Abstract
Cooperation is ubiquitous in our real life but everyone would like to maximize her own profits. How does cooperation occur in the group of self-interested agents without centralized control? Furthermore, in a hostile scenario, for example, cooperation is unlikely to emerge. Is there any mechanism to promote cooperation if populations are given and play rules are not allowed to change? In this paper, numerical experiments show that complete population interaction is unfriendly to cooperation in the finite but end-unknown Repeated Prisoner's Dilemma (RPD). Then a mechanism called soft control is proposed to promote cooperation. According to the basic idea of soft control, a number of special agents are introduced to intervene in the evolution of cooperation. They comply with play rules in the original group so that they are always treated as normal agents. For our purpose, these special agents have their own strategies and share knowledge. The capability of the mechanism is studied under different settings. We find that soft control can promote cooperation and is robust to noise. Meanwhile simulation results demonstrate the applicability of the mechanism in other scenarios. Besides, the analytical proof also illustrates the effectiveness of soft control and validates simulation results. As a way of intervention in collective behaviors, soft control provides a possible direction for the study of reciprocal behaviors.