Deep Neural Networks (DNNs) have significantly improved the accuracy of intelligent applications on mobile devices. DNN surgery, which partitions DNN processing between mobile devices and multi-access edge computing (MEC) servers, can enable real-time inference despite the computational limitations of mobile devices. However, DNN surgery faces a critical challenge: determining the optimal computing resource demand from the server and the corresponding partition strategy, while considering both inference latency and MEC server usage costs. This problem is compounded by two factors: (1) the finite computing capacity of the MEC server, which is shared among multiple devices, leading to inter-dependent demands, and (2) the shift in modern DNN architecture from chains to directed acyclic graphs (DAGs), which complicates potential solutions. In this paper, we introduce a novel Decentralized DNN Surgery (DDS) framework. We formulate the partition strategy as a min-cut and propose a resource allocation game to adaptively schedule the demands of mobile devices in an MEC environment. We prove the existence of a Nash Equilibrium (NE), and develop an iterative algorithm to efficiently reach the NE for each device. Our extensive experiments demonstrate that DDS can effectively handle varying MEC scenarios, achieving up to 1.25$\times$ acceleration compared to the state-of-the-art algorithm.

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