To enable edge AI providers to recruit edge devices and use them to deploy AI models and provision inference services, we conduct a comprehensive mathematical and algorithmic study on a novel incentive and optimization mechanism based on repeated auctions. We first model and formulate a time-cumulative social cost optimization problem to capture the challenges of the trade-off between cost and accuracy, the dependency between adjacent auctions, and the need of achieving desired economic properties. Then, to solve this intractable non-linear integer program in an online manner, we design a set of polynomial-time algorithms that work together. Our approach dynamically chooses and switches winning bids under careful control, incorporates online learning to overcome posterior inference accuracy and workload queue dynamics, and leverages randomization to strategically convert fractional decisions of model placement and query dispatch into integers. We also allocate payments to meet the necessary and sufficient conditions for the desired economic properties. Further, we rigorously prove the constant competitive ratio, the sub-linear regret and fit, and the truthfulness and individual rationality for our proposed approach. Finally, through extensive experiments using real devices, AI models, and data traces, we have validated the substantial advantages of our proposed approach compared to the baselines and the state-of-the-art methods.