相位阻尼信道条件下量子斗鸡博弈模型均衡解分析  

Equilibrium Solution Analysis of Quantum Chicken Game Model in Phase Damping Channel

作　　者：王爽 杨阳 张新立[1] WANG Shuang;YANG Yang;ZHANG Xinli(School of Mathematics,Liaoning Normal University,Dalian,Liaoning 116029,China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《经济数学》2020年第1期70-74,共5页Journal of Quantitative Economics

基　　金：辽宁省教育厅资助项目(LF201783613)。

摘　　要：利用量子博弈的相关理论,以噪音强度和记忆强度为参量,建立了相位阻尼信道条件下的量子斗鸡博弈模型,求出了模型的量子纳什均衡解,讨论了两参量对均衡解稳定性的影响,得出在无记忆相位阻尼信道条件下,当噪音强度小于阈值0.24时,纳什均衡仍然为帕累托最优解,当噪音强度大于0.24时,均衡解演变为另2个均衡解,不再是帕累托最优;在有记忆相位阻尼信道条件下,当噪音强度小于0.24,且记忆强度大于0.5时,均衡解是稳定的.特殊地,当信道是完全记忆时,均衡解的稳定性与噪音强度无关.Using the relevant theory of quantum game and taking noise and memory as parameters,a quantum Chicken game model is established by considering phase damping channel.We obtain the quantum Nash equilibrium solution of the model,and discuss the influence of two parameters on the stability of the equilibrium solution.We find that when the noise intensity is less than the threshold value of 0.24 under the condition of memoryless phase damping channel,the Nash equilibrium is still the Pareto optimal solution,while once the noise intensity is greater than 0.24,the equilibrium solution changes into two other equilibrium solutions,which are no longer Pareto optimality;When the noise intensity is less than 0.24 and the memory intensity is greater than 0.50 under the memory condition,the equilibrium solution is stable.In particular,when the channel is fully memorized,the stability of the equalization solution is independent of the noise intensity.

关 键 词：量子斗鸡博弈 相位阻尼信道 纳什均衡 

分 类 号：O29[理学—应用数学]