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.