Reinforcement fine-tuning (RFT) is increasingly used in applications where large language models (LLMs) interact with humans and other agents. Here we use social deduction games to study how RFT changes LLMs' social behaviour. We let fine-tuned and base LLM agents play hidden-role games that require hidden-state inference, social reading and vote steering. Our results show that LLM agents do not reliably acquire social-deduction ability by directly optimizing terminal win--loss outcomes, suggesting that final game results provide a sparse and noisy signal for socially interactive learning. However, RFT is particularly effective at improving social reading, including tasks that require agents to infer hidden roles from public discussion, update beliefs over time and predict other agents' future decisions. We further show that RFT can also improve social influence, including tasks that require agents to steer votes, team approvals and collective decisions, although these gains depend more strongly on behaviourally specific rewards and structured interaction settings. Finally, we show that LLMs' ability to play social deduction games can be further improved through multi-agent social-cognitive reinforcement fine-tuning, which combines social-reading and social-influence signals during same-side multi-agent training. These learned behaviours also receive more favourable human evaluations of strategic competence, persuasiveness and social usefulness. Together, these results enrich our understanding of how RFT changes LLMs' social behaviour and provide a step toward a behavioural learning theory for machine social intelligence.

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