## 1 Introduction  
With the development of Wireless Sensor Networks (WSNs), the radio spectrum resource, as one of the scarcest and expensive resources, gradually became a stumbling block. As wireless applications increase sharply, there are fewer and fewer unlicensed radio spectra, while licensed radio spectra are under-utilized. For unlicensed users lacking spectrum, solutions to the spectrum-sharing problem using dynamic spectrum borrowing and lending between unlicensed operators are inadequate [1]. Cognitive Radio (CR), which is considered to be a prospective approach to realize dynamic spectrum access (DSA) [2, 3], is widely used to improve spectrum utilization. It allows licensed users' resources to be efficiently shared with unlicensed users, in exchange for potential profits. Usually, there are many alternative licensed users for a WSN. In a CR-based WSN [4, 5, 6], the spectrum demand for a licensed user directly depends on unit price and spectrum efficiency. To attract more buyers, licensed users need to compete with each other in the terms of spectrum price. In spectrum marketing, game theory provides a set of mathematical tools that can construct economic models to analyze the behaviors of self-interested users. Each type of game model, whether it is a cooperative or non-cooperative game, certainly has advantages and disadvantages [7; 8; 9; 10]. Depending on different performances, their application environments are distinct. On the basis of the Stackelberg game, the Distributed Optimization for Cognitive Radio (DOCR) scheme [11] was designed as a hierarchical framework to optimize CR network performance. In this scheme, the spectrum of a licensed user is divided into sub-bands, each of which can only be accessed by one unlicensed user. Hence, there is no difference in that all licensed users are regarded as one. In the work presented in this paper, it is unnecessary for users to communicate with each other. Using a simple pricing function for licensed users, a distributed algorithm is introduced in the DOCR scheme to converge on Stackelberg equilibrium. The multi-leader multi-follower Stackelberg (MMS) scheme [12] was proposed as an efficient spectrum sharing scheme. As leaders, multiple licensed users played a cooperative game and collaborated with each other to fairly distribute the outcome. As followers, multiple unlicensed users played a non-cooperative game using a self-interested strategy. During step-by-step iteration, a feedback learning process is repeated to find the best solution. Under widely-diverse network environments, the MMS scheme can find an effective solution to spectrum sharing, and offer an attractive performance balance. The two-stage resource allocation scheme, with combinatorial auction and Stackelberg game in spectrum sharing (TAGS) [13] provided a feasible solution to the spectrum sharing problem, and ensured all individuals' economic properties. A geographically-restricted combinatorial auction, without consideration of spectrum recall, decided the spectrum allocations, while a Stackelberg game was designed to determine all users' strategies with respect to the potential spectrum recall. However, the existence of the broker, which collected all sealed-bid information, determined the optimal allocation, and calculated the payments and payoffs, limited the framework of the model. Recently, another game model, which is often used to solve spectrum sharing problems, is auction [14; 15; 16]. The Repeated Bayesian Auction (RBA) scheme [17] could achieve an effective solution of spectrum sharing under widely-diverse system environments. Licensed users adaptively decided their prices using a Bayesian game, and shared bandwidth based on the double auction protocol. In each auction round, the auctioneer collected all the information about offers and bids, and determined the trade price. The dynamic auction would be repeated sequentially, every time period, until an efficient auction consensus was reached.