Modeling and controlling multilayer complex network dynamics is challenging under coexisting crosslayer interactions, higher-order couplings, and decentralized strategic decisions. Most existing schemes focus on graph-based pairwise structures and overlook topological cavities, mesoscale loops, and layered self-interested actions. This paper presents TopoGame-MND, an algebraic-topological and game-theoretic framework for multilayer network dynamics. We first build a filtration-driven simplicial lifting to unify pairwise and higher-order interactions into a weighted multilayer simplicial complex. A topological state operator using generalized Hodge Laplacians and persistent homology is then constructed to characterize cross-scale diffusion, circulation, and structural inconsistency. A distributed potential-game mechanism is developed with a topology-aware utility, followed by a proximal mirror-best-response algorithm with consensus correction. We prove Nash equilibrium existence and uniqueness, global potential monotone descent, linear convergence, computational complexity, and input-to-state robustness. Simulations on multiplex and interdependent networks validate that TopoGame-MND outperforms baselines in regulation speed, oscillation energy, failure resilience, and robustness, providing a unified way to connect higher-order topology and distributed decision optimization.
Yandong Yuan (Sun,) studied this question.