The convergence of edge computing and Artificial Intelligence (AI) gives rise to Edge-AI, which enables the deployment of real-time AI applications at the network edge. A key research challenge in Edge-AI is edge inference acceleration, which aims to realize low-latency high-accuracy Deep Neural Network (DNN) inference by offloading partitioned inference tasks from end devices to edge servers. However, existing research has yet to adopt a practical Edge-AI market perspective, which would explore the personalized inference needs of AI users (e.g., inference accuracy, latency, and task complexity), the revenue incentives for AI service providers that offer edge inference services, and multi-stakeholder governance within a market-oriented context. To bridge this gap, we propose an Auction-based Edge Inference Pricing Mechanism (AERIA) for revenue maximization to tackle the multi-dimensional optimization problem of DNN model partition, edge inference pricing, and resource allocation. We develop a multi-exit device-edge synergistic inference scheme for on-demand DNN inference acceleration, and theoretically analyze the auction dynamics amongst the AI service providers, AI users and edge infrastructure provider. Owing to the strategic mechanism design via randomized consensus estimate and cost sharing techniques, the Edge-AI market attains several desirable properties. These include competitiveness in revenue maximization, incentive compatibility, and envy-freeness, which are crucial to maintain the effectiveness, truthfulness, and fairness in auction outcomes. Extensive simulations based on four representative DNN inference workloads demonstrate that AERIA significantly outperforms several state-of-the-art approaches in revenue maximization. This validates the efficacy of AERIA for on-demand DNN inference in the Edge-AI market.