This article investigates the generalized Nash equilibrium (GNE) seeking for the game with equality constraints. Each player cannot directly access all the other player's actions and the gradients of all players' payoff functions are unknown. In these scenarios, an interesting question is under what distributed algorithm the GNE can be found. To address such games, we first design a two‐time‐scale distributed algorithm based on the extremum seeking method and consensus protocol. Then, by utilizing singular perturbation techniques and Lyapunov robust analysis, we show that the players' decisions can be regulated to an arbitrarily small neighborhood of the GNE. Moreover, we further consider the ideal case in which the gradients are known. In this case, the proposed strategy can be degenerated to a gradient‐based algorithm and the players' decisions exponentially converge to the GNE. Finally, two examples along with simulation results are used to illustrate the effectiveness of the proposed algorithms.

中文翻译：

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基于共识和极值搜索的分布式广义纳什均衡方法

本文研究了具有相等约束的博弈的广义纳什均衡（GNE）。每个玩家都不能直接访问其他玩家的所有动作，并且所有玩家的支付功能的梯度都是未知的。在这些情况下，一个有趣的问题是可以在哪种分布式算法下找到GNE。为了解决这类游戏，我们首先基于极值搜索方法和共识协议设计了一种两阶段规模的分布式算法。然后，通过使用奇异摄动技术和Lyapunov鲁棒分析，我们证明了玩家的决定可以被调节到GNE的任意较小邻域中。此外，我们还考虑了已知梯度的理想情况。在这种情况下，所提出的策略可以退化为基于梯度的算法，参与者的决策以指数形式收敛到GNE。最后，通过两个例子以及仿真结果来说明所提算法的有效性。