Aspiration-Fermi 混合机制下带异质收益和时间成本的双阈值 $N$ 人雪堆博弈的演化动力学

摘要/Abstract

摘要：

基于收益的异质性和时间偏好的指数贴现视角, 该文建立了一个具有异质收益和非线性时间成本的双阈值 $N$ 人雪堆博弈模型. 结合 Aspiration 规则在个体主观方面的特性与 PW-Fermi 规则在考虑博弈环境方面的客观特点, 通过线性耦合的方式将 Aspiration 更新规则和 PW-Fermi 规则进行混合, 并运用平均动力学原理, 进一步构建 Aspiration-Fermi 混合机制下的演化动力学方程. 最后通过数值仿真和对比分析, 发现异质收益、指数非线性时间成本和 Aspiration-Fermi 混合机制能够有效地促进合作. 该文为研究复杂社会中合作的演化提供了一种新的视角.

关键词: Aspiration-Fermi 混合机制, 异质收益, 指数时间成本, 双阈值雪堆博弈

Abstract:

This study establishes a dual-threshold $N$-player snowdrift game model with heterogeneous benefits and nonlinear time costs from the perspective of benefit heterogeneity and exponential discounting of time preferences. We develop an Aspiration-Fermi hybrid mechanism by linearly coupling the Aspiration update rule with the PW-Fermi rule, and subsequently construct the corresponding evolutionary dynamics based on the mean dynamic principle. Numerical simulations and comparative analyses reveal that heterogeneous benefits, exponential nonlinear time costs, and the Aspiration-Fermi hybrid mechanism significantly enhance cooperation. This work provides new perspectives for studying the evolution of cooperation in complex societies.

Key words: Aspiration-Fermi hybrid mechanism, heterogeneous benefits benefits, exponential time costs, dual-threshold snowdrift game

中图分类号:

O225

杨柏林, 杨光惠. Aspiration-Fermi 混合机制下带异质收益和时间成本的双阈值 $N$ 人雪堆博弈的演化动力学[J]. 数学物理学报, 2026, 46(5): 2030-2039.

Bolin Yang, Guanghui Yang. Evolutionary Dynamics of a Dual-Threshold $N$-Player Snowdrift Game with Heterogeneous Benefits and Time Cost Under an Aspiration-Fermi Hybrid Mechanism[J]. Acta mathematica scientia,Series A, 2026, 46(5): 2030-2039.

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