Optimal Selection and Tracking Of Generalized Nash Equilibria in Monotone Games

• 成果类型: Article
• 署名作者: Benenati, Emilio; Ananduta, Wicak; Grammatico, Sergio
• 署名单位: Delft University of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3288372
• 发表日期: 2023
• 页码: 7644-7659
• 关键词: multiagent systems; Nash equilibrium seeking; optimization

摘要

A fundamental open problem in monotone game theory is the computation of a specific generalized Nash equilibrium (GNE) among all the available ones, e.g., the optimal equilibrium with respect to a system-level objective. The existing GNE seeking algorithms have in fact convergence guarantees toward an arbitrary, possibly inefficient, equilibrium. In this article, we solve this open problem by leveraging results from fixed-point selection theory and in turn derive distributed algorithms for the computation of an optimal GNE in monotone games. We then extend the technical results to the time-varying setting and propose an algorithm that tracks the sequence of optimal equilibria up to an asymptotic error, whose bound depends on the local computational capabilities of the agents.