The role of punishment in the spatial public goods game
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ORIGINAL PAPER
The role of punishment in the spatial public goods game Peican Zhu · Hao Guo · Hailun Zhang · Ying Han · Zhen Wang · Chen Chu
Received: 30 December 2019 / Accepted: 16 September 2020 © Springer Nature B.V. 2020
Abstract Though contradicting with natural selection, cooperative behaviors widely exist in practice and seem to be an effective measure to maintain the functioning of complex systems. As revealed by previous studies, punishment is capable of promoting cooperation and therefore various types of punishment are proposed. Previously, scholars mainly focus on investigating either peer punishment or pool punishment, whereas in social and biological systems, an individual might function as different roles when facing different players. Thus, we mainly investigate these two types of punishment together and the effects of punishmenttype transfer on the evolutionary dynamics are further provided with sufficient analyses in this manuscript. Role of different type of punishment on cooperation seems to be related to the number of punishers (being denoted as T ) among corresponding neighbors. Simulations are conducted in order to investigate the effect Peican Zhu and Hao Guo contributed equally to this work. P. Zhu · H. Zhang · Y. Han School of Computer Science and Engineering, Northwestern Polytechnical University (NWPU), Xi’an 710072, Shaanxi, China H. Guo· Z. Wang (B)· C. Chu School of Mechanical Engineering the Center for Optical Imagery Analysis and Learning (OPTIMAL), NWPU, Xi’an 710072, Shaanxi, China e-mail: : [email protected] C. Chu School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, Yunnan, China
of threshold reflecting the punishment-type switching on evolutionary dynamics, while peer punishment is proved to be more effective than pool punishment in promoting cooperation. We hope our findings here can shed some lights on the investigation of punishment. Keywords Peer punishment · Pool punishment · Evolutionary dynamics · Spatial games
1 Introduction For the purpose of maintaining public goods, cooperation seems to be a key factor for the maintenance of our modern societies [1–4] though it seems to be contradicted with competition which is the backbone of natural selection. In real world, the emergence of cooperation seems to be a challenging problem due to the conflict of interest either for social or biological systems [5,6]. This topic has attracted much attention, and numerous scholars have devoted their endless efforts to investigate the promotion of cooperation from both theoretical and experimental aspects [3,7–16]. Five mechanisms have been proposed in [1] for the sustainment of cooperation, including kin selection, direct reciprocity, indirect reciprocity, network reciprocity and group selection. Along this way, new mechanisms are also presented to further promote stable cooperation, for instance, the interplay between evolutionary games [17] and different network structures (e.g., regular networks [18], small-world networks [19,20], s
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