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This paper studies the distributed energy efficient resource management in the Internet of Things (IoT). Wireless communication networks support the IoT without limitation of distance and location, which significantly impels its development. We study the communication channel and energy management in the wireless communication network supported IoT to improve the ability of connection, communication, share and collaboration, by using the game theory and distributed learning algorithm. First, we formulate an energy efficient neighbor collaborative game model and prove that the proposed game is an exact potential game. Second, we design a distributed energy efficient channel selection learning algorithm to obtain the global optimum in a distributed manner. We prove that the proposed algorithm will asymptotically converge to the global optimum with geometric speed. Finally, we make the simulations to verify the theoretic analysis and the performance of proposed algorithm.