基于不同困境强度分布的多层空间网络演化博弈研究

Evolutionary Games in Multilayer Spatial Networks Based on Different Dilemma Intensity Distribution

摘要: 由于现实生活中存在着多种类型的通信，使得网络之间存在相互关联从而不同网络个体之间会产生相互影响，同时不同网络层上进行的博弈也可能是不同的(本文用不同困境强度刻画)。因此，本文基于马尔可夫链的状态转移，按不同秩序将囚徒困境(PD)、雪堆博弈(SD)和猎鹿博弈(SH)置于三层网络研究其合作行为的演化，模拟结果显示仅当中间层进行囚徒困境(PD)博弈时，上下两层及系统整体的合作水平会被显著降低，而其它两种情形则会提高系统整体的合作水平，特别是猎鹿博弈(SH)居于中间层时；同时模拟结果还显示随着困境强度的降低系统整体的合作水平会提高。综上所述，具有不同困境强度的网络及其排序关系、困境强度大小在一定条件下可以提高系统的合作水平。研究结果进一步加深了基于马尔可夫链在不同博弈模型上的随机演化博弈研究，对相关领域的进一步应用研究有一定的启示。

Abstract: Due to the existence of various types of communication in real life, networks are interrelated, leading to mutual influence among individuals in different networks. At the same time, the games played at different network layers may also be different (described in this article with different levels of dilemma intensity). Therefore, based on the state transition of Markov chains, this article places Prisoner’s Dilemma (PD), Snowback Game (SD), and Deer Hunting Game (SH) in a three-layer network according to different orders to study the evolution of their cooperative behavior. The simulation results show that only when the middle layer engages in Prisoner’s Dilemma (PD) game, the level of cooperation between the upper and lower layers and the overall system will be significantly reduced, while the other two situations will improve the overall level of cooperation of the system, especially when the Deer Hunting Game (SH) is in the middle layer. The simulation results also show that as the intensity of the dilemma decreases, the overall level of cooperation in the system will increase. In summary, networks with different levels of dilemma intensity and their ranking relationships, as well as the magnitude of dilemma intensity, can improve the level of cooperation of the system under certain conditions. The research results further deepen the research on stochastic evolutionary games based on Markov chains in different game models, and provide certain insights for further application research in related fields.