title: Fostering cooperation of selfish agents through public goods in relation to the loners.
abstract: Altruistic behaviors in multiplayer groups have obtained great attention in the context of the public goods game, which poses a riddle from the evolutionary viewpoint. Here we focus on a particular type of public goods game model in which the benefits of cooperation are either discounted or synergistically enhanced at the appearance of multiple cooperators in a group. Moreover, we focus on the three-strategies profile by adding the role of loners, besides the often-used cooperation and defection. Using the replicator dynamic equations, we investigate a range of dynamical portraits that characterizes the properties of the steady state. Analysis results indicate that loners and cooperators both have chances to be the stable equilibrium points in the presence of perturbations, while defectors fail to do so in this three-strategy competition. Moreover, the coexistence state, in which all three strategies exist in equilibrium, can be led by suitable parameters and stabilized for perturbations. These results elucidate the interplay between the characteristics of the public goods game and evolutionary dynamics in well-mixed systems.
authors.affiliation: Department of Automation, College of Computer and Control Engineering, Nankai University, Tianjin 300071, People's Republic of China and Tianjin Key Laboratory of Intelligent Robotics, Computer and Control Engineering, Nankai University, Tianjin 300071, People's Republic of China.
authors.forename: Jianlei
authors.initials: J
authors.lastname: Zhang
authors.affiliation: Department of Automation, College of Computer and Control Engineering, Nankai University, Tianjin 300071, People's Republic of China and Tianjin Key Laboratory of Intelligent Robotics, Computer and Control Engineering, Nankai University, Tianjin 300071, People's Republic of China.
authors.forename: Zengqiang
authors.initials: Z
authors.lastname: Chen
authors.affiliation: Department of Automation, College of Computer and Control Engineering, Nankai University, Tianjin 300071, People's Republic of China and Tianjin Key Laboratory of Intelligent Robotics, Computer and Control Engineering, Nankai University, Tianjin 300071, People's Republic of China.
authors.forename: Zhongxin
authors.initials: Z
authors.lastname: Liu