关键词: Ising模型/
有限尺度标度理论/
蒙特卡罗模拟/
自我质疑更新规则
English Abstract
Phase transition properties for the spatial public goods game with self-questioning mechanism
Yang Bo1,2,Fan Min1,2,
Liu Wen-Qi1,2,
Chen Xiao-Song3,4
1.Data Science Research Center, Kunming University of Science and Technology, Kunming 650500, China;
2.Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China;
3.Institute of Theoretical Physics, Key Laboratory of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China;
4.School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China}
Fund Project:Scientific Research Foundation for Introduced Scholars, Kunming University of Science and Technology(Grant No. KKSY201607047) and the National Natural Science Foundation of China (Grant No. 61573173).Received Date:27 May 2017
Accepted Date:04 July 2017
Published Online:05 October 2017
Abstract:The spatial public goods game is one of the most popular models for studying the emergence and maintenance of cooperation among selfish individuals. A public goods game with costly punishment and self-questioning updating mechanism is studied in this paper. The theoretical analysis and Monte Carlo simulation are involved to analyze this model. This game model can be transformed into Ising model with an external field by theoretical analysis. When the costly punishment exists, the effective Hamiltonian includes the nearest-, the next-nearest-and the third-nearest-neighbor interactions and non-zero external field. The interactions are only determined by costly punishment. The sign of the interaction is always greater than zero, so it has the properties of ferromagnetic Ising. The external field is determined by the factor r of the public goods game, the fine F on each defector within the group, and the relevant punishment cost C. The Monte Carlo simulation results are consistent with the theoretical analysis results. In addition, the phase transitions and critical behaviors of the public goods game are also studied using the finite size scaling theory. The results show that the discontinuous phase transition has the same finite size effects as the two-dimensional Ising model, but the continuous phase transitions is inconsistent with Ising model.
Keywords: ising model/
finite size scaling theory/
Monte Carlo simulations/
self-questioning update rules
