亲缘选择下间接互惠的量子鹰鸽博弈模型合作演化稳定性

Cooperative evolution stability of quantum hawk-dove game with indirect reciprocity under kin selection

针对鹰鸽博弈困境,将合作机制和量子博弈结合,建立亲缘选择下间接互惠的量子鹰鸽博弈模型。然后依据复制动态方程及其雅可比矩阵,计算博弈均衡点的稳定条件。结果表明:当纠缠度、辨别度小于临界值时,演化稳定策略为(背叛,合作)和(合作,背叛);当纠缠度大于临界值时,演化稳定策略为(合作,合作)。最后通过理论分析和数值仿真得到纠缠度、相关度和辨别度均可正向促进博弈合作,为使博弈系统稳定合作,应增大三参数的数值。

In response to the dilemma of Hawk-Dove game,this study establishes a quantum Hawk-Dove game model with indirect reciprocity under kin selectionby combining cooperation mechanisms with quantum Hawk-Dove game.Then,based on the replicated dynamic equation and the corresponding Jacobian matrix,it calculates the stability conditions of the game equilibrium point.The results show that when the entanglement and discrimination are less than the critical values,the evolutionary stability strategies are(betray,cooperation)and(cooperation,betray).When the entanglement is larger than the critical value,the evolutionary stability strategy is(cooperation,cooperation).Finally,theoretical analysis and numerical simulation finds that entanglement,correlation,and discrimination can all positively promote game cooperation.To ensure stable cooperation in the game system,the values of the three parameters should be increased.