Economics of Mobile Data Offloading
Lin Gao∗ , George Iosifidis† , Jianwei Huang∗ , and Leandros Tassiulas†
∗
†
Dept. of Information Engineering, The Chinese University of Hong Kong, Hong Kong
Dept. of Computer and Communication Engineering, University of Thessaly, and CERTH, Greece
Abstract— Mobile data offloading is a promising approach to
alleviate network congestion and enhance quality of service (QoS)
in mobile cellular networks. In this paper, we investigate the
economics of mobile data offloading through third-party WiFi or
femtocell access points (APs). Specifically, we consider a marketbased data offloading solution, where macrocellular base stations
(BSs) pay APs for offloading traffic. The key questions arising in
such a marketplace are following: (i) how much traffic should each
AP offload for each BS? and (ii) what is the corresponding payment
of each BS to each AP? We answer these questions by using the
non-cooperative game theory. In particular, we define a multileader multi-follower data offloading game (DOFF), where BSs
(leaders) propose market prices, and accordingly APs (followers)
determine the traffic volumes they are willing to offload. We characterize the subgame perfect equilibrium (SPE) of this game, and
further compare the SPE with two other classic market outcomes:
(i) the market balance (MB) in a perfect competition market
(i.e., without price participation), and (ii) the monopoly outcome
(MO) in a monopoly market (i.e., without price competition). Our
results analytically show that (i) the price participation (of BSs)
will drive market prices down, compared to those under the MB
outcome, and (ii) the price competition (among BSs) will drive
market prices up, compared to those under the MO outcome.
I. I NTRODUCTION
We are witnessing an unprecedented worldwide growth of
mobile data traffic, which is expected to reach 10.8 exabytes
per month by 2016, an 18-fold increase over 2011 [1]. However, traditional network expansion methods by acquiring more
spectrum licenses, deploying new macrocells of small size, and
upgrading technologies (e.g., from WCDMA to LTE/LTE-A)
are costly and time-consuming [2]. Clearly, network operators
must find novel methods to resolve the mismatch between demand and supply growth, and mobile data offloading appears
as one of the most attractive solutions.
Simply speaking, mobile data offloading is the use of complementary network technologies, such as WiFi and femtocell,
for delivering data traffic originally targeted for cellular networks. A growing number of studies have been devoted to
the potential performance benefits of mobile data offloading
and the technologies to support it [3]–[12]. Specifically, the
benefit of macrocellular data offloading through WiFi networks
(called WiFi offloading) was studied and quantified using real
data traces in [3]–[6]. It is shown that in a typical urban
environment, WiFi can offload about 65% cellular traffic
and save 55% battery energy for mobile users (MUs) [3].
This work is supported by the General Research Funds (Project Number
CUHK 412710 and CUHK 412511) established under the University Grant
Committee of the Hong Kong Special Administrative Region, China. This
work is also supported by the EINS, the Network of Excellence in Internet
Science, through FP7-ICT grant 288021 from the European Commission. This
work is also supported by the “ARISTEIA” Action of the “OPERATIONAL
PROGRAMME EDUCATION AND LIFELONG LEARNING”, and is cofunded by the European Social Fund (ESF) and National Resources.
MU11
MU12
AP1
BS1
AP4 MU13
MU21
AP5
MU32
MU31
BS2
MU22
MU23
AP6
AP3
BS3
MU33
AP2
Fig. 1. An instance of the data offloading scenario with M = 3 macrocellular
BSs and N = 6 APs. Each AP can offload the macrocellular traffic generated
by those MUs within its coverage area. In this example, BS 1 offloads the
traffic of MU11 to AP 1, and the traffic of MU13 to AP 4; and BS 2 and BS
3 offload the traffic of MU23 and MU31 to AP 6, respectively.
This performance gain can be further enlarged with the use
of delaying transmission [3]–[5] and the prediction of WiFi
availability [6]. In addition to WiFi offloading, femtocells
are another primary option for macrocellular data offloading.
The potential benefits and costs of deploying femtocells were
surveyed in [7]–[9]. The authors in [10] and [11] investigated
the network operators’ profit gains from offering dual services
through both macrocells and femtocells. In [12], the authors
studied the network cost savings by femtocell networks. All of
these studies have reached consensus that offloading through
WiFi and femtocell networks is a cost-effective and energyprudent solution for network congestion.1
However, the above results focused on the technical aspect
of data offloading, without considering the economic incentive for WiFi or femtocells access points (APs) to admit
macrocellular traffic (i.e., to operate in the so-called open
access mode [13]). This incentive issue is particularly important for the scenario where APs are privately owned by
third-party entities, who are expected to be reluctant to admit
non-registered users’ traffic without proper incentives. In [14]
and [15], the authors considered the incentive framework for
the so-called user-initiated data offloading, where MUs initiate
the offloading process (i.e., when and where to offload their
traffic), and hence MUs offer necessary incentives in order to
access to APs. In this paper, we consider the network-initiated
data offloading, where cellular networks initiate the offloading
process (of each MUs), and hence the network operators are
responsible of incentivizing APs. In our model, we assume
that MUs are either (i) compliant or properly incentivized,2
such that they will offload their traffic exactly as the networks
intended, or (ii) unaware of the offloading process at all, that
1 As evidence, many network operators have already started to deploy their
own WiFi or femtocell networks for data offloading (e.g., AT&T [17]), or
initiate collaborations with other WiFi networks (as O2 did with BT [18]).
2 For example, network operators can offer MUs certain rebate for compensating their QoS degradations (e.g., delay) induced by the data offloading.
2
is, data offloading is totally transparent to MUs.3
Specifically, we consider the network-initiated mobile data
offloading through third-party WiFi or femtocell APs, and
focus on the economic interactions between network operators
and APs. In particular, we focus on the incentives that network
operators need to provide to APs in order to encourage cooperative data offloading. Figure 1 illustrates an instance of data
offloading between 3 macrocellular base stations (BSs) and 6
APs. Each BS can offload traffic (of its MUs) to multiple APs,
and each AP can admit traffic from multiple BSs.
We study the incentive design problem by adopting a
market-based data offloading solution, where network operators share the data offloading benefits with APs through market
mechanisms. Namely, network operators pay APs with certain
monetary compensation for offloading traffic. Therefore, the
key problems for such a market are to determine: (a) traffic
offloading volumes: how much traffic should each AP offload
for each BS? and (b) pricing rules: what is the corresponding
payment of each BS to each AP?4 We answer these questions
by using the non-cooperative game theory.
More specifically, we introduce a two-stage multi-leader
multi-follower game, called data offloading game (DOFF),
where BSs act as leaders and APs as followers. In the first
stage, each BS proposes the price that it is willing to pay to
each AP for offloading its traffic. In the second stage, each
AP decides how much traffic to offload for each BS. We
characterize the Nash equilibrium, NE, (or more precisely, the
subgame perfect equilibrium, SPE) of this game. We show
that under the SPE, (i) every AP rejects all BSs except those
proposing the highest price, and (ii) the highest (BS) price to
every AP equalizes the maximum marginal cost reduction (of
all BSs) and the marginal payment (to the AP).5
We further compare the SPE with the outcomes of two other
classic market settings: (i) the perfect competition market,
and (ii) the monopoly market. The first case corresponds to
the scenario where the market prices are determined by an
external controller (e.g., a price regulator), and BSs and APs
act as price-takers, i.e. do not estimate the impact of their
strategies on the prices. In this sense, the market players do
not participate directly in the determination of prices (no price
participation). The second case arises when all BSs act as
one single player, either because they are managed by the
same operator or because they collude and create an effective
monopoly. Thus, there is no price competition. We analytically
show that the equilibrium price (arises in the SPE of our DOFF
game) is upper-bounded by the market clearing price (arises in
3 This is natural for the femtocell offloading. For the WiFi offloading,
this approach can be achieved by recent technological advances such as the
Hybrid Calling technology used by Republic Wireless Inc. [19], which address
seamless roaming between WiFi networks and cellular networks.
4 Our data offloading market model differs from the spectrum market
models in wireless networks (e.g., [20]–[22]) in the following aspects: (i)
the offloading benefit for each BS is AP-specific, and the offloading cost for
each AP is BS-specific; (ii) the offloading solution is constrained by the BSs’
traffic profiles and the APs’ resource limits; and (iii) the offloading solutions
between different BSs and APs are coupled.
5 The detailed definitions of the marginal cost reduction and the marginal
payment are given in Definitions 1 and 5, respectively.
the equilibrium of the perfect competition market), and lowerbounded by the monopoly price (arises in the equilibrium of
the monopoly market).
The main contributions of this work are the following:
• To the best of our knowledge, this is the first work that
considers a mobile data offloading market with multiple
macrocellular BSs and multiple APs, and applies game
theoretic modeling and analysis of the equilibrium.
• We systematically study the economic interactions of BSs
and APs. Specifically, we define a multi-leader multifollower data offloading game–DOFF, with BSs as leaders
and APs as followers; and analytically characterize the
subgame perfect equilibrium–SPE.
• We compare the SPE of the DOFF game with the
outcomes of perfect competition market (no price participation) and monopoly market (no price competition). Our
results analytically show the impact of price participation
abd price competition on market prices.
The rest of this paper is organized as follows. In Section II,
we present the system model. In Sections III, we provide the
social optimality and market balance. In Section IV, we study
the DOFF game in details. Finally, we conclude in Section V.
II. S YSTEM M ODEL
A. System Description
We consider a system that includes a set M , {1, ..., M }
of macrocellular base stations (BSs) and a set N , {1, ..., N }
of third-party WiFi or femtocell access points (APs). BSs may
have overlapping coverage areas, while APs are assumed to
be non-overlapping with each other. Each BS serves a set of
mobile users (MUs) randomly distributed within its coverage
area. The traffic of an MU can be offloaded to an AP, only if
it is covered by that AP (e.g., MU11 and AP 1 in Figure 1).
Figure 1 illustrates such a two-tier network.
Let Smn denote the total (maximum) BS m’s traffic that
can be offloaded to AP n, i.e., those generated by all MUs
of BS m in the coverage area of AP n. Let Sm0 denote the
total BS m’s traffic that cannot be offloaded to any AP, i.e.,
those generated by all MUs of BS m not covered by any AP.
Obviously, Smn ≡ 0 if there is no overlap between a BS m
and an AP n (e.g., BS 1 and AP 2 in Figure 1). The traffic
profile of BS m is denoted by
S m , (Sm0 , Sm1 , ..., SmN ).
Due to the uncertainty of MUs’ data usage and mobility,
S m changes randomly over time. We consider a quasi-static
network scenario, where S m , ∀m ∈ M, remains unchanged
within every data offloading period (e.g., one minute in our
simulation), while changes across periods.
We define the transmission efficiency of a communication
link (between a BS and an MU, or an AP and an MU) as the
average volume of traffic (Mbits) that can be supported by one
unit of spectrum resource (MHz), denoted by θ (measured in
Mbits/MHz). For convenience, we normalize the transmission
efficiency within θ ∈ [0, 1]. Since each AP’s coverage area
is very small, we assume that: (i) the transmission efficiency
3
parameters between each AP and its covered MUs are identical, and attain the maximum value θ = 1; and (ii) the
transmission efficiency parameters between each BS m and
its served MUs covered by the same AP (say n) are also
identical, denoted by θmn ∈ [0, 1]. We further denote θm0
as the average transmission efficiency between BS m and
all of its served MUs whose traffic cannot be offloaded. The
transmission efficiency profile of BS m is denoted by
θ m , (θm0 , θm1 , ..., θmN ).
We similarly assume that θ m , ∀m remains unchanged within
every offloading period, while changes across periods.
Let xmn ∈ [0, Smn ] denote the traffic offloaded from BS
m to AP n, and zmn ∈ [0, +∞) denote the corresponding
payment from BS m to AP n. Then, the traffic offloading
matrix can be written as X , (xmn )m∈M,n∈N , and the
payment matrix can be written as Z , (zmn )m∈M,n∈N .
B. Macrocellular BS Modeling
Let Cm (b) denote the serving cost of BS m for b units of
spectrum resource consumption. Such a serving cost may include the energy cost, operating cost, coordinating cost, etc.
We generally assume that Cm (b) is strictly increasing and
convex, that is, C0m (b) > 0 and C00m (b) ≥ 0, ∀m ∈ M.
Denote xm , (xm1 , ..., xmN ) and zm , (zm1 , ..., zmN ) as
the traffic offloading profile and payment profile of BS m, corresponding to the m-th rows of X and Z, respectively. Given
any xm , the BS m’s total spectrum resource consumption for
delivering all remaining un-offloaded traffic is
PN
−xmn
m0
+ n=1 Smnθmn
.
(1)
bm (xm , S m , θ m ) = Sθm0
For clarity, we will write bm (xm , S m , θ m ) as bm hereafter.
Therefore, the total cost of BS m (including both the serving
cost and the payment to APs) under xm and zm is
PN
TOT
(xm ; zm ) = Cm (bm ) + n=1 zmn .
Cm
(2)
The payoff of every BS m is defined as the cost reduction
achieved from data offloading. Formally,
TOT
TOT
BS
(xm ; zm )
(0; 0) − Cm
Um
(xm ; zm ) = Cm
(3)
PN
= Rm (xm ) − n=1 zmn ,
where Rm (xm ) = Cm (b0m ) − Cm (bm ) is thePBS m’s serving
N
mn
cost reduction, and b0m = bm (0, S m , θ m ) = n=0 Sθmn
is the
BS m’s total resource consumption without data offloading.
C. AP Modeling
Each AP is owned by a private owner, and has its own
traffic demand. Let ξn denote the AP n’s own traffic demand,
which changes randomly over time. Denote fn (ξ) and Fn (ξ)
as the PDF and CDF of ξn , respectively.6 Let Bn denote the
total spectrum resource available for AP n. Then, the expected
profit of AP n (from its own traffic) is7
WnAP (Bn ) = (wn − cn ) · Eξn min{Bn , ξn } ,
(4)
6 Note that the deterministic case where ξ keeps unchanged within a single
n
data offloading period is a special case of our model here.
7 Here we consider the linear serving cost for APs (as used in [16]).
Extending to a general serving cost function is straightforward.
where wn is the average unit revenue from its own traffic,
cn is the unit cost for its resource consumption, and Eξn [·]
denotes the expectation with respect to ξn .
Denote xn , (x1n , ..., xM n ) and zn , (z1n , ..., zM n ) as
the traffic offloading profile and payment profile to AP n,
corresponding to the n-th columns of X and Z, respectively.
When
PM admitting xn , the resource for BSs’ traffic is xn ,
m=1 xmn , and thus the resource left for its own traffic is
Bn − xn . Obviously, a feasible xn satisfies: xn ≤ Bn . Under
any feasible xn and zn , the total profit of AP n is
PM
WnTOT (xn ; zn ) = WnAP (Bn − xn ) − cn · xn + m=1 zmn . (5)
The payoff of every AP n is defined as the profit improvement achieved from data offloading, i.e.,
UnAP (xn ; zn ) = WnTOT (xn ; zn ) − WnTOT (0; 0)
(6)
PM
= Qn (xn ) + m=1 zmn ,
where Qn (xn ) = WnAP (Bn − xn ) − WnAP (Bn ) − cn xn is the
AP n’s own profit loss by offloading BSs’ traffic.
D. Social Welfare
The social welfare is defined as the aggregate payoff of all
BSs and APs, and denoted by
P
P
BS
Ψ(X; Z) = m∈M Um
(xm ; zm ) + n∈N UnAP (xn ; zn )
P
P
(7)
= m∈M Rm (xm ) + n∈N Qn (xn ).
We will also write Ψ(X; Z) as Ψ(X), since it is independent
of the payment transfers between BSs and APs.
III. S OCIAL O PTIMALITY AND M ARKET BALANCE
In this section, we first derive the centralized optimal solution (social optimality) which maximizes the social welfare.
Then we study how to achieve the social optimality in a perfect
competition market with price-taking BSs and APs.
A. Social Optimality
The social welfare optimization problem (SWO) is
(SWO) max Ψ(X)
X
(8)
(i) 0 ≤ xmn ≤ Smn , ∀m ∈ M, n ∈ N ;
P
(ii)
m∈M xmn ≤ Bn , ∀n ∈ N .
For convenience, we first introduce the following concepts.
s.t.
Definition 1 (Marginal Cost Reduction of BS m).
BS
MCm
(xm ) , C0m (bm ).
(9)
Definition 2 (Marginal Profit Loss of AP n).
MLnAP (xn ) , wn − (wn − cn ) · Fn (Bn − xn ).
(10)
BS
Intuitively, the marginal cost reduction MCm represents the
decrease of BS m’s serving cost induced by reducing one
additional unit of resource consumption. The marginal profit
loss MLnAP represents the decrease of AP n’s profit induced by
offloading one additional units of traffic for BSs.
Then, the first-order derivative of Ψ(X) can be written as:
BS
∂Ψ(X)
AP
−1
(11)
∂xmn = θmn · MCm (xm ) − MLn (xn ).
We can further show that the SWO (8) is a convex optimization
(see Appendix-A in [24]), and thus can be solved by the
Karush-Kuhn-Tucker (KKT) conditions [23]. Formally,
4
Lemma 1 (Social Optimality). The socially optimal solution
X◦ is given by the following optimality conditions:
BS
−1
(A.1) θmn
· MCm
(x◦m ) − MLnAP (x◦n ) − µ◦mn + λ◦mn − ηn◦ = 0,
(A.2) µ◦mn · (SmnP
− x◦mn ) = 0, λ◦mn · x◦mn = 0,
M
◦
ηn · (Bn − m=1 x◦mn ) = 0,
for all m ∈ M and n ∈ N , where µ◦mn , λ◦mn and ηn◦ are the
corresponding optimal Lagrange multipliers.
B. Market Balance in Perfect Competition Market
Now we consider a perfect competition market, also called
price-taking market, where market prices (pricing rules) are
set by a central controller (e.g., price regulator) in order to
match (balance) the market supply and demand. BSs and APs
are price takers, responding to the announced prices without
considering the impact of their strategies on the market prices.
The individual optimization problems for price-taking BSs
(BSO) and APs (APO) are, respectively,8
A. Data Offloading Game Formulation
We formulate the interactions between BSs and APs in the
free market as a two-stage non-cooperative game, called data
offloading game (DOFF). In the first stage (Stage-I), every BS
proposes a price to every AP within its coverage area. In the
second stage (Stage-II), every AP indicates the traffic volume
it is willing to offload for every BS who has proposed to it. In
the context of multi-stage game, we refer to BSs as leaders,
and APs as followers. Obviously, under such a game situation,
BSs are price-setters, while APs are still price-takers.11
Let Nm denote the set of APs within the coverage area of
BS m, and Mn denote the set of BSs whose coverage areas
contains AP n. In the example of Figure 1, N1 = {AP1 , AP4 ,
AP5 , AP6 }, and M6 = {BS1 , BS2 , BS3 }. The strategy of BS
m is the price profile pm , (pmn )n∈Nm , where pmn is the
price BS m proposes to AP n; and the strategy of AP n is
the traffic profile xn , (xmn )m∈Mn , where xmn is the traffic
offloading volume AP n responds to BS m.
BS
(xm ; zm (xm )), s.t. xmn ∈ [0, Smn ], ∀n ∈ N .
(BSO) max Um
xm
Definition 4 (Subgame PerfectEquilibrium - SPE). A strategy
P
AP
profile {p∗m }m∈M , {x∗n }n∈N is a subgame perfect equilib(APO) max Un (xn ; zn (xn )), s.t.
m∈M xmn ≤ Bn .
xn
equilibrium at every stage, i.e., rium if∗ it represents aBSNash
∗
†
†
†
Um xm (P∗−m , pm ); pm x∗m (P∗−m , pm ) ,
Let xm , (xm1 , ..., xmN ) denote the optimal individual  I: pm = arg max
pm
‡
decision of BS m (i.e., the solution of BSO), and xn , 
II: x∗n = x∗n (p∗n ) = arg max UnAP xn ; p∗n xn ,
‡
‡
xn
(x1n , ..., xM n ) denote the optimal individual decision of AP n
12
(i.e., the solution of APO). Intuitively, we can also view x†mn for all BSs m ∈ M at Stage-I and APs n ∈ N at Stage-II.
‡
as the demand of BS m for AP n’s resource, and xmn as the
B. An Illustrative Model with One BS and One AP
supply of AP n’s resource intended for BS m.
We first look at an illustrative model with one BS and one
Definition 3 (Market Balance - MB). The offloading market is AP. In this case, the DOFF game degenerates to a conventional
considered balanced when x†mn = x‡mn , ∀m ∈ M, n ∈ N .
Stackelberg game. We use this simple model to illustrate (i) the
By interpreting the Lagrange multipliers as shadow prices, best individual decisions of APs and BSs, and (ii) the impact
of price participation on the market outcome.
we define the following market clearing prices:
For notational consistency, we denote the BS as m and the
AP
◦
◦
◦
(12)
pn , MLn (xn ) + ηn , ∀n ∈ N ,
AP as n, i.e., M = {m} and N = {n}. We solve the SPE of
each associated with one AP.9 It is easy to show that under the this game by the backward induction method.
above market clearing prices, we have: x†mn = x‡mn = x◦mn
1) Stage-II: Given the BS’s price pmn , the AP’s optimizafor all m ∈ M and n ∈ N . Therefore:
tion problem (APO) and the corresponding solution are
Observation 1 (Market Balance). The market clearing prices
(APO) max UnAP (xmn ; pmn · xmn ), s.t. xmn ∈ [0, Bn ].
xmn
(12) lead to the market balance. In addition, under the market
Lemma 2 (AP’s Optimal Decision).
balance, the social welfare is maximized.

0
if pmn < b
cn


IV. G AME T HEORETIC A NALYSIS IN THE F REE M ARKET
(-1) wn −pmn ∗
xmn = Bn − Fn
if pmn ∈ [b
cn , wn ] (13)
wn −cn
In this section, we consider a free market, where there is


Bn
if pmn > wn
no central controller, and both traffic offloading volumes and
pricing rules are determined freely by BSs and APs.
where b
cn , cn + (wn − cn ) · [1 − Fn (Bn )].
In this case, some players (e.g., BSs in our analysis10 ) are
11 This is due to the two-stage modeling assumption (i.e., BSs and APs are
given the authority to set market prices, and thus become pricenot making decisions simultaneously). Note that for a data offloading market,
setters. This is the so-called price participation. Naturally, the two-stage assumption is more reasonable than assuming that BSs and APs
price competition may occur between the price-setters. We make decisions at the same time. The key reason is that BSs usually have
are interested in addressing the following problems: what is more market power, and thus have the priority to determine market prices.
12 Here P∗
∗
∗
∗
∗
−m , (p1 , ..., pm−1 , pm+1 , ..., pM ), and p x represents the
the impact of price participation and price competition on the
inner product of two vectors p and x. Recall that (i) pm = (pm1 , ..., pmN ),
market outcome and on the social welfare achieved.
and xm = (xm1 , ..., xmN ) are all prices and traffic offloading volumes
8 Here
zm (xm ) , (zmn (·))n∈N and zn (xn ) , (zmn (·))m∈M .
implies the following pricing rules: zmn (xmn ) = p◦n ·xmn , ∀m, n.
10 The analysis is quite similar when APs are given this authority (see [24]).
9 This
related to BS m, and (ii) pn = (p1n , ..., pM n ), and xn = (x1n , ..., xM n )
are those related to AP n. By (II), every x∗mn in x∗n is a function of p∗n .
Thus, x∗m is a function of P∗ = (p∗n )n∈N , which can also be written as
P∗ = (p∗m )m∈M = (P∗−m , p∗m ).
5
Price
AP
MPn
(E)
p◦mn
p∗mn
MLnAP
(B)
SPE
MB
xn
BS
−1
MCm
· θmn
b
cn
0
1) Stage-II: First, we study every AP n’s optimal decision
x∗n when receiving multiple price proposals from BSs. Let
pn , (pmn )m∈Mn denote the prices AP n receives. The
optimization problem (APO) for AP n is
(APO) max UnAP (xn ; pn xn )
x∗mn x◦mn dmn
Traffic volume
Fig. 2. Illustration of SPE and MB for the single-BS single-AP model. The
hollow circles marked with (E) and (B) denote the conditions for SPE and MB,
respectively. Specifically, (i) under the SPE, the BS’s marginal cost reduction
−1
BS
AP
equals to the marginal payment MPn
to the AP; (ii) under the
MCm
· θmn
−1
BS
MB, the BS’s marginal cost reduction MCm ·θmn equals to the AP’s marginal
AP
profit loss MLn
(and the BS demand equals to AP supply).
Intuitively, if the BS proposes a large enough price pmn
(i.e., pmn > wn ), AP n will sell all of its resource to the BS.
On the other hand, if the price pmn is smaller than a threshold
b
cn , AP n will sell none of its resource to the BS. In this sense,
we refer to b
cn as the critical price of AP n.
2) Stage-I: Knowing the AP’s response, the BS’s optimization problem (BSO$ ) in Stage-I is
BS
(BSO$ ) max Um
x∗mn (pmn ); pmn · x∗mn (pmn )
pmn
(14)
s.t. 0 ≤ x∗mn (pmn ) ≤ Smn .
For convenience, we introduce the following concept.
Definition 5 (Marginal Payment of BS m to AP n).
MPnAP (pmn ) , x∗mn ·
∂pmn
∂x∗
mn
+ pmn
(15)
AP
Intuitively, the marginal payment MPn represents the increase
of BS’s total payment (not unit price) in order to have AP n
offload one additional unit of traffic.13
BS
Then, the first-order derivative of Um
(·; ·) can be written as
BS
∂x∗mn
∂Um
BS
AP
∗
−1
(16)
∂pmn = θmn · MCm (xmn ) − MPn (pmn ) · ∂pmn .
We can further show that problem (14) is a convex optimization, and thus can be solved by KKT analysis. Formally,
Lemma 3 (BS’s Optimal Decision). The BS m’s optimal price
p∗mn satisfies the following conditions:
BS
−1
(D.1) θmn
· MCm
(x∗mn ) − MPnAP (p∗mn ) − µ∗mn + λ∗mn = 0,
∗
(D.2) µmn · (Smn − x∗mn ) = 0, λ∗mn · x∗mn = 0,
where µ∗mn and λ∗mn are the optimal Lagrange multipliers.
3) Observation: Figure 2 illustrates the SPE and MB, from
which we can see: x∗mn ≤ x◦mn and p∗mn ≤ p◦mn . Therefore,
Observation 2. The price participation (of BSs) drives the
market price down from the market clearing price (as shown
by the SPE and MB in Figure 2).
C. A General Model with Multiple BSs and Multiple APs
We now return to the general model with multiple BSs and
multiple APs. Similarly, we apply the backward induction.
∂pmn
achieve this, the BS needs to increase the price by ∆pmn = ∂x
.
∗
mn
This leads to an additional payment that consists of two parts: (i) pmn +
∆pmn by offloading an additional unit of traffic at the new price pmn +
∆pmn , and (ii) x∗mn · ∆pmn for the existing x∗mn units of offloading traffic.
13 To
(17)
s.t. (i) xmn ≥ 0, ∀m ∈ Mn ;
P
(ii)
m∈Mn xmn ≤ Bn .
Note that (17) is a direct extension of the APO in Section
III-B. Next we provide some additional properties for the
solution of (17). Denote p+
n , maxm∈Mn pmn as the highest
price of all BSs, M+
,
{m
∈ Mn | pmn = P
p+
n
n } as the set of
BSs proposing the highest price, and Xn , m∈M+
xmn as
n
the total resource for those BSs proposing the highest price.
Lemma 4. The optimal solution x∗n of problem (17) satisfies:
(a) x∗mn = 0, ∀m ∈
/ M+
n;
∗
(b) Xn is given by (13) by replacing pmn as p+
n.
Lemma 4 shows that only the highest price is accepted by
the AP. We further notice that any feasible division of Xn∗
among BSs M+
n leads to the same payoff for the AP. That
is, the allocation of Xn∗ is irrelevant to the AP’s payoff. This
implies that the conditions in Lemma 4 are also sufficient.
Although the AP n’s benefit does not depend on the detailed
allocation of Xn∗ (among M+
n ), an explicit allocation mechanism is still necessary for analyzing the BSs’ best decisions.
We adopt the following proportional allocation:
x∗mn , ψmn · Xn∗ , ∀m ∈ M+
(18)
n,
where ψmn , P dmn+ dkn , and dmn is the BS m’s traffic ofk∈Mn
floading demand (to AP n) under the price p+
n (which is given
by the BSO in Section III-B). Intuitively, we can view that
AP n offloads Xn∗ units of traffic picked randomly and uniformly from the total demand of BSs M+
n . Note that both ψmn
and Xn∗ depends on the price p+
,
and
so
does x∗mn . Figure 2
n
illustrates the BS’s demand dmn under the price p∗mn .
2) Stage-I: We now study the price competition among BSs
in the first stage, and the resultant SPE.
We first focus on the price competition of BSs for a particular AP n, assuming that their prices to other APs are fixed. A
price competition equilibrium in AP n is a price profile p∗n ,
(p∗mn )m∈Mn such that no BSs m ∈ Mn can improve its payoff by changing its price pmn . Note that if every AP reaches
its equilibrium, we obtain the SPE of the whole game.
By the previous analysis, we can find that for any price
profile pn , only the highest price is accepted by AP n. That
is, only those BSs proposing the highest price survive in the
price competition. This implies that for any price profile, those
price proposals smaller than the highest price are irrelevant.
Therefore, to characterize the equilibrium p∗n , we only need
∗
to find (i) the highest price p+
n = maxm∈Mn pmn , and (ii) the
+
BSs Mn proposing this price (and thus survive).
We have the following necessary conditions for p∗n .
Lemma 5. The equilibrium p∗n in AP n satisfies:
BS
−1
θmn
· MCm
(0) ≤ p+
∀m ∈
/ M+
n,
n.
(19)
6
Price
MPnAP
x∗1n = ψ1n · Xn∗
(E)
p◦n
p+
n
(O)
x∗2n
(B)
pnM
MO
b
cn
0
MLnAP
MC1BS
θ1n
SPE MB
(a)
XnM Xn∗ Xn◦
(b)
(c)
MC2BS
θ2n
Traffic volume
Fig. 3.
Illustration of SPE, MB, and MO for the two-BS single-AP
model. The curve (c) is the horizontal stack of curves (a) and (b), denoting
the integrated marginal cost reduction of both BSs. The hollow circles
marked with (E), (B), and (O) denote the conditions for SPE, MB, and
MO, respectively. Specifically, (i) under the MO, the marginal cost reduction
−1
BS
AP
· MCm
of every BS m ∈ {1, 2} equals to the marginal payment MPn
θmn
−1
BS
· MCm
of
to the AP; (ii) under the MB, the marginal cost reduction θmn
AP
every BS m ∈ {1, 2} equals to the AP’s marginal profit loss MLn
(and the
AP supply Xn◦ equals to the total BS demand); and (iii) under the SPE, the
−1
largest marginal cost reduction of both BSs (i.e., θ1n
· MC1BS ) equals to the
AP
marginal payment MPn
to the AP. It is easy to show that the market price
M
◦
under the SPE (p+
n ) must be between those under the MO (pn ) and MB (pn ).
BS
−1
(0) represents the highest price under which
·MCm
Here θmn
BS m is willing to demand a positive amount of resource from
BS
−1
in
· θmn
AP n (as shown by the initial point of curve MCm
Figure 2). Thus, Lemma 5 implies that any BS proposing a
price lower than the highest price p+
/
n (i.e., those BSs m ∈
+
.
Accordingly,
any
BS
)
must
have
a
zero
demand
under
p
M+
n
n
BS
+
−1
m with a positive demand under p+
n (i.e., θmn ·MCm (0) > pn )
must propose this highest price (and thus survive). Next we
study what will be the highest price p+
n that they can propose.
∗
Lemma 6. The highest price p+
n under the equilibrium pn is
given by the following condition:
BS
+
∗
−1
(20)
MPnAP (p+
n ) = max+ θmn · MCm xmn (pn ) ,
m∈Mn
∗
where x∗mn (p+
n ) = ψmn · Xn defined by (18).
Intuitively, if there exists one BS m ∈ M+
n that has an
BS
−1
(x∗mn ) >
· MCm
incentive to increase its price (i.e., θmn
AP
+
MPn (pn )), then by Lemma 5, all other BSs with positive
demand will naturally following the newly increased price.
The highest price p+
n will continuous to increase, until the
BS
−1
largest θmn
· MCm
(x∗mn ) meets the MPnAP (p+
n ).
3) Observation: We compare the equilibrium p∗n with two
classic market outcomes: (i) the market balance (MB) defined in Section III-B, and (ii) the monopoly outcome (MO),
wherein BSs act as an integrated individual (monopolist)
and seek to maximize their aggregate payoff (see [24] for
details). Figure 3 illustrates these solution concepts for the
scenario of two BSs and one AP, from which we can find that
◦
pnM ≤ p+
n ≤ pn . Therefore, we have the following observation.
Observation 3. The price competition (of BSs) drives the market price up from the monopoly price (as shown by points MO
and SPE in Figure 3). Moreover, similar to Observation 2, the
price participation (of BSs) drives the market price down from
the market clearing price (as shown by MB and SPE).
V. C ONCLUSION
The increasing traffic demand and the network operators’
growing needs for reducing their capital and operational expenditures (CAPEX and OPEX) are expected to boost thirdparty offloading solutions. Studying the economic interactions
of the involved entities is an important step towards the
realization of this promising solution. In this paper, we study
the economics of mobile data offloading through third-party
WiFi or femtocell APs. We propose a market-based offloading
scenario, and study the market outcome by using the noncooperative game theory. We further study the impact of price
participation and competition on the market outcome. Our
analysis sheds light to many different aspects of this interesting
problem. There are many directions for future work in this
area. For example, it would be useful to study the price of
anarchy of the resulting SPE. Another interesting direction is
to study the offloading market under incomplete information.
R EFERENCES
[1] Cisco, “Cisco Visual Networking Index: Global Mobile Data Traffic
Forecast Update”, 2011-2016, February 2012.
[2] Ericsson Technical Report, “Ericsson Predicts Mobile Data Traffic to
Grow 10-fold by 2016”, http://www.ericsson.com/news/1561267, 2011.
[3] K. Lee, I. Rhee, J. lee, S. Chong, and Y. Yi, “Mobile Data Offloading:
How Much Can WiFi Deliver?”, In Proc. of ACM CoNEXT, 2010.
[4] A. Balasubramanian, R. Mahajan, and A. Venkataramani, “Augmenting
Mobile 3G Using WiFi”, ACM MobiSys, pp. 209-222, 2010.
[5] S. Dimatteo, P. Hui, B. Han, and V. Li , “Cellular Traffic Offloading
Through WiFi Networks”, In Proc. of IEEE MASS, pp. 192-201, 2011.
[6] N. Ristanovic, J. Y. Le Boudec, A. Chaintreau, and V. Erramilli, “Energy
Efficient Offloading of 3G Networks”, In Proc. of IEEE MASS, 2011.
[7] FemtoForum, “Femtocell Business Case Whitepaper,” Femto Forum.
White Paper, available at: www.femtoforum.org, June 2009.
[8] J. G. Andrews, H. Claussen, M. Dohler, etc., “Femtocells: Past, Present,
and Future”, IEEE J. Sel. Areas Commu., 2012.
[9] J. Zhang and G. de la Roche, Femtocells: Technologies and Deployment,
New York, USA: Wiley, Mar. 2010.
[10] L. Duan, J. Huang, and B. Shou, “Economic Viability of Femtocell
Service Provision”, In Proc. of Gamenets, Shanghai 2011.
[11] N. Shetty, S. Parekh, and J. Walrand, “Economics of femtocells”, In
Proc. of IEEE Globecom, pp. 1-6, Hawai, 2009.
[12] H. Claussen, L. T. W. Ho, and L. G. Samuel, “An Overview of the
Femtocell Concept,” Bell Labs Technical Journal, May 2008.
[13] H. S. Jo, P. Xia, and J. G. Andrews, “Downlink Femtocell Networks:
Open or Closed?”, In Proc. of IEEE ICC, pp. 1-5, Japan, 2011.
[14] F. Pantisano, M. Bennis, W. Saad, and M. Debbah, “Spectrum Leasing
as an Incentive towards Uplink Macrocell and Femtocell Cooperation”,
IEEE J. Sel. Areas Commu., 30(3) 617-630, 2012.
[15] S. Hua, X. Zhuo, and S.S. Panwar, “A Truthful Auction Based Incentive
Framework for Femtocell Access,” arxiv Oct. 2012.
[16] S. Y. Yun, Y. Yi, D. H. Cho, and J. Mo , “The Economic Effects of
Sharing Femtocells”, IEEE J. on Sel. Areas in Commu., 30(3) 2012.
[17] AT&T Press Release, “AT&T Expands Wi-Fi Hotzone Pilot Project to
Additional Cities”, July, 2010.
[18] BT Wifi Press Release, “O2 Brings 3,000 New Wi-Fi Hotspots to iPhone
Customers”, July, 2008.
[19] Republic Wireless Inc., http://www.republicwireless.com/.
[20] G. Vojislav, J. Huang, and B. Rimoldi, “Competition of Wireless
Providers for Atomic Users: Equilibrium and Social Optimality”, in
Allerton Conference on Communication, Control, and Computing, 2009.
[21] L. Gao, X. Wang, and Y. Xu, “Spectrum Trading in Cognitive Radio
Networks: A Contract-Theoretic Modeling Approach,” IEEE J. Sel. Areas
Commu., 29(4) 843-855, 2011.
[22] L. Gao, J. Huang, et. al., “An Integrated Contract and Auction Design
for Dynamic Spectrum Sharing,” IEEE J. Sel. Areas Commu., 2013.
[23] S. Boyd, and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.
[24] L. Gao, G. Iosifidis, J. Huang, and L. Tassiulas, Technical Report, online
at http://jianwei.ie.cuhk.edu.hk/publication/AppendixEcoDataOff.pdf