论文标题
固定时间NASH在非合作游戏中寻求均衡
Fixed-Time Nash Equilibrium Seeking in Non-Cooperative Games
论文作者
论文摘要
我们介绍了一类新颖的NASH平衡，寻求具有有限玩家数量的非合作游戏的动态，其中融合了NASH平衡的融合受KL功能的界限，其结算时间限制了一个可以独立于播放器的初始条件，并且可以由系统设计师处方的正常数，该正常与播放器的初始条件无关。从某种意义上说，动态是无模型的，那就是播放器的成本函数的数学形式是未知的。相反，为了更新自己的动作，每个玩家只需要访问其自身成本的实时评估，以及以通信图为特征的邻近玩家的辅助状态。潜在游戏和强烈单调游戏都建立了稳定性和收敛性。提出了数值示例，以说明我们的理论结果。
We introduce a novel class of Nash equilibrium seeking dynamics for non-cooperative games with a finite number of players, where the convergence to the Nash equilibrium is bounded by a KL function with a settling time that can be upper bounded by a positive constant that is independent of the initial conditions of the players, and which can be prescribed a priori by the system designer. The dynamics are model-free, in the sense that the mathematical forms of the cost functions of the players are unknown. Instead, in order to update its own action, each player needs to have access only to real-time evaluations of its own cost, as well as to auxiliary states of neighboring players characterized by a communication graph. Stability and convergence properties are established for both potential games and strongly monotone games. Numerical examples are presented to illustrate our theoretical results.
