Journal of theoretical biology
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It is one of the fundamental problems in biology and social sciences how to maintain high levels of cooperation among selfish individuals. Theorists present an effective mechanism promoting cooperation by allowing for voluntary participation in public goods games. ⋯ Our research shows that the payoffs of the loners have a significant effect in anonymous voluntary public goods games by this introduction and that the dynamics will drive the system to a fixed point, which is different from the Nash equilibrium. In addition, we also qualitatively explain the existing experimental results.