This paper investigates the integration of large language models (LLMs) as reasoning agents in repeated spectrum auctions within heterogeneous networks (HetNets). While auction-based mechanisms have been widely employed for efficient resource allocation, most prior works assume one-shot auctions, static bidder behavior, and idealized conditions. In contrast to traditional formulations where base station (BS) association and power allocation are centrally optimized, we propose a distributed auction-based framework in which each BS independently conducts its own multi-channel auction, and user equipments (UEs) strategically decide both their association and bid values. Within this setting, UEs operate under budget constraints and repeated interactions, transforming resource allocation into a long-term economic decision rather than a one-shot optimization problem. The proposed framework enables the evaluation of diverse bidding behaviors -from classical myopic and greedy policies to LLM-based agents capable of reasoning over historical outcomes, anticipating competition, and adapting their bidding strategy across episodes. Simulation results reveal that the LLM-empowered UE consistently achieves higher channel access frequency and improved budget efficiency compared to benchmarks. These findings highlight the potential of reasoning-enabled agents in future decentralized wireless networks markets and pave the way for lightweight, edge-deployable LLMs to support intelligent resource allocation in next-generation HetNets.