Efficient Estimation of Equilibria in Large Aggregative Games With Coupling Constraints

• 成果类型: Article
• 署名作者: Jacquot, Paulin; Wan, Cheng; Beaude, Olivier; Oudjane, Nadia
• 署名单位: Inria; Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3008649
• 发表日期: 2021
• 页码: 2762-2769
• 关键词: games; Couplings; sociology; statistics; cost function; Aggregates; computational modeling; Aggregative game; population game; variational inequalities (VIs); variational Nash equilibrium (VNE)

摘要

Aggregative games have many industrial applications, and computing an equilibrium in those games is challenging when the number of players is large. In the framework of atomic aggregative games with coupling constraints, we show that variational Nash equilibria of a large aggregative game can be approximated by a Wardrop equilibrium of an auxiliary population game of smaller dimension. Each population of this auxiliary game corresponds to a group of atomic players of the initial large game. This approach enables an efficient computation of an approximated equilibrium, as the variational inequality characterizing the Wardrop equilibrium is of smaller dimension than the initial one. This is illustrated in an example in the smart grid context.