Evolution of cooperation in spatial public goods games with common resource dynamics

Investment in a common resource shared by all players is difficult to evolve despite higher returns because a non-investor (free-rider) always receives more than an investor (altruist). This situation is referred to as the Tragedy of the Commons and is often observed in various biological systems including environmental problems of human society. Punishment and reputation are effective mechanisms but require cooperator's ability to identify free-riders. Volunteering can work in anonymous public goods games but this requires voluntary participation, which is not always the case. Here, we show that the evolution of altruism is possible in anonymous and obligate public goods games if we consider the spatiotemporal dynamics of the common resource that incorporate spatial diffusion and internal dynamics of the commons. The investors' strategy to counter free-riders is to increase population density and to outnumber them with the common resource level kept as low as that of the free-riders.