Current policies for sharing bandwidth increase average throughput and improve utilization of the bandwidth in the local network. However, with these policies, a central administer, which is responsible for allocating bandwidth to each network flow, cannot allocate resources based on user characteristics. Thus, it leads to unfair bandwidth allocation because it does not guarantee services based on user characteristics. Therefore, we propose a novel negotiation method to share the bandwidth in a limited bandwidth network, in which, a user negotiates with other users to gain more resource. Ideally, we use a fuzzy system to infer and determine whether a device will request bandwidth or not based on the current usage of the given device. We conduct two experiments consisting of a video streaming simulation in OPNET and a real-time video streaming in WebRTC. The results of the experiment indicate that the proposed method can flexibly share the bandwidth utilization based on user''s requirement in the network.