论文标题
通过无梯度方法在N-Coalition游戏中寻求NASH平衡
Nash Equilibrium Seeking in N-Coalition Games via a Gradient-Free Method
论文作者
论文摘要
本文研究了一个$ n $ coalition的非合作游戏问题，在同一联盟中，在定向通信图下，同一联盟的玩家合作将其本地成本功能的总和最小化，同时集体充当虚拟玩家，与其他联盟一起玩不合作游戏。此外，假定玩家无法访问明确的功能形式，而只能使用其本地成本的功能值。为了解决该问题，提出了基于梯度跟踪方法的无离散时间NASH平衡寻求策略。具体而言，梯度估计器是基于高斯平滑而在本地开发的，以估计部分梯度，并且在本地构建了梯度跟踪器，以追踪联盟中参与者中局部梯度的平均值。凭借足够小的恒定步骤尺寸，我们表明所有玩家的动作大约在强烈单调的游戏映射条件下以几何速率收敛到NASH平衡。进行数值模拟以验证所提出算法的有效性。
This paper studies an $N$-coalition non-cooperative game problem, where the players in the same coalition cooperatively minimize the sum of their local cost functions under a directed communication graph, while collectively acting as a virtual player to play a non-cooperative game with other coalitions. Moreover, it is assumed that the players have no access to the explicit functional form but only the function value of their local costs. To solve the problem, a discrete-time gradient-free Nash equilibrium seeking strategy, based on the gradient tracking method, is proposed. Specifically, a gradient estimator is developed locally based on Gaussian smoothing to estimate the partial gradients, and a gradient tracker is constructed locally to trace the average sum of the partial gradients among the players within the coalition. With a sufficiently small constant step-size, we show that all players' actions approximately converge to the Nash equilibrium at a geometric rate under a strongly monotone game mapping condition. Numerical simulations are conducted to verify the effectiveness of the proposed algorithm.
