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

IF 5.3 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

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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.

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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.