Spatial Dynamics of the Public Goods Game with Probabilistic Participation

摘要

We consider the stochasticity of individuals' behavior on participating in the spatial public goods games by endowing cooperators and defectors with two different participating probabilities, and study its effects on the evolution of cooperation. By investigating the dependence of the potential cooperator density on the participation probabilities of cooperators and defectors, we show that cooperation can be promoted in the most parameter space of these two parameters. In particular, full cooperation can be achieved if both participation probabilities are not large. We also find that, by comparing the equilibrium fraction of potential cooperators in an infinitely well-mixed population with that on the square lattice, spatial structure has a sort of double-edged sword effect on the evolution of cooperation in the coexistence dynamic regime; whereas in other dynamic regions spatial structure is beneficial for cooperation. Interestingly, it is shown that cooperation may be unexpectedly inhibited with the increment of the enhancement factor in the spatial public goods game with probabilistic participation. These results can help better understand how cooperation evolves in the structured population where individuals probabilistically participate in the interactions depending on their strategy choices.