Fixed-Time Nash Equilibrium Seeking in Non-Cooperative Games
Fixed-Time Nash Equilibrium Seeking in Non-Cooperative Games
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DOI：
10.1109/cdc42340.2020.9304146
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发表时间：
2020-12
期刊：
影响因子：
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通讯作者：
J. Poveda;M. Krstić;T. Başar
中科院分区：
文献类型：
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作者：
J. Poveda;M. Krstić;T. Başar
我们引入了一类新的纳什均衡寻求动态的非合作游戏有限数量的球员，收敛到纳什均衡是有界的一个$\mathcal{K}\mathcal{L}$功能的解决时间，可以是上界的一个正常数，是独立的初始条件的球员，并可以事先规定的系统设计者。动态是无模型的，在这个意义上说，数学形式的成本函数的球员是未知的。相反，为了更新自己的行动，每个玩家只需要访问自己的成本的实时评估，以及由通信图表征的相邻玩家的辅助状态。稳定性和收敛性建立潜在的游戏和强单调游戏。数值例子来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 $\mathcal{K}\mathcal{L}$ 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.