Bio-inspired mechanism promotes cooperation in spatial public goods games

The ant colony optimization algorithm has been extensively utilized in combinatorial optimization projects, such as route planning, scheduling problem and network optimization, owing to its benefits of distributed calculating, positive feedback and heuristic search. However, the combination of heuristic algorithms based on the bio-inspired mechanism and public goods game has not yet been studied. In this work, we introduce the ant colony optimization mechanism into the public goods game where agents use the pheromones of cooperation and defection to guide the strategy selection. Simulation results demonstrate that the ant colony optimization mechanism significantly enhances the level of cooperation compared to the traditional model, in which the heuristic factor β plays a significant regulatory role in cooperative behavior. It accelerates the spread of cooperative behavior by enhancing the sensitivity to immediate benefits. However, the pheromone weight α exhibits a dual regulatory effect. It promotes the emergence of cooperation when the synergy effect is weak, but hinders the attainment of full cooperation when the synergy effect is strong. Furthermore, the pheromone evaporation factor ρ also influences the stability of cooperation by controlling the persistence of pheromones. A small value of ρ promotes cooperation by maintaining long-term cooperation memory, while a larger value disrupts the stability of collective behavior due to the rapid elimination of historical information.