In this paper, the distributed Nash equilibrium (NE) searching problem is investigated, where the feasible action sets are constrained by nonlinear inequalities and linear equations. Different from most of the existing investigations on distributed NE searching problems, we consider the case where both cost functions and feasible action sets depend on actions of all players, and each player can only have access to the information of its neighbors. To address this problem, a continuous-time distributed gradient-based projected algorithm is proposed, where a leader-following consensus algorithm is employed for each player to estimate actions of others. Under mild assumptions on cost functions and graphs, it is shown that players’ actions asymptotically converge to a generalized NE. Simulation examples are presented to demonstrate the effectiveness of the theoretical results.

中文翻译：

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非合作博弈广义纳什均衡搜索的分布式算法

本文研究了分布式纳什均衡（NE）搜索问题，其中可行的动作集受到非线性不等式和线性方程的约束。与大多数有关分布式网元搜索问题的现有研究不同，我们考虑成本函数和可行动作集都取决于所有参与者的行为，并且每个参与者只能访问其邻居信息的情况。为了解决这个问题，提出了一种基于梯度分布的连续时间投影算法，其中针对每个参与者采用了领导者跟随共识算法来估计其他参与者的行动。在对成本函数和图形的温和假设下，证明了参与者的行为渐近地收敛于广义NE。