Gossip promotes cooperation in indirect reciprocity with private reputation

Consistent reputation information fosters cooperation in indirect reciprocity, whereas discrepancies in reputational assessments can distort decision-making and erode cooperative behavior. As a widespread information transmission mechanism, gossip offers an effective pathway to address the challenge of how cooperation can be sustained under incomplete or inconsistent information. By integrating dynamic reputation updating and gossip transmission into an evolutionary framework, this study demonstrates the key role that gossip plays in alleviating social dilemmas. Simulation results show that gossip can break the deadlock caused by private reputations, effectively suppress defection, and stabilize cooperation. More frequent gossip enhances information flow, reduces disagreement over reputations, and consequently promotes cooperation. Furthermore, the influence of trust weight on cooperation is non-monotonic, indicating the importance of maintaining independent judgment when incorporating information from others. Additionally, the impact of dual-source gossip depends on the trust weight: only when the trust weight is high, increasing dual-source gossip probability substantially strengthens group cooperation. These findings provide new insights into how gossip supports cooperative dynamics under private and imperfect reputation systems.