Dynamical reciprocity in interacting games: numerical results and mechanism analysis
Rizhou Liang School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710062, People’s Republic of China Qinqin Wang School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710062, People’s Republic of China Jiqiang Zhang School of Physics and Electronic-Electrical Engineering, Ningxia University, Yinchuan 750021, People’s Republic of China Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing 100191, People’s Republic of China Guozhong Zheng School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710062, People’s Republic of China Lin Ma School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710062, People’s Republic of China Li Chen School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710062, People’s Republic of China Robert Koch-Institute, Nordufer 20, 13353 Berlin, Germany
Abstract
We study the evolution of two mutually interacting games with both pairwise games as well as the public goods game on different topologies. On 2d square lattices, we reveal that the game-game interaction can promote the cooperation prevalence in all cases, and the cooperation-defection phase transitions even become absent and fairly high cooperation is expected when the interaction goes to be very strong. A mean-field theory is developed that points out new dynamical routes arising therein. Detailed analysis shows indeed that there are rich categories of interactions in either individual or bulk scenario: invasion, neutral, and catalyzed types; their combination puts cooperators at a persistent advantage position, which boosts the cooperation. The robustness of the revealed reciprocity is strengthened by the studies of model variants, including asymmetrical or time-varying interactions, games of different types, games with time-scale separation, different updating rules etc. The structural complexities of the underlying population, such as Newman–Watts small world networks, Erdős–Rényi random networks, and Barabási–Albert networks, also do not alter the working of the dynamical rec
中文速览
在现实社会中，人们往往同时参与多个博弈——国家之间既有贸易谈判，又有安全合作；同事之间既协作项目，又共享资源——这些博弈之间会相互影响，但主流进化博弈理论长期只研究单一博弈，忽略了这种"多游戏并行"的现实。这篇论文引入"互动博弈（interacting games）"框架，让多个博弈通过一个综合有效收益函数相互耦合，系统研究博弈间相互作用对合作演化的影响。研究发现，在二维方格网络及多种复杂网络拓扑上，博弈间的相互作用能显著促进合作：当耦合强度足够大时，合作-背叛相变甚至消失，系统趋向近乎完全合作的吸收态。通过平均场理论和微观机制分析，作者识别出三类互动模式——入侵型、中立型和催化型，它们共同为合作者提供持续优势；且随着并行博弈数量增加，合作水平持续提升。这一发现揭示了一类全新的合作机制——"动态互惠（dynamical reciprocity）"，为理解现实中多议题并发场景下人类合作的涌现提供了重要的理论基础。
原文 arXiv:2102.00360;中英对照 + 大白话阅读 https://aha.fim.ai/paper/2102.00360v2