Effects of neighborhood type and size in spatial public goods game on diluted lattice

In this paper, we show in detail a picture of the effects of neighborhood type and size on cooperation promotion in the framework of spatial public goods game. First, we explore the role of learning and interaction neighborhood via the information flow rate and the cooperator-cluster stability. Extensive simulation results indicate that learning neighbors at the rising stage is to facilitate the information exchange and to promote cooperation among agents; at the gliding stage, learning neighborhood destroys cooperative clusters and accelerates the extinction of cooperators. Opposite to learning neighbors, interaction neighbors at the rising stage pull down the cooperation fraction; at the gliding stage, they help to maintain cooperative cluster and prohibit a further decrease in Fc. Then we review this issue on a microscopic level - snapshot pattern. We find several interesting results, through intermediate states, on the pattern formation towards the final state. Cooperators in a larger interaction size case will squeeze defectors and make their existence as a form of thin line; while the cooperative cluster in a larger learning neighborhood displays more 'blurry burs' at the boundaries, indicating an instability of cooperative clusters. Current results are of interest for us to further understand the cooperator persistence in many natural, social and economic systems.