Int
ern
at
i
onal
Journ
al of Inf
orm
at
ic
s
and
Co
m
munic
at
i
on
Tec
hn
olog
y (IJ
-
I
CT)
Vo
l.
6
,
No.
3
,
D
ece
m
ber
201
7
, pp.
189
~
198
IS
S
N: 22
52
-
8776,
DOI: 10
.11
591/ijict
.
v6
i
3.p
p1
89
-
1
98
189
Journ
al
h
om
e
page
:
http:
//
ia
esj
ou
r
nal.co
m/
on
li
ne/in
dex
.php
/
IJ
ICT
Analysis
of Com
petition
Betwe
en Co
nt
ent
Provid
ers in th
e
Internet
Market
M’hame
d O
utan
ou
te
*
1
,
H
am
id G
armani
2
, Mohame
d B
as
lam
3
, Rac
hid El
Ay
achi
4
,
Be
laid Bouik
h
alene
5
1,2,3,4
Facul
t
y
of
S
ci
en
ce
s
and
T
echnique
s , Sult
an Moula
y
Slim
ane Unive
rsit
y
,
B
en
i
Mel
la
l
,
Moroc
c
o
5
Pol
y
disc
ipl
in
ar
y
F
ac
ul
t
y
,
Sult
a
n
Moula
y
Sl
imane
Univer
si
t
y
,
B
eni
Me
ll
a
l, Morocc
o
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
A
ug
10
th
,
20
17
Re
vised Oct
25
th
,
2017
Accepte
d Aug
8
th
, 201
7
In
the
Int
ern
e
t
m
ark
et
,
cont
en
t
provide
rs
(CPs
)
cont
inu
e
to
pl
a
y
a
primordial
role
in
the
pro
-
ce
ss
of
ac
ce
ss
i
ng
diffe
re
nt
t
y
p
es
of
dat
a:
Im
age
s,
Te
xts
,
Videos
.
.
et
c
.
Co
m
pet
it
ion
in
this
are
a
is
fi
erce,
customers
are
looki
ng
for
provide
rs
th
at
of
fe
r
th
em
good
c
onte
nt
(
cr
edi
bi
lit
y
of
con
te
n
t
an
d
qual
i
t
y
of
servic
e)
with
a
re
asona
bl
e
pri
ce.
In
thi
s
work,
we
anal
y
ze
thi
s
competi
tio
n
bet
wee
n
CP
s
an
d
the
e
conomic
infl
uen
ce
of
th
eir
strat
eg
ie
s
on
t
he
m
ark
et
.
W
e
form
ula
te
o
ur
proble
m
as
a
non
-
coope
ra
ti
v
e
game
among
m
ult
ipl
e
CP
s
for
the
sam
e
m
ark
et.
Thro
ugh
a
d
e
ta
i
le
d
anal
ysis,
we
prove
u
nique
ness
of
pure
Nash
Equi
l
ibri
um
(NE).
Further
-
m
ore
,
a
ful
l
y
distr
ibut
ed
algorithm
to
conve
rge
to
the
NE
point
is
pre
s
ent
ed
.
In
orde
r
t
o
quant
if
y
how
eff
icient
is
the
NE
point
,
a
det
a
il
ed
an
aly
sis
of
the
Price
of
Anarc
h
y
(PoA
)
is
adopt
ed
to
ensure
th
e
p
erf
o
rm
anc
e
of
the
sy
stem
at
equi
l
ib
rium.
Finall
y
,
we
provid
e
an
ext
ensiv
e
num
er
ic
a
l
stud
y
to
d
e
scribe
th
e
in
te
r
a
ct
ions
be
twee
n
CP
s
and
to
point
out
the
i
m
porta
nce
of
q
ual
ity
of
servi
c
e
(QoS
)
and
cr
edi
bilit
y
of
cont
en
t
in
th
e
m
ark
et.
Ke
yw
or
d:
Con
te
nt Pro
vide
rs
Gam
e Th
eor
y
Nash E
qu
il
ib
rium
Pr
ic
e
of
A
nar
c
hy
Pr
ic
in
g
-
QoS
Copyright
©
201
7
Instit
ut
e
o
f Ad
vanc
ed
Engi
n
ee
r
ing
and
S
cienc
e
.
Al
l
rights re
serv
ed
.
Corres
pond
in
g
Aut
h
or
:
M’ham
ed
O
utanoute
Faculty
of S
ci
e
nces a
nd Tec
hniq
ues, S
ultan
Mou
la
y Sl
im
a
n Un
i
ver
sit
y
Be
ni Mel
al
, Mo
r
occ
o
(00
212)6
7621
8940
Em
a
il
:
m
ha
m
e
d.ou
ta
noute@
gm
ai
l.co
m
1.
INTROD
U
CTION
The
cu
rr
e
nt intern
et
h
as e
nab
l
ed
num
ero
us
di
stribu
te
d
a
pp
li
cat
ion
s and service
s.
H
oweve
r,
provide
r
s
gen
e
r
-
al
ly
face
m
any
chall
en
ges
in
determ
i
ning
te
ch
nical
and
ec
on
om
ic
so
luti
ons
to
pr
ov
i
ding
ser
vic
es[1
]
.
Key
chall
en
ge
s
are
how
t
o
pri
ce
and
bill
these
ser
vices
and
how
to
es
ta
blish
eco
no
m
ic
relat
ion
sh
ips
with
oth
e
r
pro
vi
ders
that
are
nec
essary
to
pro
vi
de
en
d
-
to
-
e
nd
serv
ic
es
.
E
quil
ibriu
m
m
od
el
s
for
the
inte
rn
et
gen
e
rall
y
assume
basic
econ
om
ic
rela
-
ti
onsh
ips
a
nd
co
nsi
der
pri
ce
as
the
on
ly
factor
that
aff
ect
s
us
er
s
dem
and
(see
[
2][3
]
[
4]).
H
ow
ever,
in
ne
w
pa
rad
i
gm
s
fo
r
t
he
inte
rn
et
a
nd
e
ven
in
t
he
case
of
s
upply
chain
netw
orks,
pr
ic
e
is
no
t
the
only
factor
a
nd
Qu
al
it
y
of
Se
rv
ic
e
(
Q
oS
)
,
i.
e.,
the
a
bili
ty
to
pro
vid
e
different
pr
i
or
it
ie
s to
a
ppli
cat
ion
s,
u
s
er
s,
or
data
flo
ws
, co
m
es into pl
ay
(
see
[5
]
[6
]
[7
]
[8
]
[9
]
).
Our
co
ntributi
on
in
this
wor
k i
s to
exp
an
d
th
e stud
y o
n
the inter
net d
om
ai
n
by ad
ding a u
t
il
ity
m
od
el
on
i
nco
m
e
fro
m
con
te
nt
pro
vid
e
rs
(CP
s).
CPs
can
be
s
oc
ia
l
networks,
internet
sea
rch
eng
i
nes,
or
an
y
oth
er
web
sit
es.
In
th
is
fr
am
ewo
rk,
we
pro
pose
a
m
od
el
ing
com
petit
ion
bet
we
en
CPs
base
d
on
the
par
am
et
ers
of
pr
ic
e
a
nd
c
re
di
bili
ty
of
con
t
ent
that
is
us
e
d
to
m
e
asur
e
t
he
ef
fecti
ve
ne
ss
of
co
ntent
pro
vid
e
d
by
t
he
CP.
Credibili
ty
is a fun
ct
io
n
t
hat depen
ds o
n
t
he QoS a
nd quali
ty
o
f
content
(QoC).
Custom
er
beh
a
vior
is
m
od
el
ed
by
the
functi
on
dem
and
that
dep
en
ds
on
pro
vid
e
rs
poli
ci
es.
W
e
use
gam
e
theor
y
to
stu
dy
the
b
e
hav
i
or
of
CPs
in
the
inter
net.
Then
we
stu
dy
the
i
m
pact
of
their
decisi
ons
on
custom
ers
an
d
oth
e
r
CPs.
W
e
fo
c
us
our
st
ud
ie
s
on
the
non
-
c
ooper
at
iv
e
gam
es
in
te
rm
s
of
sta
ble
so
luti
ons,
wh
ic
h
are
t
he
pure
strat
e
gy
Nash
Eq
uili
br
i
a
(N
E
)
of
t
he
gam
e.
W
e
do
not
co
ns
ide
r
m
i
xed
strat
egy
e
quil
ibria,
because
our
e
nvir
on
m
ent
requires
a
co
nc
rete
strat
egy
rath
er
than
a
r
an
do
m
iz
ed
strat
egy,
wh
ic
h
w
ould
be
the
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2252
-
8776
IJECE
V
ol.
6
,
No.
3
,
Decem
ber
20
1
7
:
189
–
198
190
resu
lt
of
a
m
ixed
strat
e
gy.
H
ence,
w
hen
us
i
ng
the
te
rm
N
ash
e
qu
il
ib
riu
m
we
m
ean
pu
re
strat
egy
e
xa
ct
NE
un
le
ss
m
en
ti
on
ed othe
rw
ise
.
CPs
m
a
y
be
faced
with
t
he
qu
e
sti
on
of
”
how
t
o
ch
oose
in
w
hat
co
ntent
to
sp
eci
al
iz
e”
[10].
E.
Alt
m
an
con
si
de
rs
seve
ral CPs
that are f
aced
with a si
m
il
ar
pro
blem
an
d
stud
y t
he
im
pact
o
f
their
decisi
on
s
on
each
othe
r
usi
ng
a
gam
e
theor
et
ic
app
r
oach.
The
aut
hor
sho
ws
that
the
pro
blem
of
sel
ect
ing
the
c
on
te
nt
ty
pe
is
equ
i
valent
t
o
a
c
ongestio
n
gam
e.
In
[11],
the
a
uthors
ha
ve
stu
died
ga
m
e
pr
oble
m
s
i
nvolv
i
ng
tw
o
t
ypes
of
CPs
:
on
e
tha
t
cor
res
ponds
to
ind
e
pe
nd
e
nt
CPs,
an
d
on
e
t
hat
corre
sp
on
d
to
C
Ps
that
hav
e
e
xc
lusiv
e
agr
eem
ents
with
In
te
r
net
Ser
vice
Pr
ovid
ers
(I
SPs
).
T
he
cost
for
the
internet
us
e
rs
w
ho
are
subsc
rib
ers
of
so
m
e
IS
P
of
f
et
ching
c
onte
nt
fr
om
an
ind
e
pende
nt
CP
or
fr
om
a
CP
that
has
an
excl
us
ive
a
gr
eem
ent
with
ano
t
her
IS
P
,
w
as
assum
ed
to
be
la
r
ger
tha
n
for
fetc
hing
it
from
the
CP
that
has
an
e
xclu
sive
ag
reem
ent
with
their
own ISP
.
Weijie
Wu
et
a
l.
con
si
der
a
Stac
kelbe
rg
gam
e,
w
her
e
the
C
P
decide
s
re
wa
rd
first,
a
nd
a
fter
that,
th
e
peer
s
deci
de
a
m
ou
nt
of
ca
pa
ci
ty
[5
]
.
T
he
C
P
re
wards
t
he
p
eers
bas
ed
on
the
am
ou
nt
of
uploa
d
ca
pacit
y
they
con
t
rib
ute.
F
rom
CP
po
int
of
view,
it
ai
m
s
a
t
m
ini
m
iz
ing
it
s
total
cost,
i.e.
,
the
c
os
t
of
up
loading
a
nd
th
e
cos
t
of r
e
wardin
g
t
he peers
. T
he u
ti
lity
o
f
a
pee
r i
s the r
e
wa
rd it
r
ecei
ves
, m
inus i
ts cost
of up
l
oad co
ntri
bu
ti
on.
The
rest
of
t
he
pa
per
is
org
anized
a
s
f
ollo
ws
:
in
sect
io
n
2.
,
we
desc
r
ibe
the
pro
ble
m
m
od
el
.
In
sect
ion
3
.
, w
e f
or
m
ulate
our
m
od
el
as
a n
on
-
co
operati
ve
gam
e. W
e p
r
ese
nt
num
erical
resu
lt
s
in
sect
ion
4.
a
nd
con
cl
ud
e
ou
r work
in
secti
on
5.
2.
PROBLE
M
MO
DELIN
G
In
this
sect
io
n,
we
form
ulate
the
interact
io
n
am
on
g
co
nt
ent
pro
vid
e
rs
(
CPs)
as
a
non
-
co
operati
ve
gam
e.
Each
C
P
ch
ooses
c
re
dib
il
it
y
of
c
on
te
nt
an
d
the
c
orres
pondin
g
pr
ic
e.
W
e
co
nsi
der
a
syst
em
with
N
con
te
nt
prov
i
de
rs.
Let
pi
an
d
ci
,
be,
res
pecti
vely
,
the
ta
riff
an
d
t
he
c
red
i
bi
li
t
y
of
co
ntent
guara
nteed
by
CPi
.
Now,
eac
h
cus
tom
er s
eeks to
the co
nte
nt p
r
ovide
r
w
hich
al
lows
him
to
m
e
et
a cr
edibili
ty
of
c
on
te
nt su
f
fi
ci
ent
to
sat
isfy
his/h
er
nee
ds
,
at
sui
ta
ble
pr
ic
e.
W
e
consi
de
r
that
beh
a
vi
or
s
of
custom
er’
s
has
been
ha
ndle
d
by
a
si
m
ple
functi
on
s
o
cal
le
d
de
m
and
f
unct
ions,
see
e
qu
at
io
n
(1).
T
his
la
te
r
de
pends
on
th
e
pr
ic
e
a
nd
cre
dib
il
it
y
of co
ntent st
rategies
of
all
. C
P
s ar
e
sup
po
se
d t
o
kn
ow the e
ffec
t of thei
r
poli
cy
o
n t
he
c
us
t
om
er’
s.
2
.
1.
M
od
el
of
Conten
t Credi
bil
ity
Fu
ncti
on
We
ass
um
e
th
at
the
functi
on
of
the
c
re
dib
i
li
ty
of
con
te
nt
ci
of
CPi
is
a
functi
on
of
th
e
qu
al
it
y
of
serv
ic
e
qs
i a
nd
quali
ty
co
nte
nt
q
ci
abo
ve wh
i
ch
is
wr
it
te
n as
foll
ow
s
:
The
qual
it
y
of
co
ntent
pro
vid
ed
can
be
s
pe
ci
fied
for
a
s
pecific
do
m
ain
of
co
ntent,
e.g
.
,
vid
e
o
stream
ing
.
2.2.
Dem
an
d
M
odel
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
ICT
IS
S
N:
22
52
-
8776
An
alysis of C
omp
et
it
ion Fr
onti
ng
the
P
opul
ar
it
y
…
(
Hamid
Garma
ni
)
191
Assum
ption
1
and
2
will
be
need
e
d
to
e
ns
ure
the
un
i
quene
ss
of
the
resu
lt
in
g
eq
uili
br
ium
.
It
is
furthe
rm
or
e
a
r
easo
nab
le
c
on
diti
on
,
in
t
hat
Assum
ption
1
(r
es
p.
Assum
ption
2
)
im
plies
that
the
i
nf
l
ue
nce
of
a
CP
pr
ic
e
(r
es
p.
c
re
dib
il
it
y
of
c
on
te
nt)
is
si
gn
i
ficantl
y
gre
at
er
on
it
s
obs
erv
e
d
dem
and
than
t
he
pr
ic
es
(r
e
sp.
cred
i
bili
ti
es
of
co
ntent)
of
it
s
com
peti
-
tors.
This
c
onditi
on
c
ou
l
d
the
n
t
ake
int
o
acc
ount
t
he
prese
nc
e
of
c
us
tom
er lo
ya
lt
ie
s an
d/
or
im
per
fect
knowle
dge
of com
petito
rs
price
s
[13].
2.3.
Ut
il
it
y
m
odel
for
CP
3.
NON
-
COOPE
RA
TI
VE G
A
ME FO
R
MUL
ATION
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192
3.1. Qo
S G
am
e
3.2. Pri
ce G
am
e
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An
alysis of C
omp
et
it
ion Fr
onti
ng
the
P
opul
ar
it
y
…
(
Hamid
Garma
ni
)
193
3.3. Qo
C Ga
m
e
3.4.
Joint
Pric
e, Q
oC and
Q
oS
Gam
e
In
th
e
subsect
i
on
s
ci
te
d
ab
ov
e,
we
hav
e
s
how
n
the
e
xiste
nce
an
d
the
un
iqu
e
ness
of
N
E,
by
fi
xing
each
tim
e
on
e
of
the
pa
ram
eter
s.
The
nex
t
ta
sk
is
to
deter
m
ine
the
pr
ic
e,
Qo
S
an
d
Q
oC
at
equ
il
ibriu
m
.
This
cal
culat
ion
will
b
e
base
d on the
best r
e
spo
nse
algorit
hm
:
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194
3.5.
Pri
ce o
f A
na
rch
y
The
co
nce
pt
of
so
ci
al
welfare
[16],
is
def
i
ne
d
as
the
s
um
of
the
util
it
ie
s
of
al
l
agen
ts
in
t
he
syst
em
s
(i.e.
P
r
ov
i
der
s
)
.
It
is
well
known
in
gam
e
theor
y
that
a
ge
nt
sel
fishness,
suc
h
as
i
n
a
Nas
h
e
qu
il
ib
rium
,
do
e
s
no
t
le
ad
in
ge
ner
al
to
a
so
c
ia
ll
y
eff
ic
ie
nt
sit
uation.
As
a
m
easur
e
of
the
loss
of
ef
fici
ency
du
e
t
o
the
div
e
rg
e
nce
of
us
er
interest
s
,
we
us
e
t
he
P
ri
ce
of
An
a
rc
hy
(Po
A)
[
17
]
,
t
hi
s
la
tt
er
is
a
m
easur
e
of
t
he
l
os
s
of
eff
ic
ie
ncy
due
to
act
ors’
sel
fi
sh
ne
ss.
This
lo
ss
has
be
en
de
f
ined
i
n
[17]
as
the
w
orst
-
case
rati
o
c
om
par
in
g
the
global
ef
fici
en
cy
m
easur
e
(th
at
has
to
be
ch
os
e
n)
at
an
ou
t
com
e
of
t
he
nonc
oope
rati
ve
gam
e
play
ed
a
m
on
g
act
or
s,
to
t
he
op
ti
m
al
value
of
that
ef
fici
en
cy
m
easur
e.
A
Po
A
cl
ose
to
1
ind
ic
at
es
tha
t
the
equ
il
ib
riu
m
is
appr
ox
im
at
ely
so
ci
al
ly
op
ti
m
al
,
and
t
hu
s
t
he
con
se
quen
ces of
sel
fis
h
beh
a
vior
are
relat
iv
el
y
ben
ig
n.
T
he
te
r
m
Pr
ic
e
of
An
a
r
chy
was
first
us
ed
by
K
outso
upia
s
and
Papad
im
it
riou
[
17
]
but
the
idea
of
m
e
asur
i
ng
ineff
ic
ie
ncy
of
eq
uili
br
ium
is
old
e
r.
T
he
c
oncept
i
n
it
s
cu
r
ren
t
form
was
desig
ne
d
to
be
the
anal
ogue
of
t
he
”appr
ox
im
at
io
n
rati
o”
i
n
Appro
xim
a
ti
on
A
lgorit
hm
s
or
t
he
”com
petit
ive
rati
o”
in
O
nline
Algorithm
s.
As
i
n
[18],
we
m
eas
ur
e
the
loss
of
eff
ic
ie
ncy
du
e
to
act
or
s
sel
fishness
as
the
quotient
be
twe
en
the
so
ci
al
welfar
e
ob
ta
ine
d
at
the
Nash e
qu
il
ibri
um
an
d
the
m
a
xim
u
m
v
al
ue
of the
so
ci
al
wel
far
e:
4.
NUMER
IC
A
L IN
VESTIG
ATIO
NS
To
cl
arify
a
nd
s
how
how
to
ta
ke
a
dv
a
nt
age
f
ro
m
ou
r
theo
reti
cal
stud
y,
we
s
ugge
st
to
stu
dy
nu
m
erical
ly
the
m
ark
et
sh
are
gam
e
wh
il
e
con
side
rin
g
the
be
st
resp
onse
dy
nam
ic
s
and
expressi
on
s
of
dem
and
as
well
as
util
it
y
fu
ncti
on
s
of
CPs.
Hen
c
e,
we
c
on
si
der
a
syst
e
m
with
tree
CPs
see
king
to
m
axi
m
iz
e
their
resp
ect
ive
r
e
ve
nu
e
s.
Ta
ble
1 r
epr
ese
nts t
he
s
yst
e
m
p
aram
eter
values
c
onsi
der
e
d
i
n
this
num
erical
stud
y.
Table
1.
Syst
em
p
ara
m
et
ers
us
e
d
f
or
nu
m
erical
ex
am
ples
Figures
1,
2
a
nd
3
prese
nt
r
especti
vely
cu
rv
es
of
the
c
onve
r
gen
ce
to
Nash
E
quil
ibri
um
Pr
ic
e,
to
Nash
E
qu
i
-
li
bri
um
Qo
C
a
nd
to
Nas
h
E
quil
ibriu
m
Qo
S
.
It
is
cl
ear
t
hat
the
best
respo
ns
e
dynam
ic
s
conv
erg
e
s
to
the
uniq
ue
Nash
e
qu
il
ib
rium
pr
ic
e,
QoC
an
d
QoS.
We
al
s
o
rem
a
rk
that
the
s
pe
ed
of
co
nver
gen
ce
i
s
relat
ively
h
ig
h (ar
ound
5 rou
nds a
re e
nough t
o
c
onve
rg
e
to
t
he jo
i
nt price
a
nd QoS
equil
ib
rium
).
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An
alysis of C
omp
et
it
ion Fr
onti
ng
the
P
opul
ar
it
y
…
(
Hamid
Garma
ni
)
195
Figure
1. Pr
ic
e
g
am
e :
Conver
gen
ce
to
t
he Pr
ic
e N
as
h
E
qu
il
ibriu
m
Figure
2. Q
oC
gam
e : Con
ve
r
gen
ce
to
t
he Q
oC Nash
E
qu
il
ibriu
m
.
Figure
3. Q
oS
gam
e : Con
ve
r
gen
ce
to
t
he Q
oS
Nas
h
E
quil
ibri
um
In
the
f
ollo
wing,
we
discuss
t
he
i
m
pact
of
the
syst
e
m
par
am
et
ers
on
the
syst
e
m
eff
ic
ie
ncy
in
te
r
m
s
of
P
rice
of
A
nar
c
hy
(PoA
).
Figure
4
an
d
5
plo
t
the
va
riat
ion
cu
rve
of
P
oA
with
r
espect
to
an
d
wh
ic
h
represe
nts
the
sensiti
vity
of
CPi
to
his
pr
ic
e
pi
an
d
his
cr
edibili
ty
ci
.
In
these
fig
ures,
we
first
no
ti
ce
that
the
PoA
inc
reases
w
hen
an
d
i
nc
reases,
the
fact
that
the
PoA
increases
with
an
d
fi
nds
the
si
m
ple
intuit
ion
tha
t
increasin
g
the
sensiti
vity
of
CPs
to
t
heir
pr
ic
es
an
d
t
heir
cred
i
bili
ti
es
giv
es
m
or
e
a
nd
m
or
e
fr
ee
do
m
to
CP
s
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196
for
opti
m
iz
ing
the
Nas
h
eq
uili
br
ium
.
Wh
e
n
=
11
=
22
=
33
=
1
a
nd
=
11
=
22
=
33
=
1,
in
the
oth
e
r
word,
wh
e
n
the
se
ns
i
ti
vity
of
an
CP
to
the
pr
ic
es
of
it
s
com
petit
o
rs
is
zero,
P
oA
converges
to
1
an
d
the
e
qu
il
ibriu
m
is ap
prox
im
at
e
ly
so
ci
al
ly
o
ptim
al
.
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An
alysis of C
omp
et
it
ion Fr
onti
ng
the
P
opul
ar
it
y
…
(
Hamid
Garma
ni
)
197
5.
CONCL
US
I
O
N AND PE
RSPE
CTIVES
In
t
his
work,
we
pr
ese
nted
and
analy
zed
a
fr
am
ework
to
m
od
el
the
c
om
plex
interac
ti
on
s
am
ong
con
te
nt
pro
vide
rs
as
play
ers
t
hro
ugh
a
cl
ass
of
tw
o
pa
ram
et
er
Nas
h
eq
uili
br
ium
m
od
el
.
The
m
od
el
is
base
d
on
a
sim
ple
lin
ear
dem
and
f
un
ct
io
ns
w
hich
descr
i
be
the
beh
a
viou
r
of
c
us
tom
ers.
T
he
se
f
un
ct
io
ns
ta
ke
int
o
account
not
only
the
cha
rac
te
risti
cs
of
a
c
urren
t
bu
t
al
s
o
of
al
l
ot
her
CPs
in
prese
nc
e
of
t
wo
para
m
et
ers
descr
i
bing
eac
h
CP
se
rv
ic
e
pri
ce
an
d
cre
di
bi
li
t
y
of
c
on
te
nt.
W
e
e
sta
blishe
d
uni
qu
e
ness
of
a
N
ash
eq
uili
br
i
um
po
i
nt
an
d
sho
wed
it
with
rel
evan
t
nu
m
erical
resu
lt
s.
To
quantify
ho
w
ef
fici
ent
is
the
N
E
po
i
nt
we
use
d
PoA
m
easur
em
ent
and
sho
wed
it
s
var
ia
ti
on
acc
ordin
g
to
t
he
par
am
et
ers
of
the
m
od
el
.
O
ur
pro
pose
d
al
gorithm
fin
ds
ver
y
fast
the equil
ibri
um p
rice an
d
t
he
c
on
te
nt cr
e
dib
il
it
y t
o
be
c
hose
n by eac
h
CP
.
This
wor
k
ca
n be
dev
el
op
e
d
t
o
ac
hiev
e t
he f
ollow
i
ng pu
rpo
ses :
a.
Mod
el
in
g
t
he u
sers
c
hoic
e w
it
h
a
nonlinea
r f
un
ct
io
n w
hich i
s b
ase
d on the
Logit
m
od
el
.
b.
In
tr
oduci
ng
ad
ver
ti
sin
g
re
ve
nu
e
s
in
the
ut
il
ity
of
CPs
to
achieve
m
axim
u
m
rev
en
ue.
I
n
2010, a
dverti
sing re
v
-
e
nues
of Go
og
le
are
m
or
e
tha
n
20 b
il
li
on
s
.
c.
Takin
g
i
nto
c
onside
rati
on the
pur
c
hasin
g p
ower
of a ta
rg
et
m
ark
et
for C
Ps
.
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–
198
198
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ec
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the
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;
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olf
;
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“
A
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–
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th
eor
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r
net
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