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.