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By executing offloaded tasks from mobile users, edge computing augments mobile devices with computing/communications resources from edge nodes (ENs), thus enabling new services/applications (e.g., real-time gaming, virtual/augmented reality). However, despite being more resourceful than mobile devices, allocating ENs' computing/communications resources to a given favorable set of users (e.g., closer to edge nodes) may block other devices from their services. This is often the case for most existing task offloading and resource allocation approaches that only aim to maximize the network social welfare or minimize the total energy consumption but do not consider the computing/battery status of each mobile device. This work develops an energy-based proportionally fair task offloading and resource allocation framework for a multi-layer cooperative edge computing network to serve all user equipments …