所谓的情景方法的最新后验发展（Campi等，2018），我们为具有多重约束的可行性问题提供了概率保证。然后在多代理游戏的上下文中使用此结果，从而提供了稳健性证书，以违反给定游戏的任何NE。我们的保证可以与任何返回一些平衡解决方案的NE算法一起使用。最后，通过利用我们问题的结构，我们规避了使用计算性刺激性算法来找到不可减至的支持子样本的需求，这是场景方法核心的概念。我们的理论结果伴随着模拟研究，研究了两个不同问题的溶液的鲁棒性，即二维可行性问题和电动汽车（EV）充电控制问题。
In this paper a distribution-free methodology is presented for providing robustness guarantees for Nash equilibria (NE) of multi-agent games. Leveraging recent a posteriori developments of the so called scenario approach (Campi et al., 2018), we provide probabilistic guarantees for feasibility problems with polytopic constraints. This result is then used in the context of multi-agent games, allowing to provide robustness certificates for constraint violation of any NE of a given game. Our guarantees can be used alongside any NE seeking algorithm that returns some equilibrium solution. Finally, by exploiting the structure of our problem, we circumvent the need of employing computationally prohibitive algorithms to find an irreducible support subsample, a concept at the core of the scenario approach. Our theoretical results are accompanied by simulation studies that investigate the robustness of the solutions of two different problems, namely, a 2-dimensional feasibility problem and an electric vehicle (EV) charging control problem.
