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... leased to multiple secondary users, as long as they do not interfere. Second, the temporal dynamics of spectrum usage by the primary user implies that these leases are necessarily ephemeral [4], [7]–=-=[9]-=-, and hence the auction must be repeated periodically. Both properties lead to interesting new challenges for the design of secondary spectrum auctions. Given that spectrum auctions are repeated, achi...

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...network model and problem formulation in Section II. In Section III, we analyze the three-stage duopoly decision model through backward induction and find the duopoly leasing and pricing equilibrium. We discuss various insights obtained from the equilibrium analysis in Section IV. In Section V, we show the impact of competition on the operators’ total profit and users’ payoffs. We conclude in Section VI and outline some future research directions. A. Related Work Some recent work also looked at the interactions between cognitive network operators and the secondary users (e.g., [6], [11]–[13], [15], [16]). [6] and [11] studied the competition among two or more cognitive service providers without !"#$%&'()*+,"(,*-.('%,/0.."(1("#"02"(*3'0(,4* Spectrum owner Operator i Operator j Investment (leasing bandwidth) Pricing (selling bandwidth) Fig. 1. Network model for the cognitive network operators. giving details on the wireless spectrum sharing models. [13] derived users’ demand functions based on the acceptance probability model. [12] explored demand functions in both quality-sensitive and price-sensitive buyer population models. Both [13] and [12] obtained various interesting results mainl...

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... efficiently. In this context, recent work has proposed several dynamic spectrum auction systems that periodically auction available spectrum to wireless networks producing the best economic outcomes =-=[1]-=-– [4]. Using short time cycles, these auctions seek to match spectrum allocation to time-varying demand, exploiting temporal and spatial multiplexing to improve spectrum utilization and efficiency. Ru...

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...ferent spectrum channels to minimize interference. A truthful auction design is proposed in [4] based on the classical VCG auction. The revenue maximization of truthful spectrum auction is studied in =-=[13]-=-. Zhou et al. [5] have proposed to use double auctions for spectrum allocations recently. Their mechanism is designed for spectrum primary markets with homogeneous channels and fixed identical user de...

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...he investment and pricing decisions of cognitive network operators recently. Several auction mechanisms have been proposed to study the investment problems of cognitive network operators (e.g., [21], =-=[22]-=-). Other recent results studied the pricing decisions of the cognitive network operators who interact with a group of secondary users (e.g., [23]–[30]). [21] considered users’ queueing delays and obta...

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...imit, recently Xu et al. [26], [27] developed some mechanisms that can ensure certain truthfulness and performance guarantee under some assumptions. Using some concepts of Myerson auction, Jia et al. =-=[12]-=- designed truthful spectrum auction for spectrum access to (approximately) maximize the revenue. 4 ALGORITHM FOR PROBLEM YOM In this section, we design an approximation algorithm for problem YOM, whic...

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...fficiency and revenue. However, since maintaining budget balance is sufficient for District, revenue maximization is outside the scope of this work, some in-depth discussions of which can be found in =-=[5]-=-, [10]. Each result obtained below has been averaged over 10000 runs. District-U. As a trade reduction auction, District-U only admits top buyers with high bids to join. Specifically, the admission ra...

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...ITAS [1] is the first truthful spectrum auction based on the monotonic allocation rule. Zhou and Zheng propose TRUST [13], which is a double auction with multiple sellers (licensed users). Jia et al. =-=[14]-=- design a spectrum auction mechanism that not only encourages truthful behaviour but also computes approximately maximum revenue, which is an alternative goal to maximum social welfare. For spectrum a...

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...large areas and time periods without traffic. Unlicensed spectrum users, or secondary users, are faced with an artificial spectrum shortage [1], [21]. Recently, dynamic spectrum allocation [1], [10], =-=[11]-=-, [21] has been proposed as a possible solution to this problem. In the dynamic spectrum allocation model, a spectrum broker [22], [23] periodically pools unused portions of spectrum together. Separat...