Herdability of Nash equilibrium in neighbour-based game control system

The game-based control system is composed of a regulator and underlying agents. The regulator first makes a decision, and then each agent optimises its own payoff function to reach the possible Nash equilibrium of the non-cooperative dynamic game. When the number of regulators in the system is greater than 1, the underlying agents naturally have the problem of connecting different regulators, which can be reflected in the topological structure. Therefore, this paper proposes the neighbour-based game control system (NBGCS) with multiple regulators. Then, we define the herdability of game-based systems and provide the necessary and sufficient conditions for achieving this performance. In addition, we describe the herdability by graph theory, and draw the following conclusion: when the system is herdable, the graph corresponding to the game controllability matrix is strategy-connectable.基于博弈的控制系统由调控器（regulator）与底层智能体（underlying agents）组成。调控器率先做出决策，随后各智能体通过优化自身收益函数，以达成该非合作动态博弈的可行纳什均衡。当系统内调控器数量大于1时，底层智能体天然面临连接不同调控器的问题，这一特性可通过拓扑结构得以体现。为此，本文提出了一种搭载多调控器的基于邻域的博弈控制系统（NBGCS）。随后，本文定义了博弈系统的群聚性，并给出了实现该性能的充要条件。此外，本文借助图论对该群聚性进行描述，并得出如下结论：当系统具备群聚性时，其博弈可控性矩阵对应的图满足策略连通性。