Evolutionary dynamics of a probabilistic punishment mechanism with environmental feedback in regular networked Prisoner's Dilemma

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Chaos Solitons & Fractals Pub Date : 2025-03-20 DOI:10.1016/j.chaos.2025.116323

Jiaqi Liu, Qianwei Zhang

{"title":"Evolutionary dynamics of a probabilistic punishment mechanism with environmental feedback in regular networked Prisoner's Dilemma","authors":"Jiaqi Liu, Qianwei Zhang","doi":"10.1016/j.chaos.2025.116323","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we investigate the interconnection between players' strategies and the probability of effective punishment. We propose to integrate the environmental feedback and a punishment mechanism to construct a Prisoner's Dilemma game model within a regular network. Based on our analysis, we identify three unique system states: a single stable state where defection predominates and the probability of effective punishment is low, a single stable state where cooperation prevails and the probability of effective punishment is high, and a bi-stable condition characterized by the coexistence of two stable states. We deduce that alterations in the speed of the environmental feedback can influence the system's convergence behavior under bi-stable conditions. The conclusion could be drawn that accelerating the rate at which the probability of effective punishment is updated can be beneficial for enhancing cooperation within social systems. The findings highlight the critical role of the proposed punishment mechanism in fostering long-term stability and sustainable development within societies.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"195 ","pages":"Article 116323"},"PeriodicalIF":5.6000,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos Solitons & Fractals","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0960077925003364","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}

引用次数: 0

Abstract

In this paper, we investigate the interconnection between players' strategies and the probability of effective punishment. We propose to integrate the environmental feedback and a punishment mechanism to construct a Prisoner's Dilemma game model within a regular network. Based on our analysis, we identify three unique system states: a single stable state where defection predominates and the probability of effective punishment is low, a single stable state where cooperation prevails and the probability of effective punishment is high, and a bi-stable condition characterized by the coexistence of two stable states. We deduce that alterations in the speed of the environmental feedback can influence the system's convergence behavior under bi-stable conditions. The conclusion could be drawn that accelerating the rate at which the probability of effective punishment is updated can be beneficial for enhancing cooperation within social systems. The findings highlight the critical role of the proposed punishment mechanism in fostering long-term stability and sustainable development within societies.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

正则网络囚徒困境中具有环境反馈的概率惩罚机制的进化动力学

在本文中，我们研究了参与者的策略与有效惩罚的概率之间的联系。我们提出将环境反馈和惩罚机制结合起来，构建规则网络中的囚徒困境博弈模型。在此基础上，我们确定了三种独特的系统状态：背叛占主导地位且有效惩罚概率较低的单一稳定状态，合作占主导地位且有效惩罚概率较高的单一稳定状态，以及两种稳定状态共存的双稳定状态。我们推导出在双稳态条件下，环境反馈速度的变化会影响系统的收敛行为。可以得出的结论是，加快有效惩罚概率的更新速度有利于加强社会系统内的合作。研究结果强调了拟议的惩罚机制在促进社会长期稳定和可持续发展方面的关键作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文去求助

来源期刊

Chaos Solitons & Fractals 物理-数学跨学科应用

CiteScore

13.20

自引率

10.30%

发文量

1087

审稿时长

9 months

期刊介绍： Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.