Tolerance-based punishment and cooperation in spatial public goods game

Punishment, as a remarkable way, has been proposed to explain the emergence and persistence of cooperation in the human species. Inspired by the fact that people have a certain tolerance for free-riders before punishment, therefore, we study the effect of tolerance-based punishment on the evolution of cooperation in spatial public goods game. Cooperators punish defectors on the basis of the tolerance threshold during the evolutionary process and have to bear the relevant costs of sanction subsequently. Different from previous works, the new mechanism can reduce the frequency of punishing by controlling the tolerance for punishment. We find that this mechanism can lead to synergistic effects, and it can stabilize the circumstance of full cooperation under adverse conditions. By means of analysis of the emergence of cooperative clusters, we demonstrate that the tolerance-based punishment can promote cooperation through enhancing spatial reciprocity. In addition, the readiness of cooperation increases obviously by adjusting this kind of punishment. Our work extends the form of punishment in the evolution of spatial public goods game and the results are conducive to a better understanding of punishment. (C) 2018 Elsevier Ltd. All rights reserved.