IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 31, NO. 3, MARCH 2013 581 An Integrated Contract and Auction Design for Secondary Spectrum Trading Lin Gao, Jianwei Huang, Ying-Ju Chen, and Biying Shou Abstract—Providing proper economic incentives to all parties involved is essential for the success of dynamic spectrum access. Market-driven secondary spectrum trading is an effective way to achieve this goal, where primary spectrum owners (POs) temporarily lease their licensed spectrum bands to unlicensed secondary users (SUs). In this paper, we consider the short-term secondary spectrum trading between one PO (seller) and multiple SUs (buyers) in a hybrid spectrum market with both guaranteed contracts (futures market) and spot transactions (spot market). In particular, we focus on the PO’s expected profit maximization un- der stochastic network information. The optimal solution consists of (i) a policy that maximizes the ex-ante expected profit based on the stochastic distribution of network information, and (ii) a selling mechanism that determines the real-time allocation and charging based on the realized network information and the de- rived policy. We study the optimal solution systematically under both information symmetry and asymmetry, depending on whether the PO can observe the SUs’ realized private information. Under information symmetry, we show that the optimal solution can be achieved by a perfect price discrimination mechanism, which maximizes both the PO’s expected profit (optimality) and the social welfare (efficiency). Under information asymmetry, we pro- pose an integrated contract and auction design–ContrAuction–to elicit SUs’ private information effectively. We derive analytically the optimal ContrAuction mechanisms that maximize the PO’s expected profit with and without the constraint of efficiency, and characterize systematically the tradeoff between the PO’s profit and the social welfare. Index Terms—Contract, Auction, Secondary Spectrum Market I. I NTRODUCTION D YNAMIC spectrum access (DSA) has been recently recognized as a novel approach to increase spectrum efficiency and alleviate spectrum scarcity. The key idea of DSA is to enable unlicensed secondary users (SUs) to access the spectrum bands of primary licensed users (called primary spectrum owners, POs) opportunistically [1] [2]. The long- term success of DSA requires many innovations in technology, Manuscript received 5 June 2012; revised 16 May 2012 and 30 July 2012. This work is supported by the General Research Funds (Project No. CUHK 412710, CUHK 412511, and CityU 144209) established under the University Grant Committee of the Hong Kong Special Administrative Region, China. This work is also partially supported by grants from City University of Hong Kong (Project No. 7002517 and 7008116). L. Gao and J. Huang are with Network Communications and Economics Lab (NCEL), Department of Information Engineering, The Chinese University of Hong Kong, HK (e-mail: {lgao, jwhuang}@ie.cuhk.edu.hk). J. Huang is the corresponding author. Y.-J. Chen is with Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, California 94720 (e- mail: chen@ieor.berkeley.edu). B. Shou is with Department of Management Sciences, City University of Hong Kong, HK (e-mail: biying.shou@cityu.edu.hk). Digital Object Identifier 10.1109/JSAC.2013.130322. economics, and policy. In particular, it is essential to design a proper mechanism that offers enough incentives for POs to open their licensed spectrum for secondary sharing. Market-driven secondary spectrum trading is a promising paradigm to address the incentive issue in DSA. With sec- ondary spectrum trading, POs temporarily lease the under- utilized spectrums to SUs. Unlike traditional commodities, the availability of spectrum is often not deterministic. That is, to provide effective protection for POs’ own subscribed licensed holders (also called primary users, PUs) from potential harm- ful interferences caused by SUs, a spectrum is only available to the SUs when it is not occupied by any PU (also called idle). Due to the uncertainty of PUs’ activities, POs usually cannot obtain this availability information in advance. To this end, we study the short-term secondary spectrum trading (e.g., on a slot-by-slot basis) in this paper. We consider the trading between one PO (monopoly seller) and multiple SUs (buyers) in a hybrid spectrum market combining both the futures market and the spot market. In the futures market, each SU reaches an agreement, called a contract, with the PO. The contract specifies some key elements in trading, e.g., the SU’s demand and payment in a given period. In the spot market, SUs buy spectrums in a real-time and on-demand manner through spot transactions (e.g., auction), and multiple SUs may compete with each other for limited spectrum resource. Figure 1 illustrates such a slotted hybrid spectrum market. The futures market insures SUs against uncertainties of future supply through pre-defined contracts, while the spot market allows SUs to compete for spectrums based on the real-time demand and preference. A hybrid market has both the reliability (of the futures market) and the flexibility (of the spot market), and thus is highly non-trivial for quality of service (QoS) differentiations in dynamic spectrum access. More specifically, we focus on the PO’s profit maximization in an exogenous hybrid spectrum market, where the SUs in both markets and the contract of each futures market user are exogenously given. The key problem is therefore: • How should the PO allocate his idle spectrums among contract users and spot market users to maximize profit? Furthermore, in practice, the network information (regarding both spectrum availability and valuation for SUs) is usually stochastic. To maximize the PO’s profit under stochastic network information, we formulate the PO’s expected profit maximization problem, and study the optimal solutions under both information symmetry and asymmetry systematically. The main contributions of this paper are as follows: • New modeling and solution technique: As far as we know, this is the first paper tackling secondary spectrum trading 0733-8716/13/$31.00 c  2013 IEEE