Role of update dynamics in the collective cooperation on the spatial snowdrift games: Beyond unconditional imitation and replicator dynamics |
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| Authors: | Chengyi Xia Juan Wang Li Wang Shiwen Sun Junqing Sun Jinsong Wang |
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| Institution: | 1. School of Information Science and Engineering, Shandong Normal University, Jinan 250014, China;2. Shandong Provincial Key Laboratory for Novel Distributed Computer Software Technology, Jinan 250014, China;1. Tianjin Key Laboratory of Intelligence Computing and Novel Software Technology, Tianjin University of Technology, Tianjin 300384, PR China;2. Key Laboratory of Computer Vision and System (Ministry of Education), Tianjin University of Technology, Tianjin 300384, PR China;3. Research Institute of China Construction Bank, Beijing 100033, PR China;4. Center for Combinatorics and LPMC-TJKLC, Nankai University, Tianjin 300071, PR China;5. Institute for Intelligent Production, Faculty for Management, University of Applied Sciences Upper Austria, Steyr Campus, Austria;6. College of Computer and Control Engineering, Nankai University, Tianjin 300350, PR China;7. Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin 300350, PR China |
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| Abstract: | In this paper, we investigate the role of update or imitation rules in the spatial snowdrift game on regular lattices. Three different update rules, including unconditional imitation (UI), replicator dynamics (RD) and the Moran process, are utilized to update the strategies of focal players during the game process in the spatial snowdrift on the lattice. We observe that the aggregate cooperation level between players is largely elevated by using the Moran process in the spatial snowdrift game, when compared to the UI or replicator dynamics. Meanwhile, we carefully explore the dynamical evolution of frequency of cooperators and the cluster formation pattern for these three update rules. Moreover, it is also shown that the evolutionary behavior under the Moran update is independent of and insensitive to the randomly initial configurations of cooperators and defectors. The current results clearly indicate that the introduction of moderate randomness in the strategy update will highly promote the maintenance and persistence of cooperation among selfish individuals, which will be greatly instrumental to deeply understand the evolution of cooperation within many natural, biological and social systems. |
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