HySIM: A Hybrid Spectrum and Information Market for TV White Space Networks

1.6 MB·English

by  Yuan Luo

HySIM: A Hybrid Spectrum and Information Market
for TV White Space Networks
Yuan Luo, Lin Gao, and Jianwei Huang
Abstract— We propose a hybrid spectrum and information [11]) due to its proximity to both spectrum licensees and
market for a database-assisted TV white space network, where unlicensed devices. This means that the geo-location database
the geo-location database serves as both a spectrum market canfacilitatetheunlicensedspectrumaccesstobothunlicensed
platformandaninformationmarketplatform.Westudytheinter- and licensed TV channels.
actions among the database operator, the spectrum licensee, and
unlicensed users systematically, using a three-layer hierarchical Recently, researchers have proposed several business and
model. In Layer I, the database and the licensee negotiate the marketing models related to the database-assisted spectrum
6 commission fee that the licensee pays for using the spectrum sharing, which can be categorized into two classes: Spectrum
1 market platform. In Layer II, the database and the licensee Market and Information Market. The first class (spectrum
0 compete for selling information or channels to unlicensed users.
market[12]–[14])mainlydealswiththetradingoflicensedTV
2 InLayerIII,unlicensedusersdeterminewhethertheyshouldbuy
channels.Thekeyideaistoletspectrumlicenseestemporarily
theexclusiveusagerightoflicensedchannelsfromthelicensee,or
b lease their under-utilized licensed TV channels to unlicensed
theinformationregardingunlicensedchannelsfromthedatabase.
e
F Analyzing such a three-layer model is challenging due to the users for some additional revenue. The database serves as a
co-existence of both positive and negative network externalities market platform facilitating this trading process.1 A commer-

4 in the information market. We characterize how the network cial example of such a database-provided spectrum market
2 externalities affect the equilibrium behaviours of all parties platform is SpecEx [11], operated by SpectrumBridge.2
involved. Our numerical results show that the proposed hybrid

] marketcanimprovethenetworkprofitupto87%,comparedwith The second class (information market) has been recently
T a pure information market. Meanwhile, the achieved network introduced by Luo et al. for the unlicensed TV channels
G profit is very close to the coordinated benchmark solution (the (i.e., TV white spaces) [15], [16]. In their models, the geo-
. gap is less than 4% in our simulation). location database sells the advanced information regarding the
s
quality of unlicensed TV channels, instead of channels, to
c
[ I. INTRODUCTION the unlicensed users for profit. The key motivation is that the
database knows more information regarding TV white spaces
2 A. Background than unlicensed users,3 and hence it can provide information
v
With the explosive growth of mobile smartphones and that helps unlicensed users improve their performances. A
8
bandwidth-hunger wireless applications, radio spectrum has practical example of information market is White Space Plus
7
4 becomeincreasinglyscarce[1].TheUHF/VHFfrequencyband [17], again operated by SpectrumBridge.
2 originally assigned for broadcast television services (hereafter
In practice, both the licensed TV channels and unlicensed
0 calledTVchannels)hasbeenviewedasapromisingspectrum
TV white spaces co-exist at a particular location. Some users
. opportunity for supporting new wireless broadband services.
1 may prefer to lease the licensed TV channels from licensees
First, in many places there are many vacant (unused) TV
0 for the exclusive usage, while other users may prefer to share
5 channels (i.e., those unlicensed to any TV licensee), often
the free unlicensed TV white spaces with others. Hence, a
1 called TV white spaces [2]–[4], which can be used for sup-
joint formulation and optimization of both spectrum market
: portingunlicensednon-TVwirelessservices.Second,eventhe
v and information market is highly desirable. However, none of
licensed TV channels (i.e., allocated to certain TV licensee)
i the existing work [12]–[16] looked at the interaction between
X may be under a low utilization in most time [5], and hence
spectrum market and information market. This motivates our
canbeopportunisticallyreusedbyunlicensednon-TVwireless
r study of a hybrid spectrum and information market for the
a services with the permissions of licensees.
database in TV white space networks.
ToeffectivelyexploittheTVwhitespaceswhilenotharm-
ing the interests of licensed devices (TVs), the industry has
B. Contributions
started to adopt a database-assisted TV white space network
architecture [6]–[9]. In this architecture, unlicensed devices In this paper, we model and study a Hybrid Spectrum
obtainthelistofavailableunlicensedTVchannelsviaquerying and Information Market (HySIM) for a database-assisted TV
a certified white space geo-location database, which periodi-
cally updates information based on a repository of licensees. 1For example, it acts as a spectrum broker or agent, purchases spectrum
Meanwhile, the FCC also allows the spectrum licensees to fromlicenseesandthenresellsthepurchasedspectrumtounlicensedusers.
temporarilyleasetheirlicensedchannelstounlicenseddevices 2The (secondary) spectrum market has been extensively used in dynamic
spectrumaccessnetworks(see,e.g.,[18]–[22]),whereauction,contract,and
through, for example, auction [10]. Such spectrum trading
pricingarecommonlyusedtheoreticmodels.Theauctionandcontractmodels
(leasing) requires a market platform, and the geo-location
usuallyfocusontheinformationasymmetry.Inthiswork,wemainlyfocuson
databasecanpotentiallyserveassuchaplatform(e.g.,SpecEx the interplay between the spectrum market and information. Hence, we will
considerthebasicpricingmodelforthespectrummarket.
Thisworkissupportedby... 3Forexample,basedontheknowledgeaboutthenetworkinfrastructuresof
TheauthorsarewithDept.ofInformationEngineering,TheChineseUni- TVlicenseesandtheirlicensedchannels,thedatabasecanpredicttheaverage
versityofHongKong,HK,Email:{ly011,lgao,jwhuang}@ie.cuhk.edu.hk. interference(fromlicenseddevices)oneachTVchannelateachlocation.
2
Licensed TV Channel Licensed TV Channe Unlicensed TV Channel thelicensedTVchannels,andthedatabasedecidesthepriceof
Busy (Fully-Utilized) Idle (Under-Utilized) (TV White Space)
the advanced information (regarding the unlicensed TV chan-
nels). We analyze the equilibrium of such a price competition
Spectrum Market IInnffoorrmmaattiioonn MMaarrkkeett
game using the supermodular game theory [24].
Licensee Database
3)Layer III: User Behaving and Market Dynamics (in
Basic Info. Advanced Info. Section III): In the third layer, unlicensed users decide the
best purchasing decisions, given the database’s information
priceandthelicensee’schannelprice.Notethattheusers’best
Database Provided Platform purchasingbehavioursdynamicallychangeduetothenegative
and positive network externalities of the information market
(see Section II-C for details). We will show how the market
User 1 User 2 User 3 User 4 dynamically evolves according to the users’ best choices, and
Unlicensed Users what the market equilibrium point is.
In summary, we list the main contributions as follows.
Fig.1. Database-ProvidedHybridSpectrumandInformaitonMarket.
• Novelty and Practical Significance: To the best of
whitespacenetwork,inwhichthegeo-locationdatabaseserves our knowledge, this is the first paper that proposes
as (i) a spectrum market platform for the trading of (under- andstudiesahybridspectrumandinformationmarket
utilized)licensedTVchannelsbetweenspectrumlicenseesand for promoting the unlicensed spectrum access to both
unlicensed users, and (ii) an information market platform for licensed and unlicensed TV channels.
the trading of advanced information (regarding the unlicensed
• Modeling and Solution Techniques: We formulate the
TV white spaces) between the database itself and unlicensed
interactions as a three-layer hierarchical model, and
users. Unlicensed users can choose to lease the licensed TV
analyze the model by backward induction, using mar-
channels from licensees (via the database) for the exclusive
ketequilibriumtheory,supermodulargametheory,and
usage,ortosharethefreeTVwhitespaceswithothers.Inthe
Nash bargaining theory, respectively.
latter case, users can further decide whether to purchase the
advanced information regarding these TV white spaces from • PerformanceEvaluations:Ournumericalresultsshow
the database to enhance the performance. that the proposed hybrid market can bring up to 87%
networkprofitgain,comparedwithapureinformation
Figure 1 illustrates such a database-provided HySIM
market. The gap between our achieved network profit
framework. Unlicensed users 1 and 2 lease the licensed TV
and the coordinated benchmark is less than 4%.
channelsfromthespectrumlicensee(viathedatabase-provided
platform),andusers3and4sharethefreeunlicensedTVwhite
II. SYSTEMMODEL
spaces with others. User 4 further purchases the advanced
information to improve its performance. We consider a database-assisted TV white space network
with a geo-location database and a set of unlicensed users
In order to thoroughly understand the user behaving, the
(devices) in a particular region (e.g., a city). Unlicensed users
market evolving, and the equilibrium in such a hybrid market,
can use the unlicensed TV channels (i.e., TV white spaces)
weformulatetheinteractionsamongthegeo-locationdatabase
freely in a shared manner (e.g., using CDMA or CSMA).
(operator), the spectrum licensee, and unlicensed users as a
Meanwhile, there is a spectrum licensee, who owns the li-
three-layer hierarchical model:
censedchannelsandwantstoleasetheunder-utilizedchannels
1)Layer I: Commission Negotiation (in Section V): In to unlicensed users for additional revenue.5 Different from the
the first layer, the database and the licensee negotiate the unlicensed TV white spaces, the licensed TV channels can
commission fee that the spectrum licensee needs to pay for be used by unlicensed users in an exclusive manner (with the
usingthespectrummarketplatform.Specifically,thedatabase, permissionofthelicensee).Therefore,userscanenjoyabetter
as the spectrum market platform, helps the spectrum licensee performance (e.g., a higher data rate or a lower interference)
to display, advertise, and sell the under-utilized TV channels on the licensed channels. For convenience, let π ≥ 0 denote
L
to unlicensed users. Accordingly, it takes some commission the (licensed) channel price set by the spectrum licensee.
fee from each successful transaction between the spectrum li-
censeeandunlicensedusers.Inthiswork,weconsidertherev- A. Geo-location Database
enue sharing scheme (RSS), where the licensee shares a fixed
1)Basic Service: According to the regulation policy (e.g.,
percentage of revenue with the database,4 and study the RSS
[4]), it is mandatory for a geo-location white space database
negotiationusingtheNashbargainingtheory[23].
to provide the following information for any unlicensed user:
2)Layer II: Price Competition Game (in Section IV): (i) the list of TV white spaces (i.e., unlicensed TV channels),
In the second layer, the database and the spectrum licensee (ii) the transmission constraint (e.g., maximum transmission
compete with each other for selling information or channels power) on each channel in the list, and (iii) other optional
tounlicensedusers.Thespectrumlicenseedecidesthepriceof requirements. The database needs to provide this basic (infor-
mation) service free of charge for any unlicensed user.
4Another commonly-used commission scheme is the so-called wholesale
pricingscheme(WPS),wherethedatabasechargesthelicenseeafixedprice 5In case there are multiple spectrum licensees, we assume that they are
foreachsuccessfultransaction,regardlessoftheexactrevenueofthelicensee. coordinatedbythesinglerepresentative.Wewillleavethecasewithmultiple
WewillstudytheproblemunderWPSinourfuturework. competitivespectrumlicenseestoafuturework.
3
2)Advanced Service: Beyond the basic information, the respectively.Forconvenience,werefertoη ,η ,andη asthe
B A L
database can also provide certain advanced information re- market shares of the basic service, the advanced service, and
garding the quality of TV channels (as SpectrumBridge did the leasing service, respectively. Obviously, η ,η ,η ≥0 and
B A L
in [17]), which we call the advanced (information) service, as η +η +η =1.Then,thenormalizedpayoffs(profits)ofthe
B A L
long as it does not conflict with the free basic service. Such spectrum licensee and the database are, respectively,
an advanced information can be rather general, and a typical (cid:40) ΠSL (cid:44)ΠSL =π η (1−δ),
example is “the interference level on each channel” used in (I) L L (2)
[15], [16]. With the advanced information, the user is able to ΠDB (cid:44)ΠD(IB) =πAηA+πLηLδ.
chooseachannelwiththehighestquality(e.g.,withthelowest
interference level). Hence, the database can sell this advanced C. Positive and Negative Network Externalities
information to users for profit. This leads to an information
There are two types of network externalities coexisting in
market. For convenience, let π ≥ 0 denote the (advanced)
A the information market: (i) negative externality, which corre-
information price of the database.
sponds to the increasing level of congestion and degradation
3)Leasing Service: As mentioned previously, the geo- of user performance due to more users sharing the same
locationdatabasecanalsoserveasaspectrummarketplatform TV white space, and (ii) positive externality, which is due
for the trading of licensed channels between the spectrum to the quality increase of the (advanced) information when
licensee and unlicensed users, which we call the leasing more users purchasing the information. Next we analytically
service. By doing this, the spectrum licensee shares a fixed quantify these two network externalities.
percentage δ ∈ [0,1] of revenue with the database, which we
We first have the following intuitive observations for a
called the revenue share commission scheme (RSS).
user’s expected utilities of three strategy choices:
B. Unlicensed User • L is a constant and independent of ηA, ηB, and ηL. This
is because a user uses the licensed channels in an exclusive
Unlicenseduserscanchooseeithertopurchasethelicensed manner,henceitsperformance(onlicensedchannels)doesnot
channel from the licensee for the exclusive usage, or to share depend on the activities of others.
the free unlicensed TV white spaces with others (with or
• B is non-increasing in η + η (the total fraction of
without advanced information). We assume that all licensed A B
usersusingTVwhitespace)duetothecongestioneffect.This
and unlicensed TV channels have the same bandwidth (e.g.,
is because more users using TV white spaces (in a shared
6MHz in the USA), and each user only needs one channel
manner)willincreasethelevelofcongestiononthesechannel,
(either licensed or unlicensed) at a particular time. Formally,
hence reduce the performance of each user.
we denote s∈{b,a,l} as the strategy of a user, where
• A is non-increasing in η +η , due to the congestion
(i) s = b: Choose the basic service (i.e., share TV white A B
effect (similar as B). This is referred to as the negative
spaces with others, without the advanced information);
network externality of the information market.
(ii) s = a: Choose the advanced service (i.e., share TV
• A is non-decreasing in η , given a fixed value of
white spaces with others, with the advanced information). A
η +η . This is because more users purchasing the advanced
A B
(iii) s = l: Choose the leasing service (i.e., lease the information will increase the quality of the information. This
licensed channel from the licensee for the exclusive usage). is referred to as the positive network externality.
We further denote B, A, and L as the expected utility that For convenience, we write B as a non-increasing function
a user can achieve from choosing the basic service (s = b), f(·) of η +η (or equivalently, 1−η ), i.e.,
A B L
the advanced service (s=a), and the leasing service (s=l),
B (cid:44)f(η +η ),
respectively. The payoff of a user is defined as the difference A B
between the achieved utility and the service cost (i.e., the and write A as the combination of a non-increasing function
information price when choosing the advanced service, or the f(·) of η +η and a non-decreasing function g(·) of η , i.e.,
A B A
leasing price if choosing the leasing service). Let θ denote A(cid:44)f(η +η )+g(η ).
the user’s evaluation for the achieved utility. Then, the payoff A B A
Note that f(·) reflects the congestion effect in the information
of a user with an evaluation factor θ can be written as
θ·B, if s=b, marekt, and is identical in B and A (as users experience the
 same congestion effect in both basic and advanced services),
ΠEU = θ·A−π , if s=a, (1)
θ A andg(·)reflectstheperformancegaininducedbytheadvanced
θ·L−π , if s=l. information, i.e., the value of advanced information.
L
Each user is rational and will choose a strategy s ∈ {b,a,l}
Since there is no congestion on the licensed channels, it is
that maximizes its payoff. Note that different users may have
reasonable to assume that L>A and L>B. We can further
different values of θ (e.g., depending on application types),
assume that A > B, that is, the additional gain g(η ) from
hence have different choices. That is, users are heterogeneous the advanced information is positive.7 To facilitate tAhe later
in term of θ. For convenience, we assume that θ is uniformly
distributed in [0,1] for all users6. 7NotethatifweassumeL<B,thenuserswillneverchoosetheleasing
serviceevenwithazerochannelpriceπ .Inthiscase,ourmodeldegenerates
Let η , η , and η denote the fraction of users choosing L
B A L tothepureinformationmarket,similarasthatin[15].Moreover,ifA=B,
thebasicservice,theadvancedservice,andtheleasingservice, thenuserswillneverchoosetheadvancedserviceevenwithazeroinformation
priceπ .Inthiscase,ourmodeldegeneratestoamonopolyspectrummarket
A
6Thisassumptioniscommonlyusedintheexistingliterature.Relaxingto (wherethelicenseeisthemonopolist).Inthissense,ourhybridmarketmodel
moregeneraldistributionsoftendoesnotchangethemaininsights[25],[26]. generalizesboththepurespectrummarketandpureinformationmarket.
4
LayerI:CommissionNegotiation Basic service Advanced service Leasing
Thedatabaseandthespectrumlicenseenegotiatethecommission θ >θ
chargedetails(i.e.,δ underRSS). LB AB 0 θ θ θ 1
AB LB LA
⇓ Basic service Leasing
LayerII:PriceCompetitionGame θ <θ
LB AB
ThedatabasedeterminestheinformationpriceπA; 0 θLA θLB θAB 1
Thespectrumlicenseedeterminesthechannelpriceπ .
⇓ L Fig.3. IllustrationofθLB,θAB,andθLA.
LayerIII:UserBehavingandMarketDynamics
the user behavior dynamically evolves, and how the market
Theunlicensedusersdetermineandupdatetheirbestchoices;
Themarketdynamicallyevolvestotheequilibriumpoint. converges to an equilibrium point.
Fig.2. Three-layerHierarchicalInteractionModel
A. User’s Best Strategy
analysis, we further introduce the following assumptions on
Now we study the best strategy of users, given the prices
functions f(·) and g(·). {π ,π } and the initial market state {η0,η0,η0} where η0+
L A L A B B
Assumption 1. f(·) is non-negative, non-increasing, convex, η0+η0 =1. Notice that each user will choose a strategy that
A L
and continuously differentiable. maximizes its payoff defined in (1). Hence, for a type-θ user,
its best strategy is 8
Assumption2. g(·)isnon-negative,non-decreasing,concave,
 s =l, iff θ·L−π >max{θ·A−π , θ·B}
and continuously differentiable.  ∗θ L A
s =a, iff θ·A−π >max{θ·L−π , θ·B} (3)
∗θ A L
The non-increasing and convexity assumption of f(·) s =b, iff θ·B >max{θ·L−π , θ·A−π }
∗θ L A
reflects the increasing of marginal performance degradation
where B =f(1−η0), and A=f(1−η0)+g(η0).
undercongestion,andiswidelyusedinwirelessnetworkswith L L A
congestion effect (see, e.g., [26], [27] and references therein). To better illustrate the above best strategy, we introduce
The non-decreasing and concavity assumption of g(·) reflects the following notations:
thediminishingofmarginalperformanceimprovementinduced
by the advanced information. In this work, we use the generic θLB (cid:44) LπLB, θAB (cid:44) AπAB, θLA (cid:44) πLL−AπA.
− − −
functions f(·) and g(·), which can generalize many practical Intuitively, θ denotes the smallest θ such that a type-θ
LB
scenarios with the explicit advanced information definition user prefers the leasing service than the basic service; θ
AB
(e.g., those proposed by Luo et al. in [15], [16], where denotes the smallest θ such that a type-θ user prefers the
the advanced information is the interference level on each advanced service than the basic service; and θ denotes the
LA
channel). We provide more detailed discussion about generic smallest θ such that a type-θ user prefers the leasing service
functions and practical scenarios in the Appendix of [29]. than the advanced service. Notice that A and B are functions
ofinitialmarketshares{η0,η0,η0}.Hence,θ ,θ ,andθ
L A B LB AB LA
D. Three-Layer Interaction Model are also functions of {η0,η0,η0}.
L A B
Based on the above discussion, a hybrid spectrum and Figure 3 illustrates the relationship of θ , θ , and θ .
LB AB LA
information market involves the interactions among the geo- Intuitively, Figure 3 implies that the users with a high utility
location database, the spectrum licensee, and the unlicensed evaluation factor θ are more willing to choose the leasing
users. Hence, we formulate the interactions as a three-layer service in order to achieve a large utility. The users with a
hierarchical model illustrated in Figure 2. low utility evaluation factor θ are more willing to choose the
basicservicesothattheywillpayzeroservicecost.Theusers
Specifically, in Layer I, the database and the spectrum
with a middle utility evaluation factor θ are willing to choose
licensee negotiate the commission charge details (regarding
the advanced service, in order to achieve a relatively large
the spectrum market platform), i.e., the revenue sharing factor
utility with a relatively low service cost. Notice that when the
δ ∈[0,1]. In Layer II, the database and the spectrum licensee
information price π is high or the information value (i.e.,
compete with each other to attract unlicensed users. The A
A−B) is low, we could have θ < θ , in which no users
database determines the price π of the advanced information, LB AB
A will choose the advanced service (as illustrated in the lower
and the spectrum licensee determines the price π of the
L subfigure of Figure 3).
licensed channel. In Layer III, the unlicensed users determine
their best choices, and dynamically update their choices based Next we characterize the new market shares (called the
on the current market shares. Accordingly, the market dynam- derived market shares) resulting from the users’ best choices
ically involves and finally reaches the equilibrium point. mentionedabove.Suchderivedmarketsharesareimportantfor
analyzing the user behavior dynamics and market evolutions
In the following sections, we will analyze this three-layer
in the next subsection. Recall that θ is uniformly distributed
interaction model systematically using backward induction.
in [0,1]. Then, given any initial market shares {η0,η0}, the
L A
newly derived market shares {η ,η } are
III. LAYERIII–USERBEHAVIORANDMARKET L A
EQUILIBRIUM • Ifθ >θ ,thenη =1−θ andη =θ −θ ;
LB AB L LA A LA AB
In this section, we study the user behavior and market
8Here, “iff” stands for “if and only if”. Note that we omit the case of
dynamics in Layer III, given the database’s information price
θ·L−π =max{θ·A−π , θ·B},θ·A−π =max{θ·L−π , θ·B},
π and the licensee’s channel price π (in Layer II). In the L A A L
A L andθ·B=max{θ·L−πL,θ·A−πA},whicharenegligible(i.e.,occurring
following,wefirstdiscusstheuser’sbestchoice,andshowhow withzeroprobability)duetothecontinuousdistributionofθ.
5
• If θ ≤θ , then η =1−θ and η =0. 1
LB AB L LB A ∆ηL(ηL,ηA)=0
Formally, we have the following derived market shares. ∆ηA(ηL,ηA)=0
0.8
Lemma 1. Given any initial market shares η0 and η0, the
L A
derived market shares η and η are given by
L A 0.6
(cid:40) (cid:8) (cid:9)
ηL =max(cid:8)1−max{θLA,θLB}, 0(cid:9), (4) ηA
ηA =max min{θLA,1}−θAB, 0 . 0.4
The results in Lemma 1 assume that all users update the η∗
0.2 η2
best strategies once and simultaneously. Since θ , θ , and
LB AB η1
θmhLeanArckaeertecasfnuhnabrceetisown{rsiηtotLe,fnηiAna}istiaηalre(mηa0ar,lksηoe0t)fsuhannacrdetisηo{n(ηsηL00o,,fηηA00{})η,.L0th,ηeA0d}e,riavnedd 00 0.2 0.4 ηL 0.η60 0.8 1
L L A A L A
Fig.4. IllustrationofMarketDynamicsandMarketEquilibrium.RedCurve:
B. Market Dynamics and Equilibrium
(cid:52)η (η ,η )=0;BlueCurve:(cid:52)η (η ,η )=0.Theintersectionbetween
L L A A L A
blueandredcurveisthemarketequilibrium.
When the market shares change, the users’ payoffs (on the
very fast with η , then there exists a unique equilibrium.
advanced service and basic service) change accordingly, as A A
Note that the condition (7) is sufficient but not necessary for
and B change. As a result, users will update their best strate-
the uniqueness. In particular, we observe through numerical
giescontinuously,hencethemarketshareswillevolvedynam-
simulations that in some cases, the market converges to a
ically,untilreachingastablepoint(calledmarketequilibrium).
uniqueequilibriumforawiderangeofpricesunderwhichthe
In this subsection, we will study such a market dynamics and
condition (7) is violated. Nevertheless, the sufficient condition
equilibrium, given the prices {π ,π }.
L A in(7)leadstotheinsightthatiftheimpactofpositivenetwork
For convenience, we introduce a virtual time-discrete sys- externality is significant, there may exist multiple equilibrium
temwithslotst=1,2,...,whereuserschangetheirdecisions points.Notethatevenifthereexistmultipleequilibriumpoints,
at the beginning of every slot, based on the derived market the market always converges to a unique one of them, given
shares in the previous slot. Let (ηt,ηt) denote the market the initial market shares. Please refer to [29] for more details.
L A
shares derived at the end of slot t (which serve as the initial
For a better understanding, we illustrate the dynamics of
market shares in the next slot t+1). We further denote (cid:52)η
L market shares in Figure 4. The x-axis denotes the leasing
and (cid:52)η as the changes (dynamics) of market shares between
A service’smarketshare-η ,andthey-axisdenotestheadvanced
two successive time slots, e.g., t and t+1, that is, L
service’smarketshare-η .Noticethatafeasiblepairofmarket
(cid:52)ηL(ηLt,ηAt)=ηLt+1−ηLt, (cid:52)ηA(ηLt,ηAt) =ηAt+1−ηAt, (5) shares{ηL,ηA}satisfiesAηL+ηA ≤1.Anarrowdenotesthedy-
where (ηt+1,ηt+1) are the derived market share in slot t+1, namicsofmarketsharesunderaparticularinitialmarketshares
L A
which can be computed by Lemma 1. Obviously, if both (cid:52)η (atthestartingpointofthearrow).Forexample,fromtheinitial
tahnedn(cid:52)usηeArsarweizllernooinloangsleortcth+an1g,ei.et.h,eηirLt+s1tra=teηgLtieasnidnηtAth+e1fu=tuηrAteL., mtoaηrk1et=sh{a0re.3s2η,00.=16{}η,Lth=en0.η6,2η=A ={00.}3,5t,h0e.2m}a,raknedtwevilelnetvuoallvlye
This implies that the market achieves a stable state, which we converge to the equilibrium point η∗ ={0.33,0.24}. The red
call the market equilibrium. Formally, curve denotes the isoline of (cid:52)ηL(ηL,ηA) = 0, and the blue
curve denotes the isoline of (cid:52)η (η ,η ) = 0. By Definition
Definition 1 (Market Equilibrium). A pair of market shares A L A
1, the intersection between the blue curve and the red curve is
η∗ ={ηL∗,ηA∗} is a market equilibrium, if and only if themarketequilibriumpoint.Inthisexample,thereisaunique
(cid:52)η (η ,η )=0, and (cid:52)η (η ,η )=0. (6) market equilibrium point.
L L∗ A∗ A L∗ A∗
Suppose the uniqueness condition (7) is satisfied. We
Next,westudythe existenceanduniquenessofthemarket
characterize the unique equilibrium by the following theorem.
equilibrium, and further characterize the market equilibrium
analytically.Theseresultsareveryimportantforanalyzingthe Theorem 1 (Market Equilibrium). Suppose the uniqueness
price competition game in Layer II (Section IV). condition (7) holds. Then, for any feasible price pair (π ,π ),
L A
the unique market equilibrium is given by
Proposition 1 (Existence). Given any feasible price pair
(π ,π ), there exists at least one market equilibrium. (a) If θ (η ,η )| ≤ θ (η ,η )| , then there is
L A LB L A η =0 AB L A η =0
L A
Proposition 2 (Uniqueness). Given any feasible price pair a unique market equilibrium η† ={ηL†,ηA†} given by
(thπeLr,eπeAx)i,stthsearetuepxliests(ηa,uηni)quweitmhaηrk+etηequ≤ili1brsiuumch(tηhL∗a,t9ηA∗), if ηL† =1−θLB(ηL†,ηA†), and ηA† =0; (8)
L A L A
(b) If θ (η ,η )| > θ (η ,η )| , then there is
gg(cid:48)((ηηAA)) · LL−−BA ≤1. (7) a unLiBqueL(cid:26)maηArkeη=tL=e10q−uilθibAri(Buηm,Lηη∗A)=, η{Aη=L∗0,ηA∗} given by
A practical implication of (7) is that if the information L∗ LA L∗ A∗ (9)
η =θ (η ,η )−θ (η ,η ).
value g(ηA) (positive network externality) does not increase A∗ LA L∗ A∗ AB L∗ A∗
9Here,g(cid:48)(η )isthefirst-orderderivativeofg(·)withrespecttoη .Note Proof: First, we obtain the derived market shares by
A A
thatAisafunctionofη andη ,andB isafunctionofη . substituting the market shares given in (8) or (9) into (4).
A L L
6
Then, we can check the above derived market shares satisfy functions of market shares, i.e.,10
the equilibrium condition (6). For the detailed proof, please π (η ,η )=(1−η )·(L−f(1−η )−g(η ))
refer to [29].  L L A L L A
+(1−η −η )·g(η ), (12)
L A L
π (η ,η )=(1−η −η )·g(η ).
A L A L A A
IV. LAYERII–PRICECOMPETITIONGAME
Accordingly, the payoffs of two players can be written as:
EQUILIBRIUM
(cid:40)
Π(cid:101)SL(η ,η )=π (η ,η )·η ·(1−δ),
In this section, we study the price competition between (I) L A L L A L (13)
the database and the spectrum licensee in Layer II, given the Π(cid:101)D(IB)(ηL,ηA)=πA(ηL,ηA)·ηL+πL(ηL,ηA)·ηL·δ.
commission negotiation solution in Layer I and based on the Similarly, a pair of market shares (η ,η ) is called a Nash
L∗ A∗
marketequilibriumpredictioninLayerIII.Wewillanalyzethe equilibrium of MSCG, if η = argmax ΠSL(η ,η ) and
L∗ ηL (I) L A∗
gameequilibriumundertherevenuesharingscheme(RSS).We η =argmax ΠDB(η ,η ).
first define the price competition game (PCG) explicitly. A∗ ηA (I) L∗ A
We first show that the equivalence between the original
PCG and the above MSCG.
• Players: The database and the spectrum licensee;
Proposition3(Equivalence). If{η ,η }isaNashequilibrium
• Strategies: The database’s strategy is the price π of L∗ A∗
A of MSCG, then {π ,π } given by (12) is a Nash equilibrium
its advanced information, and the licensee’s strategy L∗ A∗
of the original price competition game PCG.
is the price π of its licensed channels;
L
• Payoffs: The payoffs of players are defined in (2) We next show that the MSCG is a supermodular game
under RSS. (withminorstrategytransformation),andthenderivetheNash
equilibrium using the supermodular game theory [24].
For convenience, we write the (unique) market equilibrium Proposition 4 (Existence). The MSCG is a supermodular
η∗ = {ηL∗,ηA∗} in Layer III as functions of prices (πL,πA), game with respect to ηA and −ηL. Hence, there exists at least
iη.e.(,·)ηaL∗n(πdLη,π(A·)) aansdthηeA∗(dπemL,aπnAd).fuInntcutiitoivneslyo,fwtheeclaicnenisneteerparnedt one Nash equilibrium (ηL∗,ηA∗).
L∗ A∗
the database, respectively.
The following proposition further gives the uniqueness
condition of the Nash equilibrium in MSCG.
Assume that the licensee shares a fixed percentage δ ∈
[0,1] of revenue with the database. Then, by (2), the payoffs Proposition 5 (Uniqueness). The MSCG has a unique Nash
of the licensee and the database can be written as: equilibrium (η ,η ), if
L∗ A∗
(cid:26)ΠΠD(S(IILB))((ππLL,,ππAA))==ππLA··ηηL∗A∗((ππLL,,ππAA))·+(1π−L·δη)L∗,(πL,πA)·δ. (10) −∂2∂Π(cid:101)(S(−IL)(ηηLL),2ηA) ≥ ∂∂2(Π(cid:101)−S(ILη)(Lη)L∂,ηηAA), − ∂2∂Π(cid:101)(D(−IB)(ηηLL),2ηA) ≥ ∂∂2ηΠ(cid:101)AD(∂IB)((−ηLη,ηL)A).
Definition 2 (Nash Equilibrium). A pair of prices (π ,π ) is The above uniqueness conditions are quite general, and
called a Nash equilibrium, if L∗ A∗ follow the standard supermodular game theory. Next we pro-
vide a specific example to illustrate these conditions more

ππL∗ ==aarrggmmπL≥aaxx0 ΠΠS(DILB)((ππL,,ππA∗)),. (11) αin1tu−itβiv1e·(lyη.A+CoηnBs)iadnedr gth(eηAf)o=lloβw2i·nηgA.eTxhaamtpisle,:bofth(ηpAo+sitiηvBe)an=d
 A∗ (I) L∗ A negative network effects change linearly with the respective
π 0
A≥ market shares. In this example, we can obtain the following
It is notable that directly solving the Nash equilibrium is uniqueness condition: L − α1 − β1 > β2. Namely, if L is
very challenging, due to the difficulty in analytically charac- large enough or β2 is small enough, there is a unique Nash
terizingthemarketequilibrium{η (π ,π ),η (π ,π )}under equilibrium in MSCG.
L∗ L A A∗ L A
athepaorrtiigciunlaalrpprriicceecpoamirpe{tiπtiLo,nπAg}a.mTeo(PthCiGs)einndt,owaneetqraunivsafolernmt weOcannceimwmeeodbiatateinlythoebtNaianshtheeqNuialisbhrieuqmuil(iηbL∗ri,uηmA∗)(oπf ,MπSC)Gof,
market share competition game (MSCG). The key idea is to theoriginalPCGby(12).ItisnotablethatwemaynoL∗tbeA∗able
view the market share as the strategy of the database or the toderivetheanalyticalNashequilibriumofMSCG,asweuse
licensee, and the prices as functions of the market shares. thegenericfunctionsf(·)andg(·).Nevertheless,thankstothe
nicepropertyofsupermodulargame,wecaneasilynumerically
Specifically, we notice that under the uniqueness condition
computetheNashequilibriumofMSCGthrough,forexample,
(7), there is a one-to-one correspondence between the market
the simple best response iteration in [29].
equilibrium {η ,η } and the prices {π ,π }.
L∗ A∗ L A
In this sense, once the licensee and the database choose V. LAYERI–COMMISSIONBARGAININGSOLUTION
the prices {π ,π }, they have equivalently chosen the market
L A Inthissection,westudythecommissionnegotiationamong
shares {η ,η }. Hence, we obtain the equivalent market share
L∗ A∗ the database and the spectrum licensee in Layer I, based on
competition game—MSCG, where the strategy of each player
their predictions of the price equilibrium in Layer II and the
is its market share (i.e., η for the licensee and η for the
L A market equilibrium in Layer III.
database), and the prices {π ,π } are functions of the market
L A
shares {ηL,ηA}. Substitute θLA = πLL−AπA and θAB = AπAB into 10We omit the trivial case in (8), where the database has a zero market
(9),wecanderivetheinversefunctio−nof(9),wherepr−icesare share,asthiswillneverthecaseatthepricingequilibriumofLayerII.
7
Specifically, we want to find a feasible revenue sharing service. Moreover, the wholesale price under strong negative
percentage δ ∈ [0,1] under RSS that is satisfactory for both networker externality is higher than that under strong positive
the database and the spectrum licensee. We formulate the network externality. This is because when the information
commission negotiation problem as a one-to-one bargaining, market is negative network externality, the increases number
and study the bargaining solution using the Nash bargaining of users will severely jeopardize the quality of unlicensed TV
theory [23]. channels.Hence,usersarewillingtochooselicensedchannels
in order to obtain guarantee quality of service. In such case,
Following the Nash bargaining framework, we first de-
the database wants to increase the wholesale price to maintain
rive the database’s and the licensee’s payoffs when reaching
its revenue.
an agreement and when not reaching any agreement (hence
reaching the disagreement). Specifically, when reaching an Figure 6 shows the equilibrium retail prices under the bar-
agreement δ, the database’s and the licensee’s payoffs are gaining solution. We can see that the equilibrium price of the
ΠDB(δ) and ΠSL(δ) derived in Section IV, respectively. When database (denoted by DB) is almost independent of L, while
(I) (I)
not reaching any agreement (reaching the disagreement), the the equilibrium price of the licensee (denote by LH) increases
licensee’s profit is ΠSL = 0, and the database’s profit is withL.Thisisbecauseahigherqualityofleasingservicewill
0
Π0DB = πA† ·ηA†(πA†), where πA† and ηA†(πA†) are the database’s attract more users to the licensed channels, and thus allows
optimal price and the corresponding market share in the pure the licensee to charge a higher service price. Moreover, the
information market.11 Then, the Nash bargaining solution is equilibrium price of licensee under strong negative network
formally given by externalityishigherthanthatunderstrongpositiveexternality.
(cid:0) (cid:1) (cid:0) (cid:1) This is because under strong negative network externality,
max ΠDB(δ)−ΠSL · ΠSL(δ)−ΠDB
(I) 0 (I) 0 the small increase of users in the information market will
δ [0,1] (14)
∈s. t. ΠDB(δ)≥ΠSL, ΠSL(δ)≥ΠDB. dramatically decreases the quality of unlicensed TV channels.
(I) 0 (I) 0 Hence, the licensee can charge a higher price due to more
Note that analytically solving (14) may be difficult, as it is users will choose leasing service.
hardtocharacterizetheanalyticalformsofΠDB(δ)andΠSL(δ).
(I) (I) 2)System Performance: Now we show the network
Nevertheless, we notice that the bargaining variable δ lies in
profit, i.e., the aggregate profit of the database and the li-
closed and bounded range of [0,1], and the objective function
censee achieved under both RSS in Figure 7 given the fixed
of(14)isbounded.Hence,theremustexistanoptimalsolution
network externality. In this figure, we use the black dash-dot
for (14), which can be found by using many one-dimensional
line (with mark +) to denote the coordination benchmark,
search methods (e.g., [28]).
where the database and the licensee act as an integrated party
Proposition 6 (δ-Bargaining Solution). There must exist an to maximize their aggregate profit. We use the red dash-dot
optimalsolution fortheproblem (14).Ifthe objectivefunction line (with mark ×) to denote the non-cooperation benchmark
of (14) is monotonic, the optimal solution is unique. (with pure information market only), where the database does
notwanttodisplaythelicensee’slicensedchannelinformation.
Thebrowndash-dotline(withmark•)denotesthecasewhere
VI. SIMULATIONRESULT
the licensee sells channels on a third-party spectrum market
In this section, we provide simulations to evaluate the platform.
system performance (e.g., the network profit, the database’s
Figure7showsthatourproposedRSSoutperformthenon-
profit,andthelicensee’sprofit)achievedunderrevenuesharing
cooperation scheme significantly (e.g., increasing the network
scheme (RSS).
profit up to 87%). It further shows that the gap between our
1)CommissionBargainingSolutionandEquilibriumRetail proposed RSS and coordination benchmark is small (e.g., less
Price: WefirstshowtheNashbargainingsolutionofRSS,and than 4%). Such a gap is caused by the imperfect coordination
the corresponding equilibrium retail prices. In this simulation: ofthedatabaseandthelicensee.Inotherwords,theycooperate
We choose the function f(ηL)=α1−β1·(1−ηL)γ1 to model somewhat but not coordinate completely. We call this gap as
the negative network externality, and choose the function g = the non-coordination loss. We can also see that our proposed
α2+(β2−α2)·ηAγ2 tomodelthepositivenetworkexternality. RSS always outperforms the scheme with a third-party plat-
We fix α1 = 1.8, α2 = 1, β1 = 0.8, β2 = 1.2, γ1 = 0.8, form, in terms of the network profit.
γ =0.6, and change the leasing service quality L from 6 to
2
10.
VII. CONCLUSION
Figure 5 shows the bargaining solution under different de-
In this paper, we proposed a database-provided hybrid
greeofnetworkexternality.Forfaircomparison,wetransform
spectrumandinformationmarket,andanalyzetheinteractions
the revenue sharing factor δ under RSS into the equivalent
∗
among the database, the licensee, and the unlicensed users
wholesale price by w = δ ·η . From this figure, we can
∗ ∗ L∗ systematically. We also analyze how the network externalities
see that the equivalent wholesale price increases with L under
(oftheinformationmarket)affecttheseinteractions.Ourwork
differentdegreeofnetworkexternality.Thisisbecauseahigher
not only captures the performance gain introduced by the
quality of leasing service attracts more users to the licensed
hybrid market, but also characterizes the impact of different
channels, and hence a higher wholesale price is desired to
degree of networker externality on the market equilibrium
compensate the database’s revenue loss from the advanced
behaviours of all parties involved. There are several possible
11Note that such an optimal price and market share can be derived in the directionstoextendthiswork.Oneistoconsideranoligopoly
samewayasinSectionIV,bysimplysettingL=0. scenariowithmultipledatabases(hencemultipleplatforms).In
8

Coordination Benchmark
Non−cooperation Benchmark
2.5 Third−Party Platform
WholesalePrice 1111....24682 SSttrroonngg PNoesgiatitvivee PriceEquilibrium123...8463 LDLDHHBB SSSSttttrrrroooonnnngggg PNPNoeoesgsgiiatatiitvtviiveveeee 00000000........34563456PriceEquilibrium fiNetworkProt1.512 RSS nlcgoooasnosin−pceoraotridoinnation
H1.2 00..22B
1 L D
0.5
0.8 0.6 00..11
0.65 Qa6lityofLeasingServ7ice–L 8 0555 Qa666lityofLeasingServ777ice–L 88800 05 6 Q7ualityo8fLeasin9gServic1e0–L
Fig. 5. Equivalent wholesale price vs L under Fig. 6. The database’s and the licensee’s retail Fig. 7. Network profit vs L under both revenue
strongpositivenetworkexternalityandstrongneg- price(whereLHdenotesLicenseeandDBdenotes sharing scheme (RSS) under fixed network exter-
ativenetworkexternality. database)vsLunderdiff.erentnetworkexternality nality.
thisscenario,databasescompetewitheachotherforunlicensed [25] M.Manshaei,etal.,“OnWirelessSocialCommunityNetworks”,IEEE
users as well as for spectrum licensees. INFOCOM,Apr.2008.
[26] N.Shetty,G.Schwartz,andJ.Walrand,“InternetQoSandRegulations”,
IEEETrans.Networking,vol.17,no.6,pp.1725-1737,Dec.2010.
REFERENCES
[27] R. Johari, G. Y. Weintraub, and B. Van Roy, “Investment and Market
[1] Cisco, “Cisco Visual Networking Index: Global Mobile Data Traffic Structure in Industries with Congestion”, Oper. Res., vol. 58, no. 5,
ForecastUpdate,2012-2017”,WhitePaper,Feb.2013 pp.1303-1317,Sept.2010.
[2] Microsoft,“CambridgeTVWhiteSpaceTrial”,Tech.Rep.,April.2012. [28] N.Nisan,AlgorithmicGameTheory,CambridgeUniv.Press,2007.
[3] OFCOM,“AConsultationonWhiteSpaceDeviceRequirements”,2012. [29] Online Technical Report, available at https://www.dropbox.com/s/
[4] FCC12-36,ThirdMemorandumOpinionandOrder,2012. 7gw10z5ahanlr2j/AppendixHySIM.pdf
[5] FCC10-174,SecondMemorandumOpinionandOrder,2010.
[6] Ofcom,“ImplementingGeolocation”,Nov.2010.
[7] GoogleSpectrumDatabase,http://www.google.org/spectrum/whitespace/
[8] Spectrum Bridge TV White Space, http://www.spectrumbridge.com/ APPENDIX
ProductsServices/WhiteSpacesSolutions/WhiteSpaceOverview.aspx
[9] MicrosoftReserachWhiteFiService,http://whitespaces.msresearch.us/
A. Property of Information Market
[10] FCC04-167,SecondReportandOrder,2004.
[11] Spectrum Bridge SpecEx, http://www.spectrumbridge.com/
In this section, we will discuss the properties of two types
ProductsServices/search.aspx
ofnetworkexternalitiesintheinformationmarket:thenegative
[12] H.Bogucka,etal.,“SecondarySpectrumTradinginTVWhiteSpaces”,
IEEECommun.Mag.,vol.50,no.11,pp.121-129,Nov.2012. network externality and the positive network externality. For
illustrationpurpose,weexplicitdefinetheadvanceinformation
[13] X.Feng,J.Zhang,andJ.Zhang,“HybridPricingforTVWhiteSpace
Database”,IEEEINFOCOM,2013. asthoseproposedbyLuoetal.in[15],[16].Inthefollowing,
[14] S.Liu,etal.,“LocationPrivacyPreservingDynamicSpectrumAuction we first define the advanced information as the interference
inCognitiveRadioNetwork”,IEEEICECS,July.2013. level on each channel, then we characterize the information
[15] Y. Luo, L. Gao, and J. Huang, “Trade Information, Not Spectrum: A value to the users. Based on that, we can further characterize
NovelTVWhiteSpaceInformationMarketModel”,IEEEWiOpt,2014. the properties of the information market.
[16] Y. Luo, L. Gao, and J. Huang, “Information Market for TV White
Space”,IEEEINFOCOMWorkshoponSmartDataPricing,2014.
1)Interference Information: For each user n ∈ N oper-
[17] Spectrum Bridge White Space Plus, http://www.spectrumbridge.com/
ating on the TV channel, each channel k is associated with
ProductsServices/WhiteSpacesSolutions/OperatorsUsers.aspx
an interference level, denoted by z , which reflects the
[18] J. Huang, R.A. Berry, and M.L. Honig, “Auction-based spectrum n,k
aggregateinterferencefromallothernearbydevices(including
sharing,”MobileNetworksandApplications,2006.
TV stations and other users) operating on this channel. Due
[19] X. Zhou, et al. , “eBay in the Sky: Strategy-Proof Wireless Spectrum
Auctions”,IEEEMobicom,Sept.2008. to the fast changing of wireless channels and the uncertainty
[20] X. Zhou and H. Zheng, “TRUST: A General Framework for Truthful of users’ mobilities and activities, the interference zn,k is a
DoubleSpectrumAuctions”,IEEEINFOCOM,April.2009. random variable. We impose assumptions on the interference
[21] L. Gao, X. Wang, Y. Xu, and Q. Zhang, “Spectrum Trading in zn,k as follows.
CognitiveRadioNetworks:AContract-TheoreticModelingApproach,”
IEEEJournalonSelectedAreasinCommunications,2011. Assumption 3. For each user n ∈ N, each channel k’s in-
terference level z is temporal-independence and frequency-
[22] L. Gao, Y. Xu, and X. Wang, “MAP: Multi-Auctioneer Progressive n,k
AuctionforDynamicSpectrumAccess,”IEEETransactionsonMobile independence.
Computing,2011.
[23] J.Harsanyi,RationalBehaviorandBargainingEquilibriuminGames
andSocialSituations,CambridgeUniv.Press,1977. This assumption shows that (i) the interference zn,k on
channel k is independent identically distributed (iid) at dif-
[24] D.M.Topkis,SupermodularityandComplementarity,PrincetonUniv.
Press,1998. ferent times, and (ii) the interferences on different channels,
9
z ,k ∈ K, are also iid at the same time.12 As we are its channel selection, and thus cannot compute its
n,k
talking about a general user n, we will omit the user index interference to other users.
n in the notations (e.g., write z as z ), whenever
there is no confusion caused. Let Hn,k(·) andkh (·) denote For convenience, we denote N[a], as the set of users
z z k
the cumulative distribution function (CDF) and probability operating on channel k and subscribing to the database’s
distribution function (PDF) of z , ∀k ∈K.13 advance service (i.e., those choosing the strategy s=a), and
k
N[b] as the set of users operating on channel k and choosing
Usually, a particular user’s experienced interference z on k
k the database’s basic service (i.e., those choosing the strategy
a channel k consistss of the following three components: s = b). That is, N[a](cid:83)N[b] = N . Then, for a particular
k k k
user, its experienced interference (on channel k) known by
1) v : the interference from licensed TV stations;
k the database is
2) w :theinterferencefromanotherusermoperating
onk,tmhe same channel k; z¯k (cid:44)vk+(cid:80)m [a]wk,m, (15)
3) o : any other interference from outside systems. ∈Nk
k which contains the interference from TV licensees and all
The total interference on channel k is z = v +w +o , users (operating on channel k) subscribing to the database’s
k k k k
where w (cid:44) (cid:80) w is the total interference from all advanced service. The user’s experienced interference (on
other usekrs operamti∈nNgkonkc,mhannel k (denoted by N ). Similar channel k) not known by the database is
k
vtoarziakb,lewsewalistho atesmsupmoreatlh-iantdvepke,nwdke,nwcke,m(i,.ea.,ndiidokacarroesrsantidmome) zˆk (cid:44)ok+(cid:80)m∈Nk[b]wk,m, (16)
and frequency-independence (i.e., iid across frequency). We which contains the interference from outside systems and all
furtherassumethatw isuser-independence,i.e.,w ,m∈ users (operating on channel k) choosing the database’s basic
k,m k,m
Nk, are iid. It is important to note that different users may service. Obviously, both zˆk and z¯k are also random variables
experience different interferences v (from TV stations), with temporal- and frequency-independence. Accordingly, the
k
w (from another user operating on the same channel), total interference on channel k for a user can be written as
k,m
and ok (from outside systems) on a channel k, as we have zk =z¯k+zˆk.
omitted the user index n for all these notations for clarity.
Since the database knows only z¯ , it will provide this
k
Next we discuss these interferences in more details. information (instead of the total interference zk) as the
advanced service to a subscribing user. It is easy to see
• The database is able to compute the interference v that the more users subscribing to the database’s advanced
k
from TV stations to every user (on channel k), as it service, the more information the database knows, and the
knows the locations and channel occupancies of all more accurate the database information will be.
TV stations.
Next we can characterize the accuracy of a database’s
• Thedatabasecannotcomputetheinterferenceo from information explicitly. Note that η and η denote the fraction
k A L
outsidesystems,duetothelackofoutsideinterference of users choosing the advanced service and leasing licensed
source information. Thus, the interference o will not spectrum, respectively. Moreover, (1−η −η ) denotes the
k A L
beincludedinadatabase’sadvancedinformationsold fraction of users choosing the basic service. Hence, there
to users. are (1 − η ) · N users in the network that we consider
L
operating on the TV channels. Due to the Assumption 3, it
• The database may or may not be able to compute
is reasonable to assume that each channel k ∈ K will be
the interference wk,m from another user m, depend- occupied by an average of N ·(1−η ) users. Then, among
ing on whether user m subscribes to the database’s all N ·(1−η ) users operaKting on chLannel k, there are, on
advanced service. Specifically, if user m subscribes K L
average, N ·η users subscribing to the database’s advanced
to the advanced service, the database can predict K A
service, and N ·(1−η −η ) users choosing the database’s
its channel selection (since the user is fully rational K A L
and will always choose the channel with the lowest basicservice.Thatis,|Nk|= KN·(1−ηL),|Nk[a]|= KN·ηA,and
interferencelevelindicatedbythedatabaseatthetime |N[b]|= N ·(1−η −η ).14 Finally,bytheuser-independence
k K A L
ofsubscription),andthuscancomputeitsinterference of w , we can immediately calculate the distributions of z¯
k,m k
toanyotheruser.However,ifusermonlychoosesthe and zˆ under any given market share η and η via (15) and
k A L
database’s basic service, the database cannot predict (16).
12Notethattheiidassumptionisareasonableapproximationofthepractical 2)Information Value: Now we evaluate the value of the
scenario.Thisisbecauseuserswithbasicservicewillrandomlychooseone database’s advanced information to users, which is reflected
TV channel, hence the number of such users per channel will follow the by the user’s benefit (utility) that can be achieved from this
same distribution. For users with advanced service, they will go to the TV information.
channel with the minimum realized interference. If the interference among
eachpairofusersisiidovertime,thenstatisticallythenumberofsuchusers We first consider the expected utility of a user when
ineachchannelwillalsofollowthesamedistribution.Notethateventhough
choosingthedatabase’sbasicservice(i.e.,s=b).Inthiscase,
all channel quality distributions are the same, the realized instant qualities
the user will randomly choosing a TV channel based on the
ofdifferentchannelsaredifferent.Hence,theadvancedinformationprovided
bythedatabaseisstillvaluableassuchanadvancedinformationisaccurate
interferenceinformation. 14Notethattheabovediscussionisfromtheaspectofexpectation,andin
13Inthispaper,wewillconventionallyuseHX(·)andhX(·)todenotethe a particular time period, the realized numbers of users in different channels
CDFandPDFofarandomvariableX,respectively. maybedifferent.
10
informationprovidedinthefreebasicservice,anditsexpected
data rate is
(cid:82)
R (1−η )=E [R(z)]= R(z)dH (z), (17)
0 L Z z z
whereR(·)isthetransmissionratefunction(e.g.,theShannon
capacity) under any given interference. As shown in Section
A1, each channel k ∈ K will be occupied by an average of
N·(1−η )usersbasedontheAssumption3.Hence,R (1−η )
K L 0 L
depends only on the distribution of the total interference z ,
k
and thus depends on the fraction of users operating on TV
channels (i.e., 1−η ). Then the expected utility provided by
L
the basic service is:
(cid:18) (cid:19)
B(1−η )=U R (1−η ) , (18)
L 0 L
where U(·) is the utility function of the user. We can easily
check that the more users operating on the TV channels, the
higher value of z is, and thus the lower expected utility pro-
k
videdbythebasicservice.Hence,thebasicservice’sexpected
utilityreflectsthecongestionleveloftheTVchannels.Weuse
thefunctionf(·)tocharacterizethecongestioneffectandhave
f(1−η )=B(1−η ).
L L
Then we consider the expected utility of a user when
subscribing to the database’s advance service. In this case,
the database returns the interference {z¯ } to the user
k k
subscribing to the advanced service, together∈Kwith the basic
information such as the available channel list. For a rational
user, it will always choose the channel with the minimum z¯
k
(since {zˆ } are iid). Let z¯[l] = min{z¯ ,...,z¯ } denote
k k MIN 1 K
theminimum∈iKnterferenceindicatedbythedatabase’sadvanced
information. Then, the actual interference experienced by a
user (subscribing to the database’s advanced service) can be
formulated as the sum of two random variables, denoted by
z = z¯ + zˆ. Accordingly, the user’s expected data rate
(a) MIN
under the strategy s=a can be computed by
(cid:2) (cid:0) (cid:1)(cid:3) (cid:82)
R (η ,η )=E R z = R(z)dH (z), (19)
a A L z(a) (a) z z(a)
where H (z) is the CDF of z . It is easy to see that R
z(a) (a) a
depends on the distributions of z¯ and zˆ , and thus depend
k k
on the market share η and η . Thus, we will write R as
L A a
R (η ,η ). Accordingly, the advanced service’s utility is:
a L A
(cid:18) (cid:19)
A(η ,η )(cid:44)U R (η ,η ) (20)
L A a L A
Note that the congestion effect also affects the value of
A. However, compared with the utility of user choosing basic
service, the benefit of a user subscribing to the database’s ad-
vancedinformationiscomingfromthez¯[l] ,i.e.,theminimum
MIN
interference indicatedby thedatabase’s advancedinformation.
As the value of z¯[l] depends on the η only, we can get
MIN A
the approximation A = f(1 − η ) + g(η ), where function
L A
g(·) characterize the benefit brought by z¯[l] and denotes the
MIN
positive network effect.
By further checking the properties of B(1 − η ) and
L
A(η ,η ), we have the Assumption 1 and Assumption 2.
L A