Promotion of cooperation due to diversity of players in the spatial public goods game with increasing neighborhood size

It is well-known that individual diversity is a typical feature within the collective population. To model this kind of characteristics, we propose an evolutionary model of public goods game with two types of players (named as A and B), where players are located on the sites of a square lattice satisfying the periodic boundary conditions. The evolution of the strategy distribution is governed by iterated strategy adoption from a randomly selected neighbor with a probability, which not only depends on the payoff difference between players, but also on the type of the neighbor. For B-type agents, we pose a pre-factor (0<w<1) to the strategy transfer probability, which implies the lower teaching activity or strategy convincing performance; but w is always set to be 1 for A-type agents, hence it means that A-type players are influential ones who own a larger strategy spreading chance. Furthermore, we also consider the competition between two opposite effects when the number of nearest neighbors (k) is increased from 4 to 24. Within a range of the portion of A-type influential players, the inhomogeneous teaching activity in strategy transfer yields a relevant increase (dependent on w) in the density of cooperators characterizing the promotion of cooperation. Current findings are of utmost importance for us to understand the evolution of cooperation under many real-world circumstances, such as the natural, biological, economic and even social systems.