We develop and analyze a new user-centric networking model for ubiquitous spectrum sharing where every user can share and use the spectrum under uncertainty of their traffic models. In this concept, users when connected to the Internet (wired/wireless) can dynamically serve as access points for other users in their vicinity. For this reason, the concept is referred to as user-centric distributed spectrum sharing. Each user in spectrum sharing mode utilizes a part of its available spectrum for its own traffic and remaining part to share with users in spectrum demanding modes. The model is designed as an operator supervised double-Stackelberg game with network operators, access points, and users as main players. We study network reliability and latency of the system under uncertainty of users' traffic patterns. The numerical results show that the proposed model, depending on different settings, can significantly improve both profit and utility for network operators and users, respectively. Furthermore, network reliability is significantly improved depending on the network parameters for both users and operators.