直接互惠下量子囚徒困境的演化稳定分析  

Evolutionary Stability Analysis of Quantum Prisoner′s Dilemmaunder Direct Reciprocity

作　　者：付子芮 王新颖 程程 张新立[1] FU Zirui;WANG Xinying;CHENG Cheng;ZHANG Xinli(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：《海南师范大学学报（自然科学版）》2023年第4期382-386,共5页Journal of Hainan Normal University（Natural Science）

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：为深入探讨直接互惠和量子纠缠如何影响合作的演化,运用演化博弈理论的方法建立了直接互惠下量子囚徒困境模型,计算博弈动态的均衡点并对均衡点进行稳定性分析,讨论直接互惠参数和纠缠对均衡点的影响。分析结果表明,当直接互惠参数、量子纠缠在不同条件下,合作策略和背叛策略为演化稳定策略,并且当纠缠大于临界值时直接互惠行为促进合作;纠缠小于临界值时直接互惠行为抑制合作。最后通过数值仿真验证了理论的正确性。In order to explore how direct reciprocity and entanglement affect the evolution of cooperation,a quantum pris⁃oner's dilemma model under direct reciprocity is established by using the method of evolutionary game theory.The equilib⁃rium points of the game dynamics are calculated and the stability of the equilibrium points is analyzed.The influences of di⁃rect reciprocity parameters and entanglement on the equilibrium points are discussed.The results show that when the direct reciprocity parameter and the quantum entanglement are different,the cooperation strategy and the betrayal strategy are evolutionarily stable,and when the entanglement is greater than the critical value,the direct reciprocity behavior promotes cooperation.When entanglement is less than critical value,direct reciprocal behavior inhibits cooperation.Finally,the cor⁃rectness of the theory is verified by numerical simulation.

关 键 词：演化博弈论 囚徒困境 直接互惠 量子纠缠度 

分 类 号：O225[理学—运筹学与控制论]