Particle swarm intelligence promotes cooperation by adapting interaction radii in co-evolutionary games

Particle swarm optimization (PSO), a population-based optimization algorithm inspired by swarm behaviors, has been applied extensively to simulate social behaviors such as migration, urban planning, or resource utilization. It capitalizes on the inherent principles of social cooperation, adaptability and learning from peers to help individuals in a population search for optima. In this work, we propose a novel co-evolutionary game model in which individuals adapt their interaction radii by applying the PSO algorithm and study how the learning factor ω in the algorithm shapes the cooperation dynamics. We find that the adaptive interaction radii based on PSO could significantly enhance cooperation, especially in the scenario with strong social dilemma. By studying the snapshots of strategy pattern and the distributions of interaction radii in the population, we further reveal that the PSO-based adapting mechanism can protect cooperators by shrinking the interaction radii in a severe environment with an appropriate ω. Nevertheless, when cooperation is favorable, the adaptation leads to a relatively wide distribution of interaction radii to facilitate the spread of cooperation. The results of this work highlight the potential of the PSO algorithm to resolve social dilemmas when combined with the evolutionary dynamics.