Thanks to the rapid development of information technology, the size of the wireless network becomes larger and larger, which makes spectrum resources more precious than ever before. To improve the efficiency of spectrum utilization, game theory has been applied to study the spectrum sharing in wireless networks for a long time. However, the scale of wireless network in existing studies is relatively small. In this paper, we introduce a novel game and model the spectrum sharing problem as an aggregative game for large-scale, heterogeneous, and dynamic networks. The massive usage of spectrum also leads to easier privacy divulgence of spectrum users actions, which calls for privacy and truthfulness guarantees in wireless network. In a large decentralized scenario, each user has no priori about other users decisions, which forms an incomplete information game. A weak mediator, e.g., the base station or licensed spectrum regulator, is introduced and turns this game into a complete one, which is essential to reach a Nash equilibrium (NE). By utilizing past experience on the channel access, we propose an online learning algorithm to improve the utility of each user, achieving NE over time. Our learning algorithm also provides no regret guarantee to each user. Our mechanism admits an approximate ex-post NE. We also prove that it satisfies the joint differential privacy and is incentive-compatible. Efficiency of the approximate NE is evaluated, and the innovative scaling law results are disclosed. Finally, we provide simulation results to verify our analysis.
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