Robust deep nonnegative rank matrix factorization to enhancing the efficiency of controllability in temporal networks using mixed-strategy game theory

Controllability in dynamic systems, especially within complex networks, remains a cornerstone of understanding and influencing complex systems. In this paper, a game theory-based controllability method (GTCM) is proposed in complex networks, in which an algorithm is designed to identify driver nodes using a mixed-strategy game. In order to adapt complex networks to the theory of bases, a novel optimal algorithm is proposed that is created using the theory of game evolution on complex networks. Then, The GTCM method captures both cooperative and adversarial interactions by modeling nodes or driver nodes as mixed-strategy agents, enabling more robust and adaptive control strategies. The results of simulating the GTCM method on real-world datasets and comparing it with conventional methods demonstrate that the proposed GTCM method is closer to the equilibrium point with a lower convergence error and a better payoff distribution than other methods. On the other hand, the results demonstrate that the proposed GTCM method has reached to full controllability in a shorter time with a smaller number of driver nodes compared to other methods.