We investigate in this paper the sharing of energy consumption among service categories in the access of a wireless network. We focus on the fixed part of the energy consumption of the network, which is known to be significantly larger than the load-dependent variable part, and propose its sharing among the service categories based on coalition game concept, the Shapley value. We consider five service categories, two large players: streaming and web browsing, and three smaller ones: download, voice and other minor services, and compare our proposal with two other sharing strategies: uniform and proportional which follows the same volume proportions. Our results, applied on a real dataset extracted from an operational network in Europe, show that our proposal is more fair both towards small services in that it reduces their shares in comparison to the uniform approach, and towards larger services as it reduces their shares in comparison with the proportional one. Indeed, our Shapley-based model accommodates both short term network behavior, in which the fixed energy component is independent of the traffic load, and longer term behavior, in which it varies with the load and infrastructure. Uniform sharing accounts only for the short term, and the proportional one only for the longer term.