具有惩罚策略的公共物品博弈与合作演化

采用演化博弈方法,研究具有代价的第二方惩罚机制对于公共物品博弈均衡选择及群体合作行为的影响.将群体策略选择过程描述成一个多维马氏过程,通过极限分布分析系统演化稳定状态.分别考虑只对背叛策略进行惩罚的一阶惩罚机制和同时对背叛及不惩罚背叛的合作(二阶背叛)都进行惩罚的二阶惩罚机制.研究发现,与一阶惩罚相比,二阶惩罚机制可以在更大参数范围内促进群体合作的产生,系统存在选择不同均衡结果的惩罚参数临界值.并将结果与复制动态模型进行了对比.

Public goods with punishment and the evolution of cooperation

Based on the evolutionary game method, influences of the costly second-party punishment mechanism on the equilibrium selection of the public goods game and the cooperative behavior of the population are investigated. The strategy evolution process of the population is described as a multidimensional Markov process. The evolutionary stable states of the system are analyzed based on the limit distribution of the stochastic process. Two kinds of punishments are considered respectively in this paper, namely, first-order punishments that only punish the defectors and second-order punishments that not only punish the defectors but also the cooperators who have not punished the defectors (second-order defection). The study reveals that compared with the first-order punishment, the second-order punishment mechanism can promote the evolution of cooperation within a larger parameter range. The system has critical values of punishment parameters for choosing different equilibrium results. The results are also compared with those of the corresponding deterministic replication dynamic model.