Controllability of game-based multi-agent system

We introduce a strategy matrix, a novel concept for ensuring controllability in game-based control systems (GBCSs). This graph-based condition is presented as an alternative to utilizing complex mathematical calculations through algebraic conditions. Moreover, to address these issues, one must first study the expression of Nash equilibrium actions. This expression yields a general formula of the game controllability matrix, which is always affected by the specific matrix (strategy matrix) comprising Nash equilibrium actions, and the matrix can not only be obtained by matrix calculation but can also be directly written through the topology, indicating the topology’s specific influence on the GBCS. Finally, we build a new game-based multi-agent system and determine the controllability relationship between the system and the general system.