时滞系统在对称博弈中的应用研究

Research on the Application of Time Delay System in Symmetric Game

摘要: 本文基于有限理性框架下，以2 × 2的对称博弈问题为研究对象，建立起带时滞的对称博弈模型。通过演化动力学理论中的复制动力学研究分析了博弈参与者进行策略选择的复制动态变化过程。数值模拟了带时滞与不带时滞两类系统下博弈的稳定状态。实验结果表明，在对称博弈中，决策者决策延时会对决策造成一定的影响，这个影响不改变策略的稳定状态，改变的仅是达到稳定状态的快慢程度，且时滞越长，演化到稳定状态的速度越快。

Abstract: Based on the framework of bounded rationality, this paper takes the 2 × 2 symmetric game prob-lem as the research object, establishes a symmetric game model with time delay. The dynamic change process of game participants’ strategy selection is analyzed by the study of replication dynamics in evolutionary dynamics theory. The stable state of the game under two kinds of systems with and without time delay is numerically simulated. The experimental results show that in a symmetric game, the decision-maker’s decision delay will have a certain impact on the decision. This impact does not change the steady state of the strategy, but only changes the speed of reaching the steady state. And the longer the time lag, the faster the evolution to the steady state.