In this paper, the generalized Nash equilibrium (GNE) seeking problem for continuous games with coupled affine inequality constraints is investigated in a partial-decision information scenario, where each player can only access its neighbors' information through local communication although its cost function possibly depends on all other players' strategies. To this end, a novel decentralized primal-dual algorithm based on consensus and dual diffusion methods is devised for seeking the variational GNE of the studied games. This paper also provides theoretical analysis to show that the designed algorithm converges linearly for the last-iterate, which, to our best knowledge, is the first to propose a linearly convergent GNE seeking algorithm under coupled affine inequality constraints. Finally, a numerical example is presented to demonstrate the effectiveness of the obtained theoretical results.
翻译:在本文中,在局部决策信息假设中,调查了在连续游戏中寻找问题的普遍纳什平衡(GNE)以及结合的同系同系不平等制约因素,每个玩家只能通过当地通信获取其邻居的信息,尽管其成本功能可能取决于所有其他玩家的战略。为此,在共识和双重传播方法的基础上,设计了一个新的分散的原始双向算法,以寻求所研究的游戏的变异性GNE。本文还提供理论分析,以表明为最后一个玩家设计的算法是线性趋近的,据我们所知,这是第一个提出线性趋同的GNE在结合的同系不平等制约下寻求算法的人。最后,提供了一个数字例子,以证明所获得的理论结果的有效性。