异质影响力下两策略演化博弈的动力学分析

The Dynamics Analysis of Two-Strategy Evolutionary Game under Heterogeneous Influence

摘要: 在网络演化博弈中，经典死亡–出生更新规则通常被认为对网络度异质性不敏感，但该结论隐含假设个体影响力是同质的。本文在死亡–出生更新框架中引入个体影响力异质性，使个体占据空位的概率同时依赖收益与传播影响力。在弱选择极限下，结合成对近似方法，推导了具有异质影响力的网络多策略演化动力学方程。结果表明，系统动力学仍可等价表示为复制动力学，但收益矩阵受到网络结构与影响力分布耦合的修正。进一步分析囚徒困境与协调博弈发现，当影响力与节点度正相关时，网络异质性能够降低合作成为演化稳定策略的门槛，并促进群体向帕累托更优均衡演化；而当影响力与节点度负相关时，网络异质性的作用被抑制，系统行为趋近经典结果。

Abstract: In evolutionary game theory on networks, the classical death-birth update rule is typically considered insensitive to network degree heterogeneity. However, this conclusion implicitly assumes homogeneous individual influence. In this paper, we introduce individual influence heterogeneity into the death-birth update framework, where the probability of an individual occupying a vacant position depends on both payoff and propagating influence. Under the weak selection limit, we derive the multi-strategy evolutionary dynamics equations for networks with heterogeneous influence using pair approximation methods. The results show that the system dynamics can still be equivalently represented by replicator dynamics, but the payoff matrix is modified by the coupling of network structure and influence distribution. Further analysis of the prisoner’s dilemma and coordination games reveals that when influence is positively correlated with node degree, network heterogeneity can lower the threshold for cooperation to become an evolutionarily stable strategy and promote the evolution of the population towards a more Pareto-optimal equilibrium. On the other hand, when influence is negatively correlated with node degree, the effect of network heterogeneity is suppressed, and the system behavior approaches the classical result.