Internet of Things(IoT) refers to an infrastructure which enables the forms of communication and collaboration between people and things,and between things themselves.In order to improve its performance,we present a tradeoff between bandwidth and energy consumption in the IoT in this paper.A service providing model is built to find the relationship between bandwidth and energy consumption using a cooperative differential game model.The game solution is gotten in the condition of grand coalition,feedback Nash equilibrium and intermediate coalitions and an allocation policy is obtain by Shapley theory.The results are shown as follows.Firstly,the performance of IoT decreases with the increasing of bandwidth cost or with the decreasing of energy cost;secondly,all the nodes in the IoT composing a grand coalition can save bandwidth and energy consumption;thirdly,when the factors of bandwidth cost and energy cost are equal,the obtained number of provided services is an optimised value which is the trade-off between energy and bandwidth consumption. Internet of Things (IoT) refers to an infrastructure which enables the forms of communication and collaboration between people and things, and between things in. Order to improve its performance, we present a tradeoff between bandwidth and energy consumption in the IoT in this paper . A service providing model is built to find the relationship between bandwidth and energy consumption using a cooperative differential game model. Game solution is gotten in the condition of grand coalition, feedback Nash equilibrium and intermediate coalitions and an allocation policy is obtainable by Shapley theory The results are shown as follows. Firstly, the performance of IoT decreases with the increasing of bandwidth cost or with the decreasing of energy cost; secondly, all of the nodes in the IoT composing a grand coalition can save bandwidth and energy consumption; thirdly, when the factors of bandwidth cost and energy cost are equal, the obtained number of provided services is an optimized value which i s the trade-off between energy and bandwidth consumption.