Swarm intelligence inspired shills and the evolution of cooperation

Abstract

Many hostile scenarios exist in real-life situations, where cooperation is disfavored and the collective behavior needs intervention for system efficiency improvement. Towards this end, the framework of soft control provides a powerful tool by introducing controllable agents called shills, who are allowed to follow well-designed updating rules for varying missions. Inspired by swarm intelligence emerging from flocks of birds, we explore here the dependence of the evolution of cooperation on soft control by an evolutionary iterated prisoner's dilemma (IPD) game staged on square lattices, where the shills adopt a particle swarm optimization (PSO) mechanism for strategy updating. We demonstrate that not only can cooperation be promoted by shills effectively seeking for potentially better strategies and spreading them to others, but also the frequency of cooperation could be arbitrarily controlled by choosing appropriate parameter settings. Moreover, we show that adding more shills does not contribute to further cooperation promotion, while assigning higher weights to the collective knowledge for strategy updating proves a efficient way to induce cooperative behavior. Our research provides insights into cooperation evolution in the presence of PSO-inspired shills and we hope it will be inspirational for future studies focusing on swarm intelligence based soft control.

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Impact of shill intervention on the evolution of cooperation

“…Wang and Han [55] pioneered the application of soft control to an evolutionary game within a complete interaction population, where shills adopted the frequency-based tit for tat (F-TFT) and were assumed to share knowledge for normal agents. Following this, the authors [56] extended soft control to a spatially structured population and studied the effects of swarm intelligence inspired shills by an iterated prisoner's dilemma (IPD) game staged on a square lattice. However, these works [55,56] can hardly represent realistic scenarios, as they both studied soft control on regular NOCs [37], where it is impossible to evaluate the impact of the degree distribution pattern of shills because every vertex has the same connectivity.…”

“…Following this, the authors [56] extended soft control to a spatially structured population and studied the effects of swarm intelligence inspired shills by an iterated prisoner's dilemma (IPD) game staged on a square lattice. However, these works [55,56] can hardly represent realistic scenarios, as they both studied soft control on regular NOCs [37], where it is impossible to evaluate the impact of the degree distribution pattern of shills because every vertex has the same connectivity. For more details of the novel notion of soft control, we refer to Refs.…”