系统直和博弈模型下的合作演化

演化博弈论是生物进化论与博弈论结合产生的理论,已成为研究合作演化行为的有力工具.本文研究了基于系统直和博弈模型下的合作演化行为.首先,利用复制者方程分析了双人双策略及三策略对称博弈的演化动力学过程.然后,以石头剪刀布模型和雪堆模型为基础,采用矩阵直和构建系统直和博弈模型,并将所构造的直和矩阵转化为含参数的系统总支付矩阵.随后,说明了这种方法可推广到n个博弈的情形.最后,利用MATLAB对系统直和博弈模型进行仿真模拟,从系统整体的角度分析合作演化.仿真结果表明,混合之后的系统直和博弈较单一博弈而言,合作策略的占比明显增加,且整个系统稳定性更好.这种合作演化机制呈现了全局互惠.

Cooperative evolution under the direct sum game model

Evolutionary game theory is a theory produced by the combination of biological evolution theory and game theory, which has become a powerful tool for the study of cooperative evolution behavior. This paper studies the cooperative evolution behavior based on the direct sum game model. Firstly, based on replicator equation, the evolutionary dynamic process of two-person two strategies and three strategies symmetric games is analyzed. Secondly, based on the rock-paperscissors model and snowdrift model, the direct sum game model is constructed by the direct sum of matrices, and the corresponding matrix is transformed into the total payment matrix with parameters. Then a detailed analysis illustrates this method can be extended to the case of n games. Finally, the direct sum game model is simulated by MATLAB, and the evolution of cooperation is analyzed from a holistic perspective. The simulation results show that the direct sum game has two characteristics: the proportion of cooperative strategy increases obviously and the stability of the whole system is better. This evolution mechanism of cooperation presents global reciprocity.