Wireless spectrum pricing (18)

In order to provide cellular network services, service providers need to purchase wireless spectrum, which is usually done by participating in a government auction. So-called “primary” spectrum holders, who are successful in purchasing spectrum, can then resell this spectrum on a temporary basis to other parties in secondary spectrum markets.

**S. Wang, P. Xu, X. Xu, S. Tang, X. Li and X. Liu** Proceedings of IEEE DySpan, 2010

The spectrum usage by a secondary user often happens in a certain geographical region and in a certain time interval, and the requests often come in an online fashion. Considering the selfish behaviors of primary users and secondary users, it is imperative to design online double spectrum auction methods. The most significant challenge is how to make the online double auction economic-robust (truthful in particular). Unfortunately, existing designs either do not consider the online requests or become untruthful when applied to scenarios when both primary users and secondary users could be selfish. In this paper, we address this problem by proposing TODA, a general framework for truthful online double auction for spectrum allocation. We assume that there is a central auctioneer, and the arrivals of secondary users' requests follow Poisson distribution. Upon receiving online spectrum requests, the central auctioneer will decide immediately which secondary and primary users will win the auction, and match winning primary users and secondary users, as well as decide how much secondary users should pay and primary users should get. To preempt existing spectrum usage is not allowed. We study the case in which the conflict graph of secondary users is a complete graph, which occurs in the urban area where the distribution of the secondary users is very dense. In this case, we design strategyproof (truthful) mechanisms for both the primary users and secondary users. To the best of our knowledge, we are the first to design truthful online double auction mechanisms for spectrum allocation. Our simulation results show that the expected social efficiency ratio of our mechanism is always above 80% compared with the off-line VCG mechanism and the spectrum utilization ratio is around 70% when the system is highly loaded.

**O. Ileri, D. Samardzija and N. B. Mandayam** Proceedings of IEEE DySpan, 2005

In this paper we develop a framework for competition of future operators likely to operate in a mixed commons/property-rights regime under the regulation of a spectrum policy server (SPS). The operators dynamically compete for customers as well as portions of available spectrum. The operators are charged by the SPS for the amount of bandwidth they use in their services. Through demand responsive pricing, the operators try to come up with convincing service offers for the customers, while trying to maximize their profits. We first consider a single-user system as an illustrative example. We formulate the competition between the operators as a non-cooperative game and propose an SPS-based iterative bidding scheme that results in a Nash equilibrium of the game. Numerical results suggest that, competition increases the user's (customer's) acceptance probability of the offered service, while reducing the profits achieved by the operators. It is also observed that as the cost of unit bandwidth increases relative to the cost of unit infrastructure (fixed cost), the operator with superior technology (higher fixed cost) becomes more competitive. We then extend the framework to a multiuser setting where the operators are competing for a number of users at once. We propose an SPS-based bandwidth allocation scheme in which the SPS optimally allocates bandwidth portions for each user-operator session to maximize its overall expected revenue resulting from the operator payments. Comparison of the performance of this scheme to one in which the bandwidth is equally shared between the user-operator pairs reveals that such an SPS-based scheme improves the user acceptance probabilities and the bandwidth utilization in multiuser systems

**G. S. Kasbekar and S. Sarkar** Proceedings of ACM MobiHoc, 2010

In cognitive radio networks (CRN), primary users can lease out their unused bandwidth to secondary users in return for a fee. We study price competition in a CRN with multiple primaries and e secondaries in a region, where each primary tries to attract secondaries by setting a lower price for his bandwidth than other primaries. A CRN has two distinctive features, which makes the price competition very different from that in traditional commodity markets. First, in every slot, each primary may or may not have unused bandwidth available. So primaries are uncertain about the number of other primaries from whom they face competition. Second, spectrum is a commodity that allows spatial reuse: the same band can be simultaneously used at far-off locations without interference; on the other hand, simultaneous transmissions at neighboring locations on the same band interfere with each other. As a result, a primary cannot offer bandwidth at all locations, but must select an independent set of locations at which to offer it. Also, the choice of the independent set and the prices at those locations must be made jointly. We formulate price competition in a CRN as a game, taking into account both bandwidth uncertainty and spatial reuse. We analyze the game in a single slot, as well as its repeated version. In each case, we not only prove the existence of a Nash equilibrium, but also explicitly compute it. The expressions we obtain provide interesting insights into how the price competition evolves for different values of the system parameters. Moreover, for the game in a single slot, we prove the uniqueness of the Nash equilibrium in the class of symmetric equilibria.

**J. Jia and Q. Zhang** Proceedings of ACM MobiHoc, 2008

Dynamic spectrum access can significantly improve the spectrum utilization. For wireless service providers, the emergence of dynamic spectrum access brings new opportunities and challenges. The flexible spectrum acquisition gives a particular provider the chance to easily adapt its system capacity to fit end users' demand. However, the competition among several providers for both spectrum and end users complicates the situation. In this paper, we propose a general three-layer spectrum market model for the future dynamic spectrum access system, in which the interaction among spectrum holder, wireless service providers and end users are considered. We study a duopoly situation, where two wireless service providers participate in bandwidth competition in spectrum purchasing and price competition to attract end users, with the aim of maximizing their own profit. We believe we are the first one to explicitly study the relation of these two competitions in dynamic spectrum market. We formulate the wireless service providers' competition as a non-cooperative two-stage game. We first analyze the static game when full information is available for providers. Under general assumptions about the price and demand functions, a unique pure Nash equilibrium is identified as the outcome of the game, which shows the stability of the market. We further evaluate the market efficiency of the equilibrium in a symmetric case, and show that the gap with the social optimal is bounded within a small constant ratio. When the market information is limited, we provide myopically optimal adjustment algorithms for the providers. With such strategies, short term price updating converges to the Nash equilibrium of the given subgame, while long term bandwidth updating converges to a point close to the Nash equilibrium of the full game.

**L. Duan, J. Huang and B. Shou** IEEE Transactions on Mobile Computing, 10(11): 1590—1604, 2011

This paper studies the optimal investment and pricing decisions of a cognitive mobile virtual network operator (C-MVNO) under spectrum supply uncertainty. Compared with a traditional MVNO who often leases spectrum via long-term contracts, a C-MVNO can acquire spectrum dynamically in short-term by both sensing the empty “spectrum holes” of licensed bands and dynamically leasing from the spectrum owner. As a result, a C-MVNO can make flexible investment and pricing decisions to match demands of the secondary unlicensed users. Compared to dynamic spectrum leasing, spectrum sensing is typically cheaper, but the obtained useful spectrum amount is random due to primary licensed users' stochastic traffic. The C-MVNO needs to determine the optimal amounts of spectrum sensing and leasing by evaluating the trade-off between cost and uncertainty. The C-MVNO also needs to determine the optimal price to sell the spectrum to the secondary unlicensed users, taking into account wireless heterogeneity of users such as different maximum transmission power levels and channel gains. We model and analyze the interactions between the C-MVNO and secondary unlicensed users as a Stackelberg game. We show several interesting properties of the network equilibrium, including threshold structures of the optimal investment and pricing decisions, the independence of the optimal price on users' wireless characteristics, and guaranteed fair and predictable QoS among users. We prove that these properties hold for general SNR regime and general continuous distributions of sensing uncertainty. We show that spectrum sensing can significantly improve the C-MVNO's expected profit and users' payoffs.

**S. Sengupta and M. Chatterjee** IEEE/ACM Transactions on Networking, 17(4): 1200—1213, 2009

The concept of dynamic spectrum access will allow the radio spectrum to be traded in a market like scenario allowing wireless service providers (WSPs) to lease chunks of spectrum on a short-term basis. Such market mechanisms will lead to competition among WSPs where they not only compete to acquire spectrum but also attract and retain users. Currently, there is little understanding on how such a dynamic trading system will operate so as to make the system feasible under economic terms. In this paper, we propose an economic framework that can be used to guide i) the dynamic spectrum allocation process and ii) the service pricing mechanisms that the providers can use. We propose a knapsack based auction model that dynamically allocates spectrum to the WSPs such that revenue and spectrum usage are maximized. We borrow techniques from game theory to capture the conflict of interest between WSPs and end users. A dynamic pricing strategy for the providers is also proposed. We show that even in a greedy and non-cooperative behavioral game model, it is in the best interest of the WSPs to adhere to a price and channel threshold which is a direct consequence of price equilibrium. Through simulation results, we show that the proposed auction model entices WSPs to participate in the auction, makes optimal use of the spectrum, and avoids collusion among WSPs. We demonstrate how pricing can be used as an effective tool for providing incentives to the WSPs to upgrade their network resources and offer better services.

**H. Mutlu, M. Alanyali and D. Starobinski** Proceedings of IEEE INFOCOM, 2008

Recent deregulation initiatives enable cellular providers to sell excess spectrum for secondary usage. In this paper, we investigate the problem of optimal spot pricing of spectrum by a provider in the presence of both non-elastic primary users, with long-term commitments, and opportunistic, elastic secondary users. We first show that optimal pricing can be formulated as an infinite horizon average reward problem and solved using stochastic dynamic programming. Next, we investigate the design of efficient single pricing policies. We provide numerical and analytical evidences that static pricing policies do not perform well in such settings (in sharp contrast to settings where all the users are elastic). On the other hand, we prove that deterministic threshold pricing achieves optimal profit amongst all single-price policies and performs close to global optimal pricing. We characterize the profit regions of static and threshold pricing, as a function of the arrival rate of primary users. Under certain reasonable assumptions on the demand function, we show that the profit region of threshold pricing can be far larger than that of static pricing. Moreover, we also show that these profit regions critically depend on the support of the demand function rather than specific form of it. We prove that the profit function of threshold pricing is unimodal in price and determine a restricted interval in which the optimal threshold lies. These two properties enable very efficient computation of the optimal threshold policy that is far faster than that of the global optimal policy.

**D. Niyato and E. Hossain** IEEE Journal on Selected Areas in Communications, 26(1): 192—202, 2008

We address the problem of spectrum pricing in a cognitive radio network where multiple primary service providers compete with each other to offer spectrum access opportunities to the secondary users. By using an equilibrium pricing scheme, each of the primary service providers aims to maximize its profit under quality of service (QoS) constraint for primary users. We formulate this situation as an oligopoly market consisting of a few firms and a consumer. The QoS degradation of the primary services is considered as the cost in offering spectrum access to the secondary users. For the secondary users, we adopt a utility function to obtain the demand function. With a Bertrand game model, we analyze the impacts of several system parameters such as spectrum substitutability and channel quality on the Nash equilibrium (i.e., equilibrium pricing adopted by the primary services). We present distributed algorithms to obtain the solution for this dynamic game. The stability of the proposed dynamic game algorithms in terms of convergence to the Nash equilibrium is studied. However, the Nash equilibrium is not efficient in the sense that the total profit of the primary service providers is not maximized. An optimal solution to gain the highest total profit can be obtained. A collusion can be established among the primary services so that they gain higher profit than that for the Nash equilibrium. However, since one or more of the primary service providers may deviate from the optimal solution, a punishment mechanism may be applied to the deviating primary service provider. A repeated game among primary service providers is formulated to show that the collusion can be maintained if all of the primary service providers are aware of this punishment mechanism, and therefore, properly weight their profits to be obtained in the future.

**X. Zhou, S. Gandhi, S. Suri and H. Zheng** Proceedings of ACM MobiCom, 2008

Market-driven dynamic spectrum auctions can drastically improve the spectrum availability for wireless networks struggling to obtain additional spectrum. However, they face significant challenges due to the fear of market manipulation. A truthful or strategy-proof spectrum auction eliminates the fear by enforcing players to bid their true valuations of the spectrum. Hence bidders can avoid the expensive overhead of strategizing over others and the auctioneer can maximize its revenue by assigning spectrum to bidders who value it the most. Conventional truthful designs, however, either fail or become computationally intractable when applied to spectrum auctions. In this paper, we propose VERITAS, a truthful and computationally-efficient spectrum auction to support an eBay-like dynamic spectrum market. VERITAS makes an important contribution of maintaining truthfulness while maximizing spectrum utilization. We show analytically that VERITAS is truthful, efficient, and has a polynomial complexity of O(n3k) when n bidders compete for k spectrum bands. Simulation results show that VERITAS outperforms the extensions of conventional truthful designs by up to 200% in spectrum utilization. Finally, VERITAS supports diverse bidding formats and enables the auctioneer to reconfigure allocations for multiple market objectives.

**Z. Ji and K. J. R. Liu** IEEE Journal on Selected Areas in Communications, 26(1): 182—191, 2008

In order to fully utilize scarce spectrum resources, dynamic spectrum allocation becomes a promising approach to increase the spectrum efficiency for wireless networks. However, the collusion among selfish network users may seriously deteriorate the efficiency of dynamic spectrum sharing. The network users' behaviors and dynamics need to be taken into consideration for efficient and robust spectrum allocation. In this paper, we model the spectrum allocation in wireless networks with multiple selfish legacy spectrum holders and unlicensed users as multi-stage dynamic games. In order to combat user collusion, we propose a pricing-based collusion-resistant dynamic spectrum allocation approach to optimize overall spectrum efficiency, while not only keeping the participating incentives of the selfish users but also combating possible user collusion. The simulation results show that the proposed scheme achieves high efficiency of spectrum usage even with the presence of severe user collusion.

**A. Gopinathan and Z. Li** Proceedings of IEEE INFOCOM, 2011

Secondary spectrum access is emerging as a promising approach for mitigating the spectrum scarcity in wireless networks. Coordinated spectrum access for secondary users can be achieved using periodic spectrum auctions. Recent studies on such auction design mostly neglect the repeating nature of such auctions, and focus on greedily maximizing social welfare. Such auctions can cause subsets of users to experience starvation in the long run, reducing their incentive to continue participating in the auction. It is desirable to increase the diversity of users allocated spectrum in each auction round, so that a trade-off between social welfare and fairness is maintained. We study truthful mechanisms towards this objective, for both local and global fairness criteria. For local fairness, we introduce randomization into the auction design, such that each user is guaranteed a minimum probability of being assigned spectrum. Computing an optimal, interference-free spectrum allocation is NP-Hard; we present an approximate solution, and tailor a payment scheme to guarantee truthful bidding is a dominant strategy for all secondary users. For global fairness, we adopt the classic max-min fairness criterion. We tailor another auction by applying linear programming techniques for striking the balance between social welfare and max-min fairness, and for finding feasible channel allocations. In particular, a pair of primal and dual linear programs are utilized to guide the probabilistic selection of feasible allocations towards a desired tradeoff in expectation.

**S. H. Chun and R. J. La** IEEE/ACM Transactions on Networking, 21(1): 176—189, 2013

Recently, dynamic spectrum sharing has been gaining interest as a potential solution to scarcity of available spectrum. We investigate the problem of designing a secondary spectrum-trading market when there are multiple sellers and multiple buyers and propose a general framework for the trading market based on an auction mechanism. To this end, we first introduce a new optimal auction mechanism, called the generalized Branco's mechanism (GBM). The GBM, which is both incentive-compatible and individually rational, is used to determine the assigned frequency bands and prices for them. Second, we assume that buyers of the spectrum are selfish and model their interaction as a noncooperative game. Using this model, we prove that when the sellers employ the GBM to vend their frequency bands, they can guarantee themselves the largest expected profits by selling their frequency bands jointly. Third, based on the previous finding, we model the interaction among the sellers as a cooperative game and demonstrate that, for any fixed strategies of the buyers, the core of the cooperative game is nonempty. This suggests that there exists a way for the sellers to share the profits from the joint sale of the spectrum so that no subset of sellers will find it beneficial to vend their frequency bands separately without the remaining sellers. Finally, we propose a profit-sharing scheme that can achieve any expected profit vector in the nonempty core of the cooperative game while satisfying two desirable properties.

**Q. Huang, Y. Tao and F. Wu** Proceedings of IEEE INFOCOM, 2013

The problem of dynamic spectrum redistribution has been extensively studied in recent years. Auction is believed to be one of the most effective tools to solve this problem. A great number of strategy-proof auction mechanisms have been proposed to improve spectrum allocation efficiency by stimulating bidders to truthfully reveal their valuations of spectrum, which are the private information of bidders. However, none of these approaches protects bidders' privacy. In this paper, we present SPRING, which is the first Strategy-proof and PRivacy preservING spectrum auction mechanism. We not only rigorously prove the properties of SPRING, but also extensively evaluate its performance. Our evaluation results show that SPRING achieves good spectrum redistribution efficiency with low overhead.

**S.-P. Sheng and M. Liu** Proceedings of IEEE INFOCOM, 2013

In this paper we formulate a contract design problem where a primary license holder wishes to profit from its excess spectrum capacity by selling it to potential secondary users/buyers. It needs to determine how to optimally price the excess spectrum so as to maximize its profit, knowing that this excess capacity is stochastic in nature, does not come with exclusive access, and cannot provide deterministic service guarantees to a buyer. At the same time, buyers are of different {\em types}, characterized by different communication needs, tolerance for the channel uncertainty, and so on, all of which a buyer's private information. The license holder must then try to design different contracts catered to different types of buyers in order to maximize its profit. We address this problem by adopting as a reference a traditional spectrum market where the buyer can purchase exclusive access with fixed/deterministic guarantees. We fully characterize the optimal solution in the cases where there is a single buyer type, and when multiple types of buyers share the same, known channel condition as a result of the primary user activity. In the most general case we construct an algorithm that generates a set of contracts in a computationally efficient manner, and show that this set is optimal when the buyer types satisfy a monotonicity condition.

**W. Dong, S. Rallapalli, L. Qiu, K. K. Ramakrishnan and Y. Zhang** Proceedings of IEEE INFOCOM, 2014

Wireless spectrum is a precious resource and must be allocated and used efficiently. The conventional spectrum allocation lets a government (e.g., FCC) sell a given portion of spectrum to one provider. This is not only restrictive, but also limits spectrum reuse and may lead to significant under-utilization of spectrum. In this paper, we develop a novel truthful double auction scheme to let any resource owner (e.g., a cellular provider), who has spare spectrum at a given time, sell to one or more providers that need additional spectrum at that time. Spectrum auction is fundamentally different from conventional auction problems since spectrum can be re-used and competition pattern is complex due to wireless interference. We propose the first double auction design for spectrum allocation that explicitly decouples the buyer side and seller side auction design while achieving (i) truthfulness, (ii) individual rationality, and (iii) budget balance. To accurately capture wireless interference and support spectrum reuse, we partition the conflict graph so that buyers with strong direct and indirect interference are put into the same subgraph and buyers with no or weak interference are put into separate subgraphs and then compute pricing independently within each subgraph. We develop a merge scheme to combine spectrum allocation results from different subgraphs and resolve potential conflicts. Using conflict graphs generated from real cell tower locations, we extensively evaluate our approach and demonstrate that it achieves high efficiency, revenue, and utilization.

**H. Zhou, R. A. Berry, M. L. Honig and R. Vohra** Proceedings of the 3rd IEEE International Workshop on Smart Data Pricing, 2014

Opening “prime” spectrum to unlicensed usage can lower the costs for offering wide area wireless services but may also lead to greater congestion due to multiple providers operating in the same band. To mitigate congestion, service providers may invest in more infrastructure or better technology. The costs of such investments must be weighed against the potential gains in revenue, which in turn will depend on the investments of other competing providers in the shared spectrum. This paper studies such trade-offs for multiple competing providers in a common unlicensed band. We extend models from earlier work on price competition with congestible resources to include the investment decisions of service providers using a common band of spectrum. Several models are considered to capture different ways investment might impact the congestion due to both a provider's own customers and those of other providers. For each model, we study a game in which providers decide on both the level of investment and the price of their service. Interestingly, in most cases, the equilibrium of the resulting game is shown to be that only a single provider invests and charges monopoly prices. On the other hand, multiple providers may enter the market when the dominant effect of investment is to reduce congestion due to the customers of other providers.

**D. Yang, X. Zhang and G. Xue** Proceedings of IEEE INFOCOM, 2014

Auctions provide a platform for licensed spectrum users to trade their underutilized spectrum with unlicensed users. Existing spectrum auctions either do not apply to the scenarios where multiple sellers and buyers both make offers, or assume the knowledge of the users' valuation distribution for maximizing the profit of the auction. To fill this void, we design PROMISE, a framework for spectrum double auctions, which jointly considers spectrum reusability, truthfulness, and profit maximization without the distribution knowledge. We propose a novel technique, called cross extraction, to compute the bid representing a group of secondary users, who can share a common channel. We prove that PROMISE is computationally efficient, individual-rational, and truthful. In addition, PROMISE is guaranteed to achieve an approximate profit of the optimal auction.

**Y. Yi, J. Zhang, Q. Zhang and T. Jiang** Proceedings of IEEE INFOCOM, 2012

The concept of femtocell that operates in licensed spectrum to provide home coverage has attracted interest in the wireless industry due to high spatial reuse, and extensive deployments of femtocells is expected in the future. In this paper, we consider the scenario that a femtocell service provider (FSP) expects to rent spectrum from the coexisting macrocell service provider (MSP) to serve its end users. In addition to the spectrum leasing payment, the FSP may allow hybrid access of macrocell users to improve the utilities of itself and MSP, which are defined as the sum of data traffic and payment/revenue. We propose the spectrum leasing framework taking hybrid access into consideration. The whole procedure is modeled as a three-stage Stackelberg game, where MSP and FSP determine the spectrum leasing ratio, spectrum leasing price and open access ratio sequentially to maximize their utilities, and the existence of the Nash Equilibrium of the sequential game is analyzed. We characterize the equilibrium, in terms of access price, spectrum acquisition of FSP, the open access ratio, and price of anarchy via simulation. Numerical results show that both MSP and FSP can benefit from spectrum leasing, and hybrid access of femtocell can further improve their utilities, which provide sufficient incentive for their cooperation.

Two-sided pricing (15) |

QoS-aware pricing (14) |