This paper addresses the cost-efficiency aspect of Reinforcement Learning from Human Feedback (RLHF). RLHF leverages datasets of human preferences over outputs of large language models (LLM)s to instill human expectations into LLMs. Although preference annotation comes with a monetized cost, the economic utility of a preference dataset has not been considered by far. What exacerbates this situation is that, given complex intransitive or cyclic relationships in preference datasets, existing algorithms for fine-tuning LLMs are still far from capturing comprehensive preferences. This raises severe cost-efficiency concerns in production environments, where preference data accumulate over time. In this paper, we discuss the fine-tuning of LLMs as a monetized economy and introduce an auction mechanism to improve the efficiency of preference data collection in dollar terms. We show that introducing an auction mechanism can play an essential role in enhancing the cost-efficiency of RLHF, while maintaining satisfactory model performance. Experimental results demonstrate that our proposed auction-based protocol is cost-effective for fine-tuning LLMs concentrating on high-quality feedback.