Indirect reciprocity, which means helping those who have helped others, is difficult to sustain among decentralized, self-interested LLM agents without reliable reputation systems. We address this challenge with the Agentic Linguistic Gossip Network (ALIGN), an automated framework that enables decentralized agents to form reputations, evaluate trustworthiness, and coordinate social norms by strategically sharing open-ended gossip with hierarchical tones. We demonstrate that ALIGN consistently improves indirect reciprocity and resists malicious entrants by identifying and ostracizing defectors. Notably, we find that stronger reasoning capabilities in LLMs lead to more incentive-aligned cooperation, whereas chat models often over-cooperate even when strategically suboptimal. These results suggest that leveraging LLM reasoning through decentralized gossip is a promising path for maintaining social welfare in agentic ecosystems. Our code is available at https://github.com/shuhui-zhu/ALIGN.

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