Hybrid multi-agent consensus with game-driven dynamics and connectivity-based partition

Current research on the consensus problem in hybrid game-based multi-agent systems (HGBMASs) faces limitations such as insufficient engineering modularity, idealized topological assumptions, and passive game mechanisms. To overcome these issues, this paper introduces an enhanced framework that integrates topology with game theory and incorporates hierarchical macro-regulation. The main contributions are threefold: (i) Achieving modular decoupling between the game decision layer and the system dynamics layer to meet the heterogeneous modular requirements of practical engineering; (ii) Moving beyond merely verifying consensus existence to actively designing systems for it. This involves adapting the game mechanism to topological structures via connectivity-based partitioning (exclusive vs. common parts); (iii) An enhanced consensus mechanism is established, wherein agents in the common part converge to the convex combinations of the exclusive parts, while the game mechanism drives shrinkage via Nash equilibrium; the entire scheme applies to networks with non-negative edge weights. The hierarchical structure enables game strategies to regulate the system via the novel perspective in this paper, which constitutes an extra mechanism-based way to achieve game regulation and enriches the implementation paths of game theory as another regulatory measure for the system. Although employing standard quadratic cost functions and Nash equilibrium solutions, this work redefines their design logic (linking them to topology partitioning) and elevates their objective from individual optimization to global coordination. This establishes a closed-loop where "topology guides game design, and the game optimizes topological functionality." Theoretical analysis and simulations confirm the framework's effectiveness in solving multi-agent consensus problems, highlighting its potential for applications like air traffic control and human-machine collaborative systems.