Nonsmooth Continuous-Time Distributed Algorithms for Seeking Generalized Nash Equilibria of Noncooperative Games via Digraphs
研究了多智能体网络中非合作博弈的分布式广义纳什均衡求解问题，提出一种基于共识和原始对偶的连续时间算法，适用于成本函数非光滑且约束含共享线性方程的场景。
In this article, the problem of distributed generalized Nash equilibrium (GNE) seeking in noncooperative games is investigated via multiagent networks, where each player aims to minimize his or her own cost function with a nonsmooth term. Each player's cost function and feasible action set in the noncooperative game are both determined by actions of others who may not be neighbors, as well as his/her own action. Particularly, feasible action sets are constrained by private convex inequalities and shared linear equations. Each player can only have access to his or her own cost function, private constraint, and a local block of shared constraints, and can only communicate with his or her neighbours via a digraph. To address this problem, a novel continuous-time distributed primal-dual algorithm involving Clarke's generalized gradient is proposed based on consensus algorithms and the primal-dual algorithm. Under mild assumptions on cost functions and graph, we prove that players' actions asymptotically converge to a GNE. Finally, a simulation is presented to demonstrate the effectiveness of our theoretical results.