This paper addresses a multi-agent scheduling problem with uniform parallel machines owned by a resource agent and competing jobs with dynamic arrival times that belong to different consumer agents. All agents are self-interested and rational with the aim of maximizing their own objectives, resulting in intense resource competition among consumer agents and strategic behaviors of unwillingness to disclose private information. Within the context, a centralized scheduling approach is unfeasible, and a decentralized approach is considered to deal with the targeted problem. This study aims to generate a stable and collaborative solution with high social welfare while simultaneously accommodating consumer agents' preferences under incomplete information. For this purpose, a dynamic iterative auction-based approach based on a decentralized decision-making procedure is developed. In the proposed approach, a dynamic auction procedure is established for dynamic jobs participating in a real-time auction, and a straightforward and easy-to-implement bidding strategy without price is presented to reduce the complexity of bid determination. In addition, an adaptive Hungarian algorithm is applied to solve the winner determination problem efficiently. A theoretical analysis is conducted to prove that the proposed approach is individually rational and that the myopic bidding strategy is a weakly dominant strategy for consumer agents submitting bids. Extensive computational experiments demonstrate that the developed approach achieves high-quality solutions and exhibits considerable stability on large-scale problems with numerous consumer agents and jobs. A further multi-agent scheduling problem considering multiple resource agents will be studied in future work.