Between local and global strategy updating in public goods game

Abstract

In the spatial public goods game, agents interact with local neighbors. In a well-mixed system, agents interact with the global population randomly. In this work, we explore the middle ground between the two from the perspective of strategy updating. As an intuitive idea, each agent selects the reference agent for learning by global selection with a probability. The results show that local selection favors cooperation more given a lower synergy factor, because cooperation can aggregate to defend against the invasion of defection. Given a higher synergy factor, both local and global selection favors cooperation, while combining the two disfavors cooperation. More importantly, we consider the different tendencies of cooperative and defective agents to global selection. The results show that when global selection is frequently accessed by defectors but hardly accessed by cooperators, the system disfavors cooperation most: defection near the cooperation aggregation is hard to affect by cooperation around, while cooperation interacts locally and is invaded by defection around. However, when global selection is moderately accessed by defection and hardly accessed by cooperation, the system favors the cooperation domination most: defection near the cooperation aggregation has a chance to learn the strategy of cooperation, and defection far away from the aggregation also has the chance to learn the strategy of aggregated cooperation; meanwhile, the aggregated cooperation hardly learns defection and can avoid being invaded remotely. The global selection in cooperation and defection play different roles in evolution, because the spatial behavior of the two is different: it is cooperation that aggregates to resist defection. The present work provides a further understanding of the different spatial behaviors of cooperation and defection from the perspective of global interactions.