Evolution of cooperation through dynamic probabilistic punishment under individual camouflage

In real-world social systems, individual defection is often concealed. The presence of camouflage strategies introduces challenges to conventional punishment mechanisms, particularly in terms of imperfect identification and delayed enforcement. To address this issue, this study introduces individual camouflage strategies within the framework of the public goods game. We develop a probabilistic punishment mechanism that integrates dynamic accumulation of behavioral responsibility, emotional retaliation preferences, and reputation feedback, and we systematically analyze the evolution of cooperation. The numerical results indicate that increasing the punishment intensity and reducing the punishment cost both facilitate the spread of cooperation, whereas extending the punishment scope from first-order to second-order raises institutional costs and increases the threshold for the emergence of cooperation. In an environment with camouflaged defection, the camouflage cost and the mechanism of accumulated historical defection jointly form a strong endogenous constraint. By transforming the strategic concealment of defectors into a long-term evolutionary disadvantage, the system’s tolerance to camouflage pressure is significantly enhanced. In addition, the results show that reputation sensitivity generates a positive feedback mechanism by biasing payoff allocation toward high-reputation individuals, thereby accelerating the evolution of cooperation. By contrast, stronger emotional retaliation preferences suppress the expansion of defection by increasing the frequency of punishment activation, yet they remain insufficient to sustain stable cooperation on their own under conditions of low synergistic returns. These findings provide a new perspective for understanding how the concealed nature of defection and its underlying psychological motivations shape the emergence of cooperation in complex social systems.