论文标题
通过基于共识的无梯度方法，分布式NASH平衡寻求具有有限成本功能知识的有限功能知识
Distributed Nash Equilibrium Seeking with Limited Cost Function Knowledge via A Consensus-Based Gradient-Free Method
论文作者
论文摘要
本文考虑了分布式的纳什均衡寻求问题，在这些问题中，玩家只能部分访问其他玩家的行动，例如邻居的行动。因此，玩家应该相互交流以估计其他玩家的行为。为了解决该问题，提出了提出了无领导者共识的无梯度分布式NASH均衡算法。该算法仅利用玩家的本地成本功能的测量值，而无需了解其明确表达或对其平稳性的要求。因此，在整个更新过程中，该算法是无梯度的。此外，研究算法分别研究了NASH平衡收敛性的分析，分别既减少又有恒定的阶梯尺寸。具体而言，在减小的阶梯尺寸的情况下，这表明玩家的动作几乎可以肯定地融合到NASH平衡，而在固定的踏板尺寸的情况下，可以达到与NASH平衡邻居的收敛。通过数值模拟验证了所提出的算法的性能。
This paper considers a distributed Nash equilibrium seeking problem, where the players only have partial access to other players' actions, such as their neighbors' actions. Thus, the players are supposed to communicate with each other to estimate other players' actions. To solve the problem, a leader-following consensus gradient-free distributed Nash equilibrium seeking algorithm is proposed. This algorithm utilizes only the measurements of the player's local cost function without the knowledge of its explicit expression or the requirement on its smoothness. Hence, the algorithm is gradient-free during the entire updating process. Moreover, the analysis on the convergence of the Nash equilibrium is studied for the algorithm with both diminishing and constant step-sizes, respectively. Specifically, in the case of diminishing step-size, it is shown that the players' actions converge to the Nash equilibrium almost surely, while in the case of fixed step-size, the convergence to the neighborhood of the Nash equilibrium is achieved. The performance of the proposed algorithm is verified through numerical simulations.
