Between Local and Global Strategy Updating in Public Goods Game

Abstract

In the spatial public goods game (PGG), agents interact with local neighbors. In a well-mixed population, agents globally interact with the whole population. In this work, we explore the middle ground between the two from the perspective of strategy imitation. First, we assume each agent can select the reference agent for imitation by global interactions with a probability and otherwise local interactions. The results show that local interactions can maintain cooperation better under a strong dilemma, because cooperators can aggregate to defend against the invasion of defection. For a weak dilemma, both local and global interactions are beneficial to cooperation, because the dilemma is weak; however, the combination of the two is harmful to cooperation. Secondly, we consider different possibilities for cooperative and defective agents to select global references. The results show that when global interactions are frequently accessed by defectors but hardly accessed by cooperators, the system is most unfavorable for cooperation: defectors near the cooperation aggregation are hard to affect by cooperators around, while cooperators interact locally and are invaded by defectors around. However, when global interactions are moderately accessed by defectors and hardly accessed by cooperators, the system is most favorable for the cooperation domain: defectors near the cooperation aggregation have chances to imitate the strategy of cooperation, defectors far away from the aggregation also have chances to imitate the strategy of aggregated cooperators. Meanwhile, the aggregated cooperators hardly imitate defection and can avoid being invaded remotely. The present work unveils the evolutionary behavior of cooperation in the middle of structured and well-mixed pairwise imitation dynamics.

Keywords: Evolutionary dynamics, Public goods game, Pairwise comparison, Global interaction