Impact of shill intervention on the evolution of cooperation

• We introduce shills into the public goods game on a scale free network and study the impact on the evolution of cooperation.
• High-level cooperation and better social welfare could be simultaneously induced by tuning the distribution coefficient αα.
• Desirable outcomes are associated with large αα for tense dilemma and small αα in relaxed cases.
• We observe a transition of the composition of equilibrium cooperators.
• These results are somehow affected when we attenuate the heterogeneity of the network.

The practical significance of effective intervention in collective behavior has its roots not only in frequent migration in the modern society, but also in the actual demands of real-world applications for system efficiency improvement. Within the framework of soft control, this paper focuses on an evolutionary public goods game staged on a scale free network and explores the dependence of the evolution of cooperation on the intervention of a fraction of shills, who follow the Fixed-Cost-per-Player paradigm while the locals follow the Fixed-Cost-per-Game paradigm. We demonstrate that higher cooperation levels and better social welfare could be simultaneously induced by tuning the distribution coefficient αα, where desirable outcomes are associated with large α>0α>0 for tense dilemmas while small α<0α<0 leads to satisfactory results when the enhancement factor γγ increases. Moreover, we observe a transition of the composition of equilibrium cooperators from full dominance of shills to co-existence of shills and locals, and the boundary has a positive correlation with αα. These results are somehow affected when we attenuate the heterogeneity of the network by relating individual fitness to payoffs averaged over its connectivity. Our findings may not only shed some light on the mechanism behind the evolution of cooperation from the perspective of external intervention, but also provide a feasible way to effectively intervene in the evolutionary outcomes of negative scenarios.