Li Angsheng, Yong Xi
State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, P. R. China.
State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, P. R. China; University of Chinese Academy of Science, Beijing, P. R. China.
PLoS One. 2015 Feb 2;10(2):e0116429. doi: 10.1371/journal.pone.0116429. eCollection 2015.
Recently, the authors proposed a quantum prisoner's dilemma game based on the spatial game of Nowak and May, and showed that the game can be played classically. By using this idea, we proposed three generalized prisoner's dilemma (GPD, for short) games based on the weak Prisoner's dilemma game, the full prisoner's dilemma game and the normalized Prisoner's dilemma game, written by GPDW, GPDF and GPDN respectively. Our games consist of two players, each of which has three strategies: cooperator (C), defector (D) and super cooperator (denoted by Q), and have a parameter γ to measure the entangled relationship between the two players. We found that our generalised prisoner's dilemma games have new Nash equilibrium principles, that entanglement is the principle of emergence and convergence (i.e., guaranteed emergence) of super cooperation in evolutions of our generalised prisoner's dilemma games on scale-free networks, that entanglement provides a threshold for a phase transition of super cooperation in evolutions of our generalised prisoner's dilemma games on scale-free networks, that the role of heterogeneity of the scale-free networks in cooperations and super cooperations is very limited, and that well-defined structures of scale-free networks allow coexistence of cooperators and super cooperators in the evolutions of the weak version of our generalised prisoner's dilemma games.
最近，作者基于诺瓦克和梅的空间博弈提出了一种量子囚徒困境博弈，并表明该博弈可以经典地进行。利用这一思想，我们基于弱囚徒困境博弈、完全囚徒困境博弈和归一化囚徒困境博弈分别提出了三种广义囚徒困境（简称GPD）博弈，分别记为GPDW、GPDF和GPDN。我们的博弈由两个参与者组成，每个参与者有三种策略：合作者（C）、背叛者（D）和超级合作者（记为Q），并有一个参数γ来衡量两个参与者之间的纠缠关系。我们发现我们的广义囚徒困境博弈有新的纳什均衡原理，即在无标度网络上我们的广义囚徒困境博弈演化中，纠缠是超级合作出现和收敛（即保证出现）的原理，纠缠为无标度网络上我们的广义囚徒困境博弈演化中的超级合作相变提供了一个阈值，无标度网络的异质性在合作和超级合作中的作用非常有限，并且定义良好的无标度网络结构允许在我们广义囚徒困境博弈弱版本的演化中合作者和超级合作者共存。
