Swarm intelligence inspired shills and the evolution of cooperation

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.

[1]  Xin Wang,et al.  Special Agents Can Promote Cooperation in the Population , 2011, PloS one.

[2]  Martin A Nowak,et al.  Evolving cooperation. , 2012, Journal of theoretical biology.

[3]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[4]  Long Wang,et al.  Adaptive role switching promotes fairness in networked ultimatum game , 2013, Scientific reports.

[5]  M. Milinski TIT FOR TAT in sticklebacks and the evolution of cooperation , 1987, Nature.

[6]  M. Brede Short Versus Long Term Benefits and the Evolution of Cooperation in the Prisoner's Dilemma Game , 2013, PloS one.

[7]  Jiang Wu,et al.  Max-Min Adaptive Ant Colony Optimization Approach to Multi-UAVs Coordinated Trajectory Replanning in Dynamic and Uncertain Environments , 2009 .

[8]  M. Nowak,et al.  Tit for tat in heterogeneous populations , 1992, Nature.

[9]  Vijay Krishna,et al.  Finitely Repeated Games , 1985 .

[10]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[11]  Yuhui Shi,et al.  Predator–Prey Brain Storm Optimization for DC Brushless Motor , 2013, IEEE Transactions on Magnetics.

[12]  K. J. Ray Liu,et al.  Cooperation Stimulation for Multiuser Cooperative Communications Using Indirect Reciprocity Game , 2012, IEEE Transactions on Communications.

[13]  Shinsuke Suzuki,et al.  Indirect reciprocity is sensitive to costs of information transfer , 2013, Scientific Reports.

[14]  W. Hamilton,et al.  The evolution of cooperation. , 1984, Science.

[15]  M. Nowak,et al.  Evolutionary games and spatial chaos , 1992, Nature.

[16]  M. Nowak,et al.  Chaos and the evolution of cooperation. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[17]  Yuhui Shi,et al.  An Optimization Algorithm Based on Brainstorming Process , 2011, Int. J. Swarm Intell. Res..

[18]  Attila Szolnoki,et al.  Interdependent network reciprocity in evolutionary games , 2013, Scientific Reports.

[19]  J. M. Smith The theory of games and the evolution of animal conflicts. , 1974, Journal of theoretical biology.

[20]  Michael Doebeli,et al.  Spatial structure often inhibits the evolution of cooperation in the snowdrift game , 2004, Nature.

[21]  Haibin Duan,et al.  New development thoughts on the bio-inspired intelligence based control for unmanned combat aerial vehicle , 2010 .

[22]  Luis Mario Floría,et al.  Evolution of Cooperation in Multiplex Networks , 2012, Scientific Reports.

[23]  Zhen Wang,et al.  If players are sparse social dilemmas are too: Importance of percolation for evolution of cooperation , 2012, Scientific Reports.

[24]  Ming Li,et al.  Soft Control on Collective Behavior of a Group of Autonomous Agents By a Shill Agent , 2006, J. Syst. Sci. Complex..

[25]  Ronen I. Brafman,et al.  On Partially Controlled Multi-Agent Systems , 1996, J. Artif. Intell. Res..

[26]  Attila Szolnoki,et al.  Percolation threshold determines the optimal population density for public cooperation , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  J. M. Smith,et al.  The Logic of Animal Conflict , 1973, Nature.

[28]  M. Perc Coherence resonance in a spatial prisoner's dilemma game , 2006 .

[29]  Matjaz Perc,et al.  Coveting thy neighbors fitness as a means to resolve social dilemmas , 2011, Journal of theoretical biology.

[30]  Antonio Cabrales,et al.  Three is a crowd in iterated prisoner's dilemmas: experimental evidence on reciprocal behavior , 2012, Scientific Reports.

[31]  Sarah Mathew,et al.  When does optional participation allow the evolution of cooperation? , 2009, Proceedings of the Royal Society B: Biological Sciences.

[32]  M. Perc,et al.  Resolution of the Stochastic Strategy Spatial Prisoner's Dilemma by Means of Particle Swarm Optimization , 2011, PloS one.

[33]  Attila Szolnoki,et al.  Rewarding evolutionary fitness with links between populations promotes cooperation , 2014, Journal of theoretical biology.

[34]  Attila Szolnoki,et al.  Reward and cooperation in the spatial public goods game , 2010, ArXiv.

[35]  Attila Szolnoki,et al.  Optimal interdependence between networks for the evolution of cooperation , 2013, Scientific Reports.

[36]  M. Nowak Five Rules for the Evolution of Cooperation , 2006, Science.

[37]  Wenwu Yu,et al.  On pinning synchronization of complex dynamical networks , 2009, Autom..

[38]  Yuhui Shi,et al.  Optimal Satellite Formation Reconfiguration Based on Closed-Loop Brain Storm Optimization , 2013, IEEE Computational Intelligence Magazine.

[39]  J. Cuesta,et al.  Heterogeneous networks do not promote cooperation when humans play a Prisoner’s Dilemma , 2012, Proceedings of the National Academy of Sciences.

[40]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.

[41]  Pei Li,et al.  Robustness of cooperation on scale-free networks in the evolutionary prisoner's dilemma game , 2014 .

[42]  Luis A. Martinez-Vaquero,et al.  Generosity Pays in the Presence of Direct Reciprocity: A Comprehensive Study of 2×2 Repeated Games , 2012, PloS one.

[43]  C. Hauert,et al.  Via Freedom to Coercion: The Emergence of Costly Punishment , 2007, Science.

[44]  Qiang Li,et al.  Effects of adaptive degrees of trust on coevolution of quantum strategies on scale-free networks , 2013, Scientific Reports.

[45]  Aya Hagishima,et al.  Direct Reciprocity in Spatial Populations Enhances R-Reciprocity As Well As ST-Reciprocity , 2013, PloS one.

[46]  Long Wang,et al.  Moving Away from Nasty Encounters Enhances Cooperation in Ecological Prisoner's Dilemma Game , 2011, PloS one.

[47]  Long Wang,et al.  A tale of two contribution mechanisms for nonlinear public goods , 2013, Scientific Reports.

[48]  Yuhui Shi,et al.  ?Hybrid Particle Swarm Optimization and Genetic Algorithm for Multi-UAV Formation Reconfiguration , 2013, IEEE Computational Intelligence Magazine.

[49]  Xiaoming Xu,et al.  Evolutionary Prisoner's Dilemma Game in Flocks , 2009, Complex.

[50]  R. Axelrod The Complexity of Cooperation , 2011 .

[51]  Zhen Wang,et al.  Impact of Social Punishment on Cooperative Behavior in Complex Networks , 2013, Scientific Reports.

[52]  J. Maynard Smith,et al.  THE IMPORTANCE OF THE NERVOUS SYSTEM IN THE EVOLUTION OF ANIMAL FLIGHT , 1952 .

[53]  Zhen Wang,et al.  Heterogeneous Aspirations Promote Cooperation in the Prisoner's Dilemma Game , 2010, PloS one.

[54]  Attila Szolnoki,et al.  Evolution of public cooperation on interdependent networks: The impact of biased utility functions , 2012, ArXiv.

[55]  Zhuo Chen,et al.  Evolutionary prisoner’s dilemma game in flocks , 2009, 0905.1456.

[56]  G. Szabó,et al.  Impact of aging on the evolution of cooperation in the spatial prisoner's dilemma game. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[57]  Zhen Wang,et al.  Spontaneous Symmetry Breaking in Interdependent Networked Game , 2014, Scientific Reports.

[58]  Alexander J. Stewart,et al.  From extortion to generosity, evolution in the Iterated Prisoner’s Dilemma , 2013, Proceedings of the National Academy of Sciences.

[59]  Joel Sobel,et al.  Tit for tat: Foundations of preferences for reciprocity in strategic settings , 1999, J. Econ. Theory.

[60]  Tianping Chen,et al.  Pinning Complex Networks by a Single Controller , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.