Multi-agent task forwarding model based on game algorithm integrated with finite state machine

In multi-agent systems, to improve task completion efficiency, tasks need to be forwarded among agents to reach as many agents as possible. Existing studies suffer from limitations such as over-reliance on global information, low efficiency in state synchronization, and poor practicality. To address these issues, this paper proposes a task forwarding model inspired by game theory. The model considers agent distribution, communication environment, and the agents' own willingness, and conducts research on a 2D square lattice network based on a public goods game with differentiated contributions. Furthermore, the concept of finite state machines (FSM) is introduced, with the improved deterministic finite automaton (DFA) algorithm and non-deterministic finite automaton (NFA) algorithm incorporated sequentially. Results show that under the same conditions, integrating the aforementioned algorithms increases the proportion of agents adopting forwarding strategies and accelerates game convergence, while the model also responds rapidly to dynamic external environments. Additionally, this paper explores how agent density in the model affects the evolutionary speed of the game. Findings indicate that in this model, higher agent density does not necessarily result in faster game evolution; on the contrary, an opposite pattern may emerge under certain environmental conditions.