Evolution of Cooperation in Public Goods Games

We investigate the evolution of cooperation with evolutionary public goods games based on finite populations, where four pure strategies: cooperators, defectors, punishers and loners who are unwilling to participate are considered. By adopting approximate best response dynamics, we show that the magnitude of rationality not only quantitatively explains the experiment results in [Nature (London) 425 (2003) 390], but also it will heavily influence the evolution of cooperation. Compared with previous results of infinite populations, which result in two equilibriums, we show that there merely exists a special equilibrium and the relevant high value of bounded rationality will sustain cooperation. In addition, we characterize that loner's payoff plays an active role in the maintenance of cooperation, which will only be warranted for the low and moderate values of loner's payoff. It thus indicates the effects of rationality and loner's payoff will influence the cooperation. Finally, we highlight the important result that the introduction of voluntary participation and punishment will facilitate cooperation greatly.