间接互惠下亲缘选择量子囚徒困境的合作行为演化  

The Evolution of Cooperative Behavior in the Quantum Prisoner's Dilemma of Kinship Selection under Indirect Reciprocity

作　　者：程程 付子芮 王新颖 张新立[1] CHENG Cheng;FU Zi-rui;WANG Xin-ying;ZHANG Xin-li(School of Mathematics,Liaoning Normal University,Dalian 116029,China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《数学的实践与认识》2023年第12期114-122,共9页Mathematics in Practice and Theory

基　　金：教育部人文社会科学规划项目(21YJA630116);辽宁省教育厅基本科研项目(LJKMZ20221412)。

摘　　要：运用演化博弈理论,构建间接互惠机制下亲缘选择的量子囚徒困境动态模型,分析策略的演化稳定性,并探讨纠缠度、亲缘选择和间接互惠共同对合作行为演化的影响.研究表明:当纠缠度大于一阈值时,合作成为演化稳定策略;当知道对方声誉的概率较小时,纠缠度越大,双方越容易实现合作,演化系统越稳定;在不同条件下,亲缘关系对合作行为分别有促进或抑制作用;充分了解对方的声誉将有利于促进合作的产生和演化.Based on the evolutionary game theory,this paper constructs a quantum prisoner's dilemma dynamic model of kinship selection under indirect reciprocity mechanism.The paper analyzes the evolutionary stability of the strategy,and discusses the influence of entanglement,kinship selection and indirect reciprocity on the evolution of cooperative behavior.The research shows that:when the degree of entanglement is greater than a threshold value,cooperation becomes an evolutionary stability strategy;when the probability of knowing the opponent's reputation is small,the greater the degree of entanglement,the easier it is for both parties to cooperate,and the more stable the evolutionary system is;under different conditions,kinship can promote or inhibit cooperative behavior,respectively;the full understanding of each other's reputation will help to promote the emergence and evolution of cooperation.

关 键 词：量子囚徒困境 亲缘选择 间接互惠 合作演化分析 

分 类 号：F224.32[经济管理—国民经济]