hysim: a hybrid spectrum and information market for tv white...

HySIM: A Hybrid Spectrum and Information Marketfor TV White Space Networks

Yuan Luo, Lin Gao, and Jianwei Huang

Abstract—We propose a hybrid spectrum and informationmarket for database-assisted TV white space networks, where ageo-location white space database serves as the platform for boththe spectrum market and the information market. We study theinteractions among the database operator, the spectrum licensee,and unlicensed users systematically, using a three-layer hierar-chical model. In Layer I, the licensee negotiates with the databaseregarding the commission fee of using the spectrum marketplatform. In Layer II, the database and the licensee competefor selling information or channels to unlicensed users. In LayerIII, unlicensed users determine whether to buy the exclusiveusage right of licensed channels from the licensee, or to buy theinformation regarding unlicensed channels from the database.Analyzing such a three-layer model is challenging, due to the co-existence of both positive and negative network externalities inthe information market. We characterize the market equilibriumsystematically, and analyze how the network externalities affectthe equilibrium behaviours of all parties involved. Our numericalresults show that the proposed hybrid market can improve thenetwork profit more than 80%, compared with a pure informationmarket. Meanwhile, the achieved network profit is very close tothe coordinated benchmark (e.g., the gap is less than 4%).

I. INTRODUCTION

A. Background

With the explosive growth of mobile smartphones andbandwidth-hungry wireless applications, radio spectrum hasbecome increasingly scarce and congested [1]. The UHF/VHFfrequency band originally assigned for broadcast televisionservices (hereafter called TV channels) has been viewed asa high potential spectrum band for supporting new wirelessbroadband services. First, in some places especially rural areas,TV channels may not be fully allocated (licensed) to TVlicensees. That is, some TV channels may be unlicensed toany TV licensee. These vacant (unlicensed) channels are oftenreferred to as TV white spaces [2], [3], and can be potentiallyused for supporting non-TV wireless services. Second, eventhe licensed TV channels (i.e., those licensed to some TVlicensees) may be under a low utilization at some time [4], andhence can be opportunistically reused by unlicensed non-TVwireless services with the permissions of licensees.

To effectively exploit the (unlicensed) TV white spaceswhile not harming the interests of licensed devices (of TVlicensees), some spectrum regulators (such as FCC in the USA[5] and Ofcom in the UK [6]) have proposed a database-assisted TV white space network architecture, and the industryhas started to adopt such an architecture [7]–[9]. Specifically,in this database-assisted architecture, unlicensed devices obtainthe list of available TV white spaces via querying a certified

This work is supported by the General Research Funds (Project NumberCUHK 412713 and CUHK 14202814) established under the University GrantCommittee of the Hong Kong Special Administrative Region, China.

The authors are with Dept. of Information Engineering, The Chinese Uni-versity of Hong Kong, HK, Email: {ly011, lgao, jwhuang}@ie.cuhk.edu.hk.

white space database called geo-location. To achieve this, thegeo-location database needs to house and periodically updateda repository of TV licensees (e.g., their network infrastructuresand channel occupancies). Before using any TV white spaces,unlicensed devices first report their location information to thedatabase, and then database computes and returns the availableTV white space list. According to the current policies of FCCand Ofcom, these unlicensed TV white spaces must be used ina licensed-exempt (shared) manner [5], [6]. Hence, interferencemanagement is an important issue when multiple unlicensedusers sharing the same TV white space.

Moreover, spectrum regulators in many counties (includ-ing FCC in the USA) also allows the spectrum licenseesto temporarily lease their licensed channels to unlicenseddevices [10]. Note that an unlicensed device can use theleased channels exclusively, depending on the agreement withthe associated spectrum licensee. Such a secondary spectrumleasing (trading) requires a market platform connecting thebuyers (unlicensed users) and sellers (spectrum licensees). Thegeo-location database can potentially serve as such a platform(see, e.g., SpecEx [11]) due to its proximity to both spectrumlicensees and unlicensed devices. Based on the above, the geo-location database can facilitate the unlicensed access to bothunlicensed and licensed TV channels.

B. Motivation

In this work, we study the business modelling for adatabase-assisted TV white space network, with both unli-censed TV white spaces and licensed TV channels. Recently,researchers have proposed several business and marketingmodels related to the database-assisted TV channel sharing,which can be categorized into two classes: Spectrum Market[12]–[14]) and Information Market [15], [16].

The spectrum market model mainly deals with the tradingof licensed TV channels between spectrum licensees andunlicensed users [12]–[14].1 The key idea is to let spectrumlicensees temporarily lease their under-utilized channels tounlicensed users for additional revenue. The database servesas a market platform facilitating this trading process.2 A com-mercial example of such a database-provided spectrum marketplatform is SpecEx [11], operated by Spectrum Bridge.

The information market model has been recently proposedand analyzed in [15], [16], for the unlicensed TV channels(i.e., TV white spaces) sharing. In their models, the geo-location database sells the advanced information regarding the

1The (secondary) spectrum market has been extensively used in dynamicspectrum access networks (see, e.g., [18]–[22]), where auction, contract, andpricing are commonly used in theoretic models. The auction and contractmodels usually focus on the information asymmetry. In this work, we mainlyfocus on the interplay between the spectrum market and information market.Hence, we will consider the basic pricing model for the spectrum market.

2For example, it may act as a spectrum broker or agent, purchasing spectrumfrom licensees and then reselling the purchased spectrum to unlicensed users.

2015 IEEE Conference on Computer Communications (INFOCOM)

978-1-4799-8381-0/15/$31.00 ©2015 IEEE 900

Information MarketInformation Market

Database Provided Platform

Spectrum Market

Licensee

Basic Info.

Database

Unlicensed UsersUser 1

User 2 User 3 User 4

Advanced Info.

Licensed TV ChannelBusy (Fully-Utilized)

Licensed TV ChanneIdle (Under-Utilized)

Unlicensed TV Channel(TV White Space)

Fig. 1. Database-Provided Hybrid Spectrum and Informaiton Market.

quality of TV white spaces to the unlicensed users for profit.The key motivation of such an information market model isthat the database knows more information regarding TV whitespaces than unlicensed users,3 which can be potentially used byunlicensed users for improving their performances. A practicalexample of information market is White Space Plus [17], againoperated by Spectrum Bridge.

In the above studies, researches studied the spectrummarket (for licensed TV channels) and information market (forunlicensed TV white spaces) separately. In practice, however,the licensed TV channels and unlicensed TV white spacesoften co-exist at the same location. Some users may preferto lease the licensed TV channels for the exclusive usage,while other users may prefer to share the free unlicensedTV white spaces with others. Hence, a joint study of bothspectrum market and information market is highly desirable.This motivates our study of a hybrid spectrum and informationmarket for database-assisted TV white space networks.

C. Contributions

In this paper, we model and study a Hybrid Spectrumand Information Market (HySIM) for a database-assisted TVwhite space network, in which the geo-location databaseserves as (i) a spectrum market platform, for trading (under-utilized) licensed TV channels between spectrum licensees andunlicensed users, and (ii) an information market platform, fortrading advanced information (regarding the unlicensed TVwhite spaces) between the database itself and unlicensed users.Unlicensed users can choose to lease the licensed TV channelsfrom licensees (via the database) for the exclusive usage, or toshare the free TV white spaces with others. In the latter case,users can further decide whether to purchase the advancedinformation regarding these TV white spaces from the databaseto enhance the performance.

Figure 1 illustrates such a database-provided HySIMframework, where user 1 and user 2 lease the licensed TVchannels from the spectrum licensee (via the database-providedplatform), and user 3 and user 4 share the free unlicensedTV white spaces with others. User 4 further purchases theadvanced information to improve its performance.

3For example, based on the knowledge about the network infrastructuresof TV licensees and their channel occupancies, the database can predict theaverage interference (from licensed devices) on each channel at each location.

In order to thoroughly understand the user behavior insuch a hybrid market as well as the market evolution andequilibrium, we formulate the interactions among the geo-location database (operator), the spectrum licensee, and un-licensed users as a three-layer hierarchical model:

1) Layer I: Commission Negotiation (in Section V): In thefirst layer, the database and the spectrum licensee negotiateon the commission fee that the spectrum licensee needs topay for using the spectrum market platform. Specifically, thedatabase, as the market platform, helps the spectrum licenseeto display, advertise, and sell the under-utilized TV channelsto unlicensed users. Accordingly, it takes some commissionfee from each successful transaction between the spectrumlicensee and unlicensed users. In this work, we consider therevenue sharing commission scheme, where the spectrum li-censee shares a fixed percentage of revenue with the database.4We study the commission negotiation (for the revenue sharingpercentage) using the Nash bargaining theory [23].

2) Layer II: Price Competition Game (in Section IV):In the second layer, the database and the spectrum licenseecompete with each other for selling information or channelsto unlicensed users. The spectrum licensee decides the priceof the licensed TV channels, and the database decides theprice of the advanced information (regarding the unlicensedTV channels). Hence, the interplay of both prices forms aprice competition game with heterogeneous items. We analyzethe equilibrium of such a price competition game using thesupermodular game theory [24].

3) Layer III: User Behavior and Market Dynamics (inSection III): In the third layer, unlicensed users decide theirbest purchasing decisions, given the database’s informationprice and the spectrum licensee’s channel price. Note that auser’s best purchasing behaviour changes with other users’ pur-chasing behaviours, due to the negative and positive networkexternalities of the information market (see Section II-C fordetails). We will show how the market dynamically evolvesalong the user purchasing behaviour dynamics, and what isthe market equilibrium point it evolves to.

In summary, we list the main contributions as follows.

• Novelty and Practical Significance: To the best of ourknowledge, this is the first paper that studies a hy-brid spectrum and information market, for promotingthe unlicensed spectrum access to both licensed andunlicensed TV channels.

• Modeling and Solution Techniques: We formulate theinteractions as a three-layer hierarchical model, andanalyze the model by backward induction, using mar-ket equilibrium theory, supermodular game theory, andNash bargaining theory.

• Performance Evaluations: Numerical results show thatthe proposed hybrid market can improve network prof-it more than 80%, compared with a pure informationmarket. The gap between our achieved network profitand the coordinated benchmark is less than 4%.

4Another widely-used commission scheme is the wholesale pricing scheme,where the database charges the spectrum licensee a fixed price for eachsuccessful transaction, regardless of the spectrum licensee’s actual revenue.We will study this commission scheme in our future work.


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II. SYSTEM MODEL

We consider a database-assisted TV white space networkwith a geo-location database and a set of unlicensed users(devices) in a particular region (e.g., a city). Unlicensed userscan use the unlicensed TV channels (i.e., TV white spaces) ina shared manner (e.g., using CDMA or CSMA). Meanwhile,there is a spectrum licensee, who owns the licensed channelsand wants to lease the under-utilized channels to unlicensedusers for additional revenue.5 Different from the unlicensedTV white spaces, the licensed TV channels can be used byunlicensed users in an exclusive manner (with the permissionof the licensee). Therefore, users can enjoy a better perfor-mance (e.g., a higher data rate or a lower interference) onthe licensed channels. For convenience, let πL ≥ 0 denote the(licensed) channel price set by the spectrum licensee.

A. Geo-location Database

1) Basic Service: According to the regulation policy (e.g.,[5]), it is mandatory for a geo-location white space database toprovide the following information for any unlicensed user: (i)the list of TV white spaces (i.e., unlicensed TV channels), and(ii) the transmission constraint (e.g., maximum transmissionpower) on each channel in the list. The database needs toprovide this basic (information) service free of charge for anyunlicensed user.

2) Advanced Service: Beyond the basic information, thedatabase can also provide certain advanced information re-garding the quality of TV channels (as Spectrum Bridge did in[17]), which we call the advanced (information) service. Suchan advanced information can be rather general, and a typicalexample is “the interference level on each channel” used in[15], [16]. With the advanced information, the user is able tochoose a channel with the highest quality (e.g., with the lowestinterference level). Hence, the database can sell this advancedinformation to users for a profit. This leads to an informationmarket. For convenience, let πA ≥ 0 denote the (advanced)information price of the database.

3) Leasing Service: As mentioned previously, the geo-location database can also serve as a spectrum market platformfor trading licensed channels between the spectrum licenseeand unlicensed users, which we call the leasing service. Bydoing this, the spectrum licensee shares a fixed percentageδ ∈ [0, 1] of revenue with the database, which we call therevenue share commission scheme (RSS).

B. Unlicensed User

Unlicensed users can choose either to purchase the licensedchannel from the licensee for the exclusive usage, or to sharethe free unlicensed TV white spaces with others (with orwithout advanced information). We assume that all licensedand unlicensed TV channels have the same bandwidth (e.g.,6MHz in the USA), and each user only needs one channel(either licensed or unlicensed) at a particular time. Formally,we denote s ∈ {b,a, l} as the strategy of a user, where

(i) s = b: Choose the basic service (i.e., share TV whitespaces with others, without the advanced information);

5In case there are multiple spectrum licensees, we assume that they arecoordinated by the single entity. We will leave the case with multiplecompetitive spectrum licensees to a future work.

(ii) s = a: Choose the advanced service (i.e., share TVwhite spaces with others, with the advanced information).

(iii) s = l: Choose the leasing service (i.e., lease thelicensed channel from the licensee for an exclusive usage).

We further denote B, A, and L as the expected utility thata user can achieve from choosing the basic service (s = b),the advanced service (s = a), and the leasing service (s = l),respectively. The payoff of a user is defined as the differencebetween the achieved utility and the service cost (i.e., theinformation price when choosing the advanced service, or theleasing price if choosing the leasing service). Let θ denotethe user’s evaluation for the achieved utility. Then, the payoffof a user with an evaluation parameter θ can be written as

ΠEUθ =

θ ·B, if s = b,θ ·A− πA, if s = a,θ · L− πL, if s = l.

(1)

Each user is rational and will choose a strategy s ∈ {b,a, l}that maximizes its payoff. Note that different users may havedifferent values of θ (e.g., depending on application types),hence have different choices. That is, users are heterogeneousin term of θ. For convenience, we assume that θ is uniformlydistributed in [0, 1] for all users6.

Let ηB, ηA, and ηL denote the fraction of users choosingthe basic service, the advanced service, and the leasing service,respectively. For convenience, we refer to ηB, ηA, and ηL as themarket shares of the basic service, the advanced service, andthe leasing service, respectively. Obviously, ηB, ηA, ηL ≥ 0 andηB +ηA +ηL = 1. Then, the normalized payoffs (profits) of thespectrum licensee and the database are, respectively,{

ΠSL , ΠSL(I) = πL · ηL · (1− δ),

ΠDB , ΠDB(I) = πA · ηA + πL · ηL · δ.

(2)

C. Externalities of the Information Market

There are two types of network externalities coexistingin the information market: (i) negative externality, whichcharacterizes the increase of congestion (or the decrease ofuser performance) when more users sharing the same TVwhite space, and (ii) positive externality, which characterizesthe increase of advanced information accuracy (or the increaseof user performance) when more users purchasing the infor-mation. Next we quantify such negative and positive networkexternalities analytically.

We first have the following intuitive observations for auser’s expected utilities of three strategy choices:• L is a constant and independent of ηA, ηB, and ηL. This

is because a user uses the licensed channels in an exclusivemanner, hence its performance (on licensed channels) does notdepend on the activities of others.• B is non-increasing in ηA + ηB (the total fraction of

users using TV white space) due to the congestion effect. Thisis because more users using TV white spaces (in a sharedmanner) will increase the level of congestion on these channel,hence reduce the performance of each user.

6This assumption is commonly used in the existing literature. Relaxing tomore general distributions often does not change the main insights [25], [26].


902

• A is non-increasing in ηA + ηB, due to the congestioneffect (similar as that of B). This leads to the negative networkexternality of the information market.

• A is non-decreasing in ηA, given a fixed value ofηA + ηB. This is because more users purchasing the advancedinformation will increase the quality of the information [15],[16]. This leads to the positive network externality.

Based on the above observations, we write B as a non-increasing function f(·) of ηA + ηB (or equivalently, 1− ηL),

B , f(ηA + ηB),

and write A as the combination of a non-increasing functionf(·) of ηA + ηB and a non-decreasing function g(·) of ηA,

A , f(ηA + ηB) + g(ηA).

Note that f(·) reflects the congestion effect in the informationmarekt, and is identical in B and A (as users experience thesame congestion effect in both basic and advanced services),and g(·) reflects the performance gain induced by the advancedinformation, i.e., the value of advanced information.

Without loss of generality, we introduce the followingassumption.

Assumption 1. L ≥ A ≥ B.

The reason behind L ≥ A is that there is no congestion onthe licensed channels, and the reason behind A ≥ B is thatusers can achieve additional gain g(ηA) from the advancedinformation. Note that if A < B, then users will never choosethe advanced service even with a zero information price πA.In this case, our model degenerates to a monopoly spectrummarket (where the spectrum licensee is the monopolist). If L <B, then users will never choose the leasing service even witha zero channel price πL. In this case, our model degenerates tothe pure information market as in [15]. In this sense, our hybridmarket model generalizes both the pure spectrum market andpure information market.

To facilitate the later analysis, we further introduce thefollowing assumptions on functions f(·) and g(·).

Assumption 2. f(·) is non-negative, non-increasing, convex,and continuously differentiable.

Assumption 3. g(·) is non-negative, non-decreasing, concave,and continuously differentiable.

The non-increasing and convexity assumption of f(·)reflects the increasing of marginal performance degradationunder congestion, and is widely used in wireless networks withcongestion effect (see, e.g., [26], [27] and references therein).The non-decreasing and concavity assumption of g(·) reflectsthe diminishing of marginal performance improvement inducedby the advanced information. In this work, we use the genericfunctions f(·) and g(·), which can generalize many practical s-cenarios with the explicit advanced information definition (e.g.,those defined in [15], [16], where the advanced informationis the interference level on each channel). We provide moredetailed discussions about these generic functions and practicalscenarios in our online technical report [29].

Layer I: Commission NegotiationThe database and the spectrum licensee negotiate the commissioncharge details (i.e., the revenue sharing percentage δ).

⇓Layer II: Price Competition GameThe database determines the information price πA;The spectrum licensee determines the channel price πL .

⇓Layer III: User Behaving and Market DynamicsThe unlicensed users determine and update their best choices;The market dynamically evolves to the equilibrium point.

Fig. 2. Three-layer Hierarchical Interaction Model

D. Three-Layer Interaction Model

Based on the above discussion, a hybrid spectrum andinformation market involves the interactions among the geo-location database, the spectrum licensee, and the unlicensedusers. We formulate the interactions as a three-layer hierarchi-cal model illustrated in Figure 2.

Specifically, in Layer I, the database and the spectrumlicensee negotiate on the commission charge (regarding thespectrum market platform), i.e., the revenue sharing factorδ ∈ [0, 1]. In Layer II, the database and the spectrum licenseecompete with each other to attract unlicensed users. Thedatabase determines the price πA of the advanced information,and the spectrum licensee determines the price πL of thelicensed channel. In Layer III, the unlicensed users determinetheir best purchasing strategies, and dynamically update theirstrategies based on the current market shares. Accordingly, themarket dynamically evolves to the equilibrium.

In the following sections, we will analyze this three-layerinteraction model systematically using backward induction.

III. LAYER III – USER BEHAVIOR AND MARKETEQUILIBRIUM

In this section, we study the user behavior and marketdynamics in Layer III, given the database’s information priceπA and the licensee’s channel price πL (in Layer II). We firstdiscuss the user’s best choice, and then show how the marketdynamically evolve to an equilibrium point.

A. User’s Best Strategy

Now we study the best strategy of users, given the prices{πL, πA} and the initial market state {η0

L , η0A, η

0B} where η0

B +η0

A + η0L = 1. Notice that each user will choose a strategy that

maximizes its payoff defined in (1). Hence, for a type-θ user,its best strategy is 7

s∗θ = l, iff θ · L− πL > max{θ ·A− πA, θ ·B}s∗θ = a, iff θ ·A− πA > max{θ · L− πL, θ ·B}s∗θ = b, iff θ ·B > max{θ · L− πL, θ ·A− πA}

(3)

where B = f(1− η0L ), and A = f(1− η0

L ) + g(η0A).

To better illustrate the above best strategy, we introducethe following notations:

θLB , πL

L−B , θAB , πA

A−B , θLA , πL−πA

L−A .

7Here, “iff” stands for “if and only if”. Note that we omit the case ofθ ·L−πL = max{θ ·A−πA, θ ·B}, θ ·A−πA = max{θ ·L−πL, θ ·B},and θ ·B = max{θ ·L−πL, θ ·A−πA}, which are negligible (i.e., occurringwith zero probability) due to the continuous distribution of θ.


903

0 1

0 1

��

LB AB� ��

LB AB� ��LA�

LA�

LB�

LB�AB�

AB�

��

��

��

Fig. 3. Illustration of θLB , θAB , and θLA .

Intuitively, θLB denotes the smallest θ such that a type-θuser prefers the leasing service than the basic service; θABdenotes the smallest θ such that a type-θ user prefers theadvanced service than the basic service; and θLA denotes thesmallest θ such that a type-θ user prefers the leasing servicethan the advanced service. Notice that A and B are functionsof initial market shares {η0

L , η0A, η

0B}. Hence, θLB, θAB, and θLA

are also functions of {η0L , η

0A, η

0B}.

Figure 3 illustrates the relationship of θLB, θAB, and θLA.Intuitively, the users with a high utility evaluation factor θ aremore willing to choose the leasing service in order to achieve alarge utility; the users with a low θ are more willing to choosethe basic service so that they will pay zero service cost; theusers with a middle θ are more willing to choose the advancedservice, in order to achieve a relatively large utility with arelatively low service cost. Notice that when the informationprice πA is high or the information value (i.e., A−B) is low,we could have θLB < θAB, in which no users will choose theadvanced service (as illustrated in the lower subfigure).

Next we characterize the new market shares (called thederived market shares) resulting from the users’ best choicesmentioned above. Such derived market shares are important foranalyzing the user behavior dynamics and market evolutionsin the next subsection. Recall that θ is uniformly distributedin [0, 1]. Then, given any initial market shares {η0

L , η0A}, the

newly derived market shares {ηL, ηA} are• If θLB > θAB, then ηL = 1− θLA and ηA = θLA − θAB;• If θLB ≤ θAB, then ηL = 1− θLB and ηA = 0.

Formally, we have the following derived market shares.8

Lemma 1. Given any initial market shares η0L and η0

A, thederived market shares ηL and ηA are given by{

ηL = max{

1−max{θLA, θLB}, 0},

ηA = max{

min{θLA, 1} − θAB, 0}.

(4)

The results in Lemma 1 assume that all users update thebest strategies once and simultaneously. Since θLB, θAB, andθLA are functions of initial market shares {η0

L , η0A}, the derived

market shares {ηL, ηA} are also functions of {η0L , η

0A}, and

hence can be written as ηL(η0L , η

0A) and ηA(η0

L , η0A).

B. Market Dynamics and Market Equilibrium

When the market shares change, the users’ payoffs (on theadvanced service and basic service) change accordingly, as Aand B change. As a result, users will update their best strate-gies continuously, hence the market shares will evolve dynam-ically, until reaching a stable point (called market equilibrium).In this subsection, we will study such a market dynamics andequilibrium, given the prices {πL, πA}.

8Due to space limit, we put the detailed proof in [29].

For convenience, we introduce a virtual discrete-time sys-tem with slots t = 1, 2, . . ., where users change their decisionsat the beginning of every slot, based on the derived marketshares in the previous slot. Let (ηtL, η

tA) denote the market

shares derived at the end of slot t (which serve as the initialmarket shares in the next slot t + 1). We further denote 4ηL

and 4ηA as the changes (dynamics) of market shares betweentwo successive time slots, e.g., t and t+ 1, that is,

4ηL(ηtL, ηtA) = ηt+1

L − ηtL,4ηA(ηtL, η

tA) = ηt+1

A − ηtA,(5)

where (ηt+1L , ηt+1

A ) are the derived market share in slot t+ 1,which can be computed by Lemma 1. Obviously, if both 4ηL

and4ηA are zero in a slot t+1, i.e., ηt+1L = ηtL and ηt+1

A = ηtA,then users will no longer change their strategies in the future.This implies that the market achieves a stable state, which wecall the market equilibrium. Formally,

Definition 1 (Market Equilibrium). A pair of market sharesη∗ = {η∗L , η∗A} is a market equilibrium of Layer III, if

4ηL(η∗L , η∗A) = 0, and 4ηA(η∗L , η

∗A) = 0. (6)

Next, we study the existence and uniqueness of the marketequilibrium, and further characterize the market equilibriumanalytically. These results are important for analyzing the pricecompetition game in Layer II (Section IV).

Lemma 2 (Existence). Given any feasible price pair (πL, πA),there exists at least one market equilibrium.

Lemma 3 (Uniqueness). Given any feasible price pair(πL, πA), there exists a unique market equilibrium (η∗L , η

∗A),

if there exists a tuple (ηL, ηA) with ηL + ηA ≤ 1 such that 9

g′(ηA)g(ηA) ·

L−BL−A ≤ 1. (7)

As an example, if the information value g(ηA) (reflectingthe positive network externality) does not increase very fastwith ηA, then (7) is satisfied and there exists a unique equilib-rium. Note that condition (7) is sufficient but not necessary forthe uniqueness. In particular, we observe through numericalsimulations that in some cases, the market converges to aunique equilibrium for a wide range of prices under whichthe condition (7) is not satisfied. Nevertheless, the sufficientcondition (7) leads to the insight that if the change of positivenetwork externality is dramatic in ηA, there may exist multipleequilibrium points. Note that even if there exist multipleequilibrium points, the market always converges to a uniqueone of them given the initial market shares, as here we considerdeterministic market dynamics.

For a better understanding, we illustrate the dynamics ofmarket shares in Figure 4. The x-axis denotes the leasingservice’s market share ηL, and the y-axis denotes the advancedservice’s market share ηA. Notice that a feasible pair of marketshares {ηL, ηA} satisfies ηL + ηA ≤ 1. Each grey arrowdenotes the dynamics of market shares under a particular initialmarket share (at the starting point of the arrow). For example,from the initial market shares η0 = {ηL, ηA} = {0.6, 0},the market will evolve to η1 = {0.32, 0.16}, and then

9Here, g′(ηA) is the first-order derivative of g(·) with respect to ηA . Notethat A is a function of ηA and ηL , and B is a function of ηL .


904

ηL

η A

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1ΔηL(ηL, ηA) = 0

ΔηA(ηL, ηA) = 0

η0η1

η∗

η2

Fig. 4. Illustration of Market Dynamics and Market Equilibrium. Red Curve:4ηL(ηL, ηA) = 0; Blue Curve: 4ηA(ηL, ηA) = 0. The intersection betweenblue and red curve is the market equilibrium.

η2 = {0.35, 0.2}, and eventually converge to the equilibriumpoint η∗ = {0.33, 0.24}. The red curve denotes the isoline of4ηL(ηL, ηA) = 0, and the blue curve denotes the isoline of4ηA(ηL, ηA) = 0. By Definition 1, the intersection betweenblue and red curves is the market equilibrium point. In thisexample, there is a unique market equilibrium point.

Suppose the uniqueness condition (7) is satisfied. Wecharacterize the unique equilibrium by the following theorem.

Theorem 1 (Market Equilibrium). Suppose the uniquenesscondition (7) holds. For any feasible price pair (πL, πA), theunique market equilibrium is given by

(a) If θLB(ηL, ηA)|ηL=0 ≤ θAB(ηL, ηA)|ηA=0, then there is aunique market equilibrium η† = {η†L , η†A} satisfying

η†L = 1− θLB(η†L , η†A), and η†A = 0; (8)

(b) If θLB(ηL, ηA)|ηL=0 > θAB(ηL, ηA)|ηA=0, then there is aunique market equilibrium η∗ = {η∗L , η∗A} satisfying{

η∗L = 1− θLA(η∗L , η∗A),

η∗A = θLA(η∗L , η∗A)− θAB(η∗L , η

∗A).

(9)

Intuitively, we can obtain the derived market shares bysubstituting (8) or (9) into (4). Then, we can check the abovederived market shares satisfy the equilibrium condition (6).Please refer to [29] for the detailed proof.

IV. LAYER II – PRICE COMPETITION GAMEEQUILIBRIUM

In this section, we study the price competition betweenthe database and the spectrum licensee in Layer II, given thecommission negotiation solution in Layer I and based on themarket equilibrium prediction in Layer III.

A. Price Competition Game

We first define the price competition game (PCG) and theassociated Nash equilibrium explicitly.

Definition 2 (Price Competition Game – PCG).• Players: The database and the spectrum licensee;

• Strategies: The database’s strategy is the nonnegativeinformation price πA, and the spectrum licensee’s strategy isthe nonnegative channel price πL;• Payoffs: The players’ payoffs are defined in (2).

For clarity, we write the (unique) market equilibriumη∗ = {η∗L , η∗A} in Layer III as functions of prices (πL, πA), i.e.,η∗L (πL, πA) and η∗A(πL, πA). Intuitively, we can interpret η∗L (·)and η∗A(·) as the demand functions of the spectrum licenseeand the database, respectively. Based on (2), the payoffs ofthe spectrum licensee and the database can be written as:{

ΠSL(I)(πL, πA) = πL · η∗L (πL, πA) · (1− δ),

ΠDB(I) (πL, πA) = πA · η∗A(πL, πA) + πL · η∗L (πL, πA) · δ. (10)

We refer to the Nash equilibrium of the PCG as PricingEquilibrium. Formally,

Definition 3 (Pricing Equilibrium). A pair of prices (π∗L , π∗A)

is a pricing equilibrium of Layer II, ifπ∗L = arg max

πL≥0ΠSL

(I)(πL, π∗A),

π∗A = arg maxπA≥0

ΠDB(I) (π

∗L , πA).

(11)

Note that directly solving the pricing equilibrium ofPCG is challenging, due to the difficulty in obtainingthe closed-form characterization of the market equilibrium{η∗L (πL, πA), η∗A(πL, πA)} under a particular price pair {πL, πA}.To this end, we transform the original price competition gameinto an equivalent demand competition game. The key idea isto view the achieved market shares (i.e., demands) as strategiesof the database and the spectrum licensee, and view the pricesas functions of market shares.

B. Demand Competition Game

We notice that under the uniqueness condition (7), there isa one-to-one correspondence between the market equilibrium{η∗L , η∗A} and the prices {πL, πA} in Layer III. In this sense,once the spectrum licensee and the database choose the prices{πL, πA}, they have equivalently chosen the respective marketshares {η∗L , η∗A}.

Hence, we can define an equivalent demand competitiongame, where the strategy of each player is its demand or marketshare (ηL for the spectrum licensee and ηA for the database),and the prices {πL, πA} are functions of market shares {ηL, ηA}.Substitute θLA = πL−πA

L−A and θAB = πA

A−B into (9), we canderive the inverse functions of (9), i.e., the prices as functionsof market shares,10

πL(ηL, ηA) =(1− ηL) · (L− f(1− ηL)− g(ηA))

+ (1− ηL − ηA) · g(ηL),

πA(ηL, ηA) =(1− ηL − ηA) · g(ηA).

(12)

Accordingly, the payoffs of two players can be written as:{Π̃SL

(I)(ηL, ηA) = πL(ηL, ηA) · ηL · (1− δ),Π̃DB

(I) (ηL, ηA) = πA(ηL, ηA) · ηL + πL(ηL, ηA) · ηL · δ.(13)

10We omit the trivial case in (8), where the database has a zero marketshare, as this will never the case at the pricing equilibrium of Layer II.


905

Next, we formally define the demand competition game(DCG) and the associated Nash equilibrium.

Definition 4 (Demand Competition Game – DCG).• Players: The database and the spectrum licensee;• Strategies: The database’s strategy is its market share ηA,

and the spectrum licensee’s strategy is its market share ηL;• Payoffs: The players’ payoffs are defined in (13).

Similarly, we refer to the Nash equilibrium of the DCG asthe Demanding Equilibrium. Formally,

Definition 5 (Demanding Equilibrium). A pair of marketshares (η∗L , η

∗A) is a demanding equilibrium, if

η∗L = arg maxηL

Π̃SL(I)(ηL, η

∗A),

η∗A = arg maxηA

Π̃DB(I) (η

∗L , ηA).

(14)

The following lemma shows the equivalence between theoriginal PCG and the above DCG.

Lemma 4 (Equivalence). If {η∗L , η∗A} is a demanding equi-librium of DCG, then {π∗L , π∗A} given by (12) is a pricingequilibrium of the original PCG.

C. Game Equilibrium

Due to equivalence of PCG and DCG, we focus onfinding the demanding equilibrium of DCG in the following.Specifically, we show that the DCG is a supermodular game(with minor strategy transformation), and hence the demandingequilibrium of DCG can be easily obtained by using thesupermodular game theory [24].

Lemma 5 (Existence of Demanding Equilibrium). The DCGis a supermodular game with respect to ηA and −ηL. Hence,there exists at least one demanding equilibrium.

The following lemma further gives the uniqueness condi-tion for the demanding equilibrium of DCG.

Lemma 6 (Uniqueness of Demanding Equilibrium). The DCGhas a unique demanding equilibrium (η∗L , η

∗A), if

−∂2Π̃SL

(I)(ηL,ηA)

∂(−ηL)2 ≥ ∂2Π̃SL

(I)(ηL,ηA)

∂(−ηL)∂ηAand − ∂2Π̃DB

(I) (ηL,ηA)

∂(−ηL)2 ≥ ∂2Π̃DB

(I) (ηL,ηA)

∂ηA∂(−ηL).

The above uniqueness conditions are quite general, andfollow the standard supermodular game theory. Next, weprovide a special example to illustrate these conditions moreintuitively. Consider the following example: f(ηA + ηB) =α1−β1·(ηA+ηB) and g(ηA) = β2·ηA. That is, both positive andnegative network effects change linearly with the respectivemarket shares. By Lemma 6, we can easily obtain the followinguniqueness condition: L−α1−β1 > β2. Namely, if L is largeenough or α1 (or β1, β2) is small enough, there is a uniquedemanding equilibrium.

Once we obtain the demanding equilibrium (η∗L , η∗A) of

DCG, we can immediately obtain the pricing equilibrium(π∗L , π

∗A) of the original PCG by (12). It is notable that we may

not be able to derive the closed-form expression of demandingequilibrium of DCG, as we do not assume any specific functionforms of f(·) and g(·). Nevertheless, thanks to the nice

property of supermodular game, we can easily compute thedemanding equilibrium of DCG through, for example, thesimple best response iteration (see [29] for details).

V. LAYER I – COMMISSION BARGAINING SOLUTION

In this section, we study the commission negotiation amongthe database and the spectrum licensee in Layer I, basedon their predictions of the pricing equilibrium in Layer IIand the market equilibrium in Layer III. The purpose of thisnegotiation is to find a feasible revenue sharing percentageδ ∈ [0, 1] that is satisfactory for both the database and thespectrum licensee. We formulate the commission negotiationproblem as a bargaining problem, and study the bargainingsolution by using the Nash bargaining theory [23].

Following the Nash bargaining framework [23], we firstderive the database’s and the spectrum licensee’s payoffs whenreaching an agreement and when not reaching any agreement(hence reaching the disagreement). Specifically, when reachingan agreement δ, their payoffs are ΠDB

(I) (δ) and ΠSL(I)(δ) derived

in Section IV, respectively. When not reaching any agreement(i.e., reaching the disagreement), the spectrum licensee’s profitis ΠSL

0 = 0, and the database’s profit is ΠDB0 = π†A · η†A(π†A),

where π†A and η†A(π†A) are the database’s optimal price and thecorresponding market share in the pure information market.11

Then, the Nash bargaining solution δ∗ is given by

maxδ∈[0,1]

(ΠDB

(I) (δ)−ΠSL0

)·(ΠSL

(I)(δ)−ΠDB0

)s. t. ΠDB

(I) (δ) ≥ ΠSL0 , ΠSL

(I)(δ) ≥ ΠDB0 .

(15)

Note that analytically solving (15) may be difficult, as itis hard to characterize the analytical forms of ΠDB

(I) (δ) andΠSL

(I)(δ). Nevertheless, we notice that the bargaining variableδ lies in a closed and bounded range [0, 1], and the objectivefunction of (15) is bounded. Hence, there must be an optimalsolution for (15), which can be easily found by using manyone-dimensional search methods provided in [28].

Theorem 2 (Bargaining Solution). There exists an optimalsolution for problem (15). In addition, if the objective functionof (15) is monotonic, the optimal solution is unique.

VI. NUMERICAL RESULTS

In this section, we perform numerical studies to illustratethe market solution (e.g., the bargaining solution in Layer I andthe pricing equilibrium in Layer II) and evaluate the systemperformance (e.g., the network profit, the database’s profit, andthe licensee’s profit) in our proposed framework.

1) Simulation Configurations: For an illustrative purpose,we characterize the negative and positive network externalities(of the information market) by the following functions:

f(ηA + ηB) = α1 − β1 · (ηA + ηB)γ1 , g(ηA) = β2 · ηAγ2 .

We can easily check that these two functions satisfy Assump-tion 2 and Assumption 3. Moreover, these functions are goodapproximations of the actual negative and positive networkexternalities, when the advanced information is defined as theinterference level on each channel as in [15], [16].

11Note that such an optimal price and market share can be derived in thesame way as in Section IV, by simply setting L < B.


906

5 6 7 80.52

0.54

0.58

0.62

0.66

0.7

Qal i ty of Leasing Service – L

RevenueSharin

gPercentage–δ

Strong PositiveStrong Negative

Fig. 5. Commission Bargaining Solution in Layer I

With the above setting, if all users choose the leasingservice (purchasing the licensed TV channels), i.e., ηL = 1and ηA = ηB = 0, then the utilities of choosing basic oradvanced service is B = A = α1; if all users choose theadvanced service (sharing the unlicensed TV white spaces withthe advanced information), i.e., ηA = 1 and ηL = ηB = 0),then the utilities of choosing basic and advanced services areB = α1 − β1 and A = α1 − β1 + β2, respectively.

To further characterize which externality dominates theinformation market, we derive the first-order derivative ofA = f(ηA + ηB) + g(ηA) with respect to ηA:

∂A

∂ηA= −γ1 · β1 · (ηA + ηB)γ1−1 + γ2 · β2 · (ηA)γ2−1.

If ∂A∂ηA

> 0, the utility of users purchasing the advance informa-tion increases with the percentage ηA of users purchasing theadvanced information (i.e., the size of the information market).In this case, we will say that the positive network externalityis dominant. On the other hand, if ∂A

∂ηA< 0, the utility of users

purchasing the advance information increases with ηA, and wewill say that the negative network externality is dominant.

For easy comparison, we set γ1 = γ2 and change thevalue of β1 and β2 to achieve different degrees of networkexternality. Specifically, we introduce λ = β1/β2 to representthe degree of network externality: (i) If λ < ( ηA

ηA+ηB)γ1−1, then

∂A∂ηA

> 0, hence the information market is positive externalitydominant; and (ii) If λ > ( ηA

ηA+ηB)γ1−1, then ∂A

∂ηA< 0,

hence the information market is negative externality dominant.Intuitively, a smaller (or larger) λ implies that the informationmarket is more likely to be positive (or negative) externalitydominant. In our simulations, we use the following parametersfor the above f and g: α1 = 3 and γ1 = γ2 = 0.6. We simulatetwo different scenarios: a strongly positive externality withλ = β1/β2 = 0.1/1 = 0.1, and a strongly negative externalitywith λ = β1/β2 = 2.8/1 = 2.8.

2) Commission Bargaining Solution: We first illustrate thecommission bargaining solution in Layer I.

Figure 5 shows the commission bargaining solution δ∗ vsL (the utility of using licensed channels) under both stronglypositive (red curve) and negative externalities (blue curve).We can see that the bargaining solution δ∗ decreases with Lunder both externality cases. This is because with a higher L,

5 6 7 80

0.6

1.2

1.8

2.4

3

3.6

Qal i ty of Leasing Service – L

LH

PriceEquilib

riu

m

5 6 7 80

0.1

0.2

0.3

0.4

0.5

0.6

DB

PriceEquilib

riu

m

5 6 7 80

0.1

0.2

0.3

0.4

0.5

0.6LH Strong PositiveDB Strong PositiveeLH Strong NegativeDB Strong Negative

Fig. 6. Equilibrium of Pricing Competition Game in Layer II

the licensee can potentially charge a higher channel price andachieve a higher profit. Hence, from the social perspective, it isbetter to drive more users to the spectrum market. In this case,the licensee has more bargaining advantage and is allowed toshare less revenue with the database.

From Figure 5, we can further see that the bargainingsolution δ∗ under the strongly negative externality is smallerthan that under the strongly positive externality. This is becausewhen the negative externality is dominant in the informationmarket, the increasing number of users will severely degradethe quality of unlicensed TV channels. Hence, from the socialperspective, it is better to drive more users to the spectrummarket. In this case, the licensee has more bargaining advan-tage and is allowed to share less revenue with the database.

3) Illustration of Pricing Equilibrium: We now illustratethe pricing equilibrium of the PCG in Layer II.

Figure 6 shows the pricing equilibrium vs L, under bothstrongly positive (red curves) and negative externalities (bluecurve). We can see that the equilibrium information price ofthe database (denoted by DB) slightly increases with L, whilethe equilibrium channel price of the licensee (denote by LH)significantly increases with L, under both externality cases.This is because a larger L can attract more users to purchasethe licensed channels, and thus allows the licensee to chargea higher channel price. Accordingly, the database can chargea slightly higher information price.

From Figure 6, we can also see that the equilibrium channelprice of the licensee under the strongly negative externality ishigher than that under the strongly positive externality, whilethe equilibrium information price of the database is just theopposite. This is because under the strongly negative external-ity, a small increase of users in the information market willdramatically decreases the quality of unlicensed TV channels.Hence, the spectrum licensee can potentially charge a higherchannel price as more users are willing to purchase the licensedchannels, while the database has to charge a lower informationprice to retain users.

4) System Performance: We now evaluate the networkprofit (i.e., the aggregate profit of the database and the licensee)in our proposed framework.12 For an illustrative purpose, we

12Due to space limit, we leave the evaluations of the database’s profit andthe spectrum licensee’s profit in the online technical report [29].


907

5 6 7 8 9 100

0.5

1

1.5

2

2.5

Qual i ty of Leasing Service – L

Netw

orkProfit

Coordination BenchmarkNon−cooperation BenchmarkThird−Party PlatformRSS

cooperationgain

non−coordinationloss

Fig. 7. Network Profit vs L.

choose an intermedia value for λ in this simulation: λ =β1/β2 = 0.8/1.2 = 0.67. This implies that the informationis neither strongly negative externality dominant, nor stronglypositive externality dominant. Note that the simulation resultsfor other values of λ are similar.

Figure 7 illustrates the network profits achieved in differentschemes. The red solid line (with the mark ◦) denotes thenetwork profit achieved in our proposed three-layer schemewith the revenue sharing commission bargaining (denoted byRSS). The black dash-dot line (with the mark +) denotesthe coordinated benchmark, where the database and the li-censee act as an integrated party to maximize their aggregateprofit. The red dash-dot line (with the mark ×) denotes thenoncooperative benchmark (with the information market only),where the database does not provide the spectrum marketplatform. The brown dash-dot line (with the mark •) denotesthe performance in such a scheme where the database does notprovide the spectrum market platform, but the licensee can sellchannels on a third-party spectrum market platform.

Figure 7 shows that our proposed scheme outperformsthe non-cooperative benchmark scheme (with the informa-tion market only) significantly (e.g., increasing the networkprofit up to 87%). It also shows that our proposed schemeoutperforms the third-party spectrum market platform (e.g.,increasing the network profit around 5%). This is becauseour adopted commission bargaining scheme can motivate thedatabase and licensee cooperate and alleviate the competitionbetween the database and licensee. Moreover, the networkprofit gap achieved in our proposed scheme and in the coordi-nated benchmark is quite small (e.g., less than 4%). Such a gapis caused by the imperfect coordination of the database and thespectrum licensee. In other words, they cooperate somewhat,but are not coordinated completely. We refer to such a networkprofit gap as the non-coordination loss.

VII. CONCLUSION

In this paper, we proposed a database-provided hybrid spec-trum and information market, and analyzed the interactionsamong the database, the licensee, and the unlicensed userssystematically. We also analyzed how the network externalities(of the information market) affect these interactions. Our work

not only captures the performance gain introduced by thehybrid market, but also characterizes the impact of positiveand negative network externalitites on the market equilibriumbehaviors of all parties involved. There are several possibledirections to extend this work. One is to consider an oligopolyscenario with multiple databases (hence multiple platforms). Inthis scenario, databases compete with each other for unlicensedusers as well as for spectrum licensees.

REFERENCES

[1] Cisco, “Cisco Visual Networking Index: Global Mobile Data TrafficForecast Update, 2013-2018”, White Paper, Feb 2014.

[2] FCC 10-174, Second Memorandum Opinion and Order, 2010.[3] OFCOM, “Implementing Geolocation”, Nov. 2010.[4] T.X. Brown12, E. Pietrosemoli, M. Zennaro, et al., “A Survey of TV

White Space Measurements,” Technical Report.[5] FCC 12-36, Third Memorandum Opinion and Order, 2012.[6] OFCOM, “A Consultation on White Space Device Requirements”, 2012.[7] Google White Space Database, http://www.google.org/spectrum/

whitespace/[8] SpectrumBridge TV White Space, http://www.spectrumbridge.com[9] Microsoft Reserach WhiteFiService, http://whitespaces.msresearch.us/[10] FCC 04-167, Second Report and Order, 2004.[11] SpectrumBridge SpecEx, http://www.spectrumbridge.com/

ProductsServices/search.aspx[12] H. Bogucka, et al., “Secondary Spectrum Trading in TV White Spaces”,

IEEE Communication Magazine, 50(11) 121-129, 2012.[13] X. Feng, J. Zhang, and J. Zhang, “Hybrid Pricing for TV White Space

Database”, IEEE INFOCOM, 2013.[14] Y. Luo, L. Gao, and J. Huang, “Price and Inventory Competition in

Oligopoly TV White Space Markets,” IEEE Journal on Selected Areasin Communications, 2014.

[15] Y. Luo, L. Gao, and J. Huang, “Trade Information, Not Spectrum: ANovel TV White Space Information Market Model”, IEEE WiOpt, 2014.

[16] Y. Luo, L. Gao, and J. Huang, “Information Market for TV WhiteSpace”, IEEE INFOCOM Workshop on Smart Data Pricing, 2014.

[17] SpectrumBridge White Space Plus, http://www.spectrumbridge.com/ProductsServices/WhiteSpacesSolutions/OperatorsUsers.aspx

[18] J. Huang, R.A. Berry, and M.L. Honig, “Auction-based spectrumsharing,” Mobile Networks and Applications, 2006.

[19] X. Zhou, et al. , “eBay in the Sky: Strategy-Proof Wireless SpectrumAuctions”, ACM MobiCom, Sept. 2008.

[20] X. Zhou and H. Zheng, “TRUST: A General Framework for TruthfulDouble Spectrum Auctions”, IEEE INFOCOM, April. 2009.

[21] L. Gao, X. Wang, Y. Xu, and Q. Zhang, “Spectrum Trading inCognitive Radio Networks: A Contract-Theoretic Modeling Approach,”IEEE Journal on Selected Areas in Communications, 2011.

[22] L. Gao, Y. Xu, and X. Wang, “MAP: Multi-Auctioneer ProgressiveAuction for Dynamic Spectrum Access,” IEEE Transactions on MobileComputing, 2011.

[23] J. Harsanyi, Rational Behavior and Bargaining Equilibrium in Gamesand Social Situations, Cambridge Univ. Press, 1977.

[24] D. M. Topkis, Supermodularity and Complementarity, Princeton Univ.Press, 1998.

[25] M. Manshaei, et al., “On Wireless Social Community Networks”, IEEEINFOCOM, Apr. 2008.

[26] N. Shetty, G. Schwartz, and J. Walrand, “Internet QoS and Regulations”,IEEE Trans. Networking, vol. 17, no. 6, pp. 1725-1737, Dec. 2010.

[27] R. Johari, G. Y. Weintraub, and B. Van Roy, “Investment and MarketStructure in Industries with Congestion”, Operations Research, 58(5)1303-1317, Sept. 2010.

[28] N. Nisan, Algorithmic Game Theory, Cambridge Univ. Press, 2007.[29] Y. Luo, L. Gao, and J. Huang, “HySIM: A Hybrid Spectrum and

Information Market for TV White Space Networks,” Online TechnicalReport, url: https://arxiv.org/abs/1501.02478


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