论文标题
纳什平衡在有向图上寻求
Nash Equilibrium Seeking Over Directed Graphs
论文作者
论文摘要
在本文中，我们旨在通过有导图开发分布式的连续时间算法，以在非合作游戏中寻求NASH平衡。在最近的基于共识的设计中，我们提出了一种分布式算法，具有比例平衡的有向图的比例增益。通过进一步嵌入与图形laplacian的零特征值相关的左特征向量的分布式估计器，我们将其扩展到案例，并使用任意连接的有定向图具有可能不平衡的权重。在这两种情况下，NASH平衡均以指数收敛速率完全达到。举例说明了理论结果的有效性。
In this paper, we aim to develop distributed continuous-time algorithms over directed graphs to seek the Nash equilibrium in a noncooperative game. Motivated by the recent consensus-based designs, we present a distributed algorithm with a proportional gain for weight-balanced directed graphs. By further embedding a distributed estimator of the left eigenvector associated with zero eigenvalue of the graph Laplacian, we extend it to the case with arbitrary strongly connected directed graphs having possible unbalanced weights. In both cases, the Nash equilibrium is proven to be exactly reached with an exponential convergence rate. An example is given to illustrate the validity of the theoretical results.
