<p>Manufacturing-as-a-service (MaaS) has emerged as an innovative mode, creating a new service supply–demand matching (SDM) problem. Currently, demand-side free searching and scheduling-based service recommendations are leading SDM solutions. The complex auction-based service selection and recommendation (ASSR) has been overlooked. This study proposes a non-cooperative multi-attribute auction method to solve the SDM problem from MaaS platforms, covering attribute combinations, auction information broadcasting, bidding decision, and bid evaluation. The Bayes–Nash equilibrium bidding strategies for risk-neutral service providers are derived by considering different attribute combinations and attribute-related cost parameter distributions, namely uniform, triangular, and trapezoidal. These distributions are private information of service providers, and their effects on Bayes–Nash equilibrium bidding strategies are studied for the first time. The effects of attribute combinations and bidder crowd size on auction rules are explored, and the condition for a platform to collect and broadcast cost parameter distribution information is identified. The computational study shows the effectiveness of the proposed multi-attribute auction in winner determination and optimal bidding decision-making.</p>