Abstract
We studied the effect of population density in a spatial public goods game. We found that the effect on the evolution of cooperation is very complex when the strategy learning and mobility of players in a long range are considered in a two-dimensional lattice. As the learning range is larger than the mobility range, the system is driven to enter into a cooperation state for a low population density, because a small local group is beneficial to sustain a high level of cooperation. As population density increases to a moderate range, the mobility of players from a domain invaded by defectors supports the evolution stability of cooperation. When the mobility range is larger than the learning range, a formation of compact domains of cooperators promotes cooperation as the population density becomes high.