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.
166~
178
IS
S
N: 22
52
-
8776,
DOI: 10
.11
591/ijict
.
v6
i
3.p
p166
-
178
166
Journ
al h
om
e
page
:
http:
//
ia
esj
ou
r
nal.co
m/
on
li
ne/in
dex
.php
/
IJ
ICT
The Co
mp
etition Betw
een ISPs i
n Presen
ce of the
Net
Neutrali
ty
Mo
hame
d El
Amr
an
i*
, Ha
mi
d G
armani
,
M
ohamed
Ba
slam
,
R
achid
El
A
yachi
Sulta
n
Moul
a
y
S
li
m
ane
Univ
ersity
,
TIAD
La
bor
ator
y
,
Beni
´
Mel
l
al
,
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
20
th
, 201
7
Accepte
d
N
ov
7
th
, 201
7
In
thi
s
work,
w
e
pre
sent
an
e
c
onom
ic
m
odel
of
computer
ne
t
works
tha
t
desc
ribe
s
the
i
n
-
te
ra
ct
ion
betw
ee
n
Int
ern
et
Servic
e
Provid
ers
(ISP
),
customers
and
cont
en
t
provid
er
.
Th
e
compet
it
i
on
bet
we
en
ISP
s
m
a
y
b
e
tra
nsla
te
d
b
y
th
e
pric
es
th
e
y
re
q
uire
and
the
qu
a
li
ties
of
service
(QoS
)
they
offe
r.
The
custo
m
er
demand
for
servic
e
from
an
ISP
does
not
onl
y
de
-
pend
on
the
pri
ce
and
qualit
y
of
servi
ce
(QoS
)
of
the
ISP
,
but
it
is
in
flue
nc
ed
b
y
al
l
those
offe
r
e
d
b
y
it
s
compe
ti
tors.
Thi
s
beh
avi
or
has
b
ee
n
ext
ensiv
e
l
y
ana
l
y
z
ed
using
game
the
-
or
y
as
a
dec
ision
supp
ort
tool
.
W
e
in
terpret
a
non
-
neut
ra
l
net
work
when
a
con
te
nt
provide
r
priv
il
e
ges
ISP
s
by
o
ff
eri
ng
th
em
m
ore
bandwidt
h
to
ensure
prope
r
QoS
to
suppor
t
ap
-
pli
c
ations
tha
t
re
quir
e
m
ore
dat
a
tra
ns
port
ca
pa
ci
t
y
(v
oic
e
over
in
te
rn
et
protoc
o
l
(V
OIP
)
the
li
ve
vide
o
strea
m
ing,
onli
ne
gaming).
In
addi
ti
on,
our
wo
rk
foc
uses
o
n
the
pric
e
game
ana
l
y
sis a
nd
QoS
bet
wee
n
ISP
s in
two
ca
s
es:
neut
ra
l
net
w
ork
and
non
-
neut
ra
l
net
work.
Afte
r
show
ing
the
exi
sten
ce
and
unique
ness
of
equi
li
brium
in
te
rm
s
of
qualit
y
of
servi
ce,
we
ana
l
y
z
ed
the
impact
of
n
et
n
eut
ra
li
t
y
o
n
competi
ti
on
b
etw
ee
n
ISP
s.
We
al
so
va
li
da
te
d
our
the
ore
ti
c
al
stud
y
wit
h
num
eri
ca
l
re
sult
s,
which
show
t
hat
th
e
g
ame
ha
s
an
equ
il
ibr
ium
point
whi
c
h
depe
nds on al
l
th
e
par
amete
rs
of
t
he
s
y
s
te
m
.
Ke
yw
or
d:
Eco
no
m
ic
Mod
el
of
Netw
ork
s
Gam
e Th
eor
y
Nash E
qu
il
ib
rium
Net
Ne
utrali
ty
Qu
al
it
y o
f
Se
r
vice(
QoS)
So
ci
al
W
el
far
e
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
:
Moh
am
ed
El
Am
ran
i
TIAD
Lab
or
at
or
y,
Su
lt
a
n
Mo
ulay
Sli
m
ane
Un
i
ver
sit
y
Be
ni´
Mellal
, Mo
r
occo
Em
a
il
:
m
ed.
el
.a
m
ran
@
gm
ai
l.
com
1.
INTROD
U
CTION
Currentl
y
Net
neu
t
rali
ty
is
a
m
ajo
r
iss
ue.
This
pri
nci
ple
is
on
e
of
t
he
f
ounders
of
the
In
te
r
net
,
enab
li
ng
excl
udes
a
ny
discri
m
inati
on
of
da
ta
transm
it
te
d
over
the
net
work.
This
co
ncep
t
is
no
t
cl
early
def
i
ned,
has
a
r
ou
s
ed
great
de
bate
in
m
any
diff
e
re
nt
place
s
su
c
h
as
the
econom
y,
acade
m
ia
,
la
w,
I
nt
ern
e
t
and
c
ongress
i
ndus
try
.
C
onse
qu
e
ntly
,
net
ne
utrali
ty
has
be
com
e
an
at
tract
ive
cro
s
s
-
c
utti
ng
iss
ue
r
eq
uir
ing
the
ag
gregati
on
of
the
e
ffor
t
of
a
huge
sci
e
nt
ific
com
m
un
ity
from
diff
ere
nt
disci
plines.
The
la
c
k
of
rig
oro
us
bu
t
sim
ple
m
od
el
s,
a
nd
as
c
om
ple
te
as
poss
ible
in
the
relat
ed
do
c
um
entation
wer
e
the
m
ai
n
m
otivati
on
s
f
or
this
w
ork.
The
ne
utrali
ty
of
ne
twork
i
n
the
long
te
rm
was
i
ntr
oduce
d
as
a
res
ult
of
the
c
on
ce
p
t
of
c
omm
on
su
pp
or
t.
T
he
two
m
os
t
com
m
on
ly
po
te
ntial
beh
avi
or
s
ci
te
d
are
the
abil
it
y
of
network
pr
ovi
der
s
to
c
on
t
ro
l
acce
ss
and
pr
ic
ing
of
broa
dba
nd
fa
ci
li
ti
es
an
d
incenti
ve
s
to
pr
om
ote
the
network
of
ow
ne
d
co
ntent,
pla
ci
ng
un
a
ff
il
ia
te
d
c
onte
nt
pro
vid
e
rs
a
t a com
petit
i
ve disad
va
ntag
e [
1].
In
t
his
pa
pe
r,
we
f
oc
us
on
the
im
pact
of
t
he
sec
ond
c
on
du
ct
on
c
om
petit
ion
betwee
n
inter
net
serv
ic
e
pr
ov
i
de
rs.
Se
ver
al
w
orks
ad
dresse
d
the
issue
of
ne
twork
neu
tr
al
it
y
fr
om
diff
eren
t
aspects
[
2]
[3
]
,
[4
]
,
[5
]
,
[
6].
[
1]
prov
i
des
a
ne
w
a
nd
com
pr
e
hensi
ve
i
ns
ig
ht
into
t
he
c
on
te
xt
of
th
e
de
bat
e
on
net
ne
utra
li
ty
.
The
c
on
t
rib
ution
s
that
ar
e
m
os
t
relat
ed
to
ours
a
re
[
2],
[
5],
[
7],
[
8]
an
d
[
9].
In
t
his
pap
e
r,
we
c
on
sider
sever
al
pro
vide
rs
s
har
e
a
m
a
rk
et
a
nd
com
petit
ion
am
on
g
pro
vid
e
r
s
oc
cu
rs
in
pri
ces
an
d
in
te
rm
s
of
th
e
qu
al
it
y
of
ser
vi
ce
they
of
fer.
W
e
ass
um
e
t
hat
the
dem
and
f
or
the
ser
vi
ce
of
a
pa
rtic
ul
ar
internet
ser
vice
pro
vid
er
is
a
f
un
ct
io
n
of
the
vecto
r
of
pr
ic
e
and
qual
it
y
of
serv
ic
e
of
al
l
IS
P
s.
We
est
ablish
the
existe
nce
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
ICT
IS
S
N:
22
52
-
8776
Th
e C
ompeti
ti
on Betw
een
I
SP
s in Pre
se
nce
o
f t
he
Net
Neu
trali
ty
(
Mohamed El A
mr
ani
)
167
and
u
ni
qu
e
nes
s
of
Nas
h
eq
uili
br
ium
fo
r
both
plans
of
n
eutr
al
it
y
or
non
-
ne
utrali
ty
.
W
e
an
al
yz
e
the
eff
ect
s
of
net n
e
utrali
ty
on th
e
in
vo
ic
e
price
and
Q
oS
offe
red as the
b
e
hav
i
or of inte
r
net ser
vice
pro
vid
e
rs.
The
rest
of
th
e
pap
e
r
is
org
anized
as
f
ollo
ws.
I
n
Sect
io
n
2.
,
we
desc
ri
be
the
m
od
el
of
disco
r
d
betwee
n
inter
ne
t
serv
ic
e
pr
oviders
a
nd
t
heir
su
bsc
ri
ber
s
,
al
so
,
we
prese
nt
de
finiti
on
of
Na
sh
eq
uili
br
i
um
.
I
n
Sect
ion
s
3.
a
nd
4.
we
pr
ov
i
de
the
or
em
s
for
existe
nce
a
nd
uniq
ue
ness
of
eq
uili
br
ia
res
pecti
vely
in
c
a
se
of
net
neu
tral
it
y
and
non
-
ne
utr
al
it
y.
Sect
ion
5.
prese
nts
num
erical
stud
y
to
validat
e
our
cl
aim
s,
Sect
ion
6.
pr
ese
nts a
stu
dy
o
f
the im
pact of c
om
petition an
d
Sect
io
n 7. co
nclu
des
t
he pape
r.
2.
PROPLE
M MO
DELIN
G
Our
ec
onom
ic
m
od
el
is
com
po
s
ed
of
a
c
onte
n
t
pr
ov
i
der
(
CP
)
and
N
I
nter
net
Ser
vic
e
Pr
ovi
der
s
(
IS
Ps)
in
com
petit
ion
on
a
s
et
of
cust
om
ers.
The
fi
gure
1
il
lustrate
s
a
ty
pical
exa
m
ple
of
syst
em
s
with
a
sing
le
co
ntent
pro
vid
er
n
(
CP)
and
seve
ral
I
nter
net
Serv
ic
e
pr
ovide
rs
w
hi
ch
each
ser
ves
a
set
of
end
use
rs
(
EU)
.
Her
e,
t
he
CP
pro
vid
e
m
ul
tim
edia
con
te
nts
(eg,
m
us
ic
stream
ing
,
V
OIP,
...).
T
his
m
ul
tim
edia
con
te
nt
is
transpor
te
d
a
nd
placed
at
th
e
disposal
of
th
e
EUs
on
the
physi
cal
infr
a
str
uctu
re
of
IS
Pi.
Unde
r
the
ne
utral
netw
ork
c
onfi
gurati
on,
EUs
and
the
co
nten
t
pro
vid
e
r
pay
only
f
or
their
direct
a
ccess.
O
n
one
hand,
a
nd
accor
ding
t
o
the
rate
of
the
own
dem
and
f
or
I
SPi
,
CP
de
ci
ded
t
o
in
vest
an
d
al
locat
e
ba
ndwidt
h
_ic
to
it
.
This can
be
co
ns
ide
red
as a prefe
rr
e
d
co
ntra
ct
is b
et
ween
I
SPi
an
d
CP
.
Y
et
, as
the d
em
a
nd
of
I
SPi
inc
r
eases
as
it
beco
m
es
m
or
e
ben
e
fici
al
to
CP
to
i
nv
e
st
m
or
e
an
d
m
or
e.
On
th
e
oth
er,
eac
h
IS
Pi
cha
r
ges
to
it
s
custom
ers
an
a
m
ou
nt
pi
per
unit
of
tra
ff
ic
.
More
ov
e
r,
eac
h
I
SPi
al
locat
es
a
band
width
_i
to
it
s
custo
m
ers
t
o
gu
a
ra
ntee
th
ei
r
prom
ise
d
Q
oS
~qi.
In
the
re
st,
we
c
ons
ider
t
he
f
ol
lowing
nota
ti
on
s:
f
or
t
he
c
harge
d pr
ic
e
vecto
r a
nd the
prom
is
ed
QoS
res
pecti
vely
.
Figure
1. Sin
gl
e co
ntent
pro
vid
er
and se
ve
ral
inter
net ser
vic
e pro
vid
e
rs
2.1.
En
d
-
to
-
en
d Quali
t
y of
S
ervice
(Qo
S)
The
qu
al
it
y
of
serv
ic
e
(QoS
)
i
s
the
abili
ty
to
transm
it
in
go
od
co
ndit
ion
s
a
giv
e
n
ty
pe
of
t
raffic
,
i
n
te
rm
s
of
avail
a
bili
ty
,
throu
ghpu
t,
tra
ns
m
issio
n
delay
,
j
it
te
r,
pac
ket
loss
rat
e
...
The
gua
ra
ntees
of
t
he
qual
ity
of
se
rv
ic
e
are
i
m
po
rtant
if
the
netw
ork
c
apacit
y
is
ver
y
lim
it
ed,
especial
ly
fo
r
rea
l
-
tim
e
strea
m
i
ng
of
m
ul
tim
edia
app
li
cat
ion
s
su
c
h
as
Vo
ic
e
ove
r
I
P
(V
O
IP
),
onli
ne
gam
ing
a
nd
I
P
-
T
V
.
T
his
la
st
re
aso
n
encou
rag
es
use
rs
to
s
ubscrib
e
to
a
n
ISP
prom
isi
ng
a
good
qu
al
it
y
of
s
e
rv
ic
e.
O
bvio
usl
y,
the
e
nd
-
to
-
end
(e2
e
)
Q
oS
de
pe
nds
on
in
vest
m
ents
of
IS
P
s
and
CP
.
We
cl
aim
that
e
2e
Q
oS
im
plicitl
y
dep
en
ds
on
the
dem
and
Di(:)
for
ISPi
ser
vic
es,
the
am
ou
nt
of
ba
ndwidt
h
reserve
d
i
by
I
SPi
for
E
U
s
a
nd
t
he
am
ou
nt
of
band
width
res
erv
e
d
ic
by
th
e
con
te
nt
pro
vi
der
to
this
I
S
P
.
In
oth
e
r
w
ords,
th
e
e2e
QoS
de
pe
nd
s
on
t
he
per
cei
ved
qual
it
y
on
bo
t
h
li
nk
s
E
U
-
IS
P
a
nd
ISP
-
C
P
.
Ce
rtai
nly,
the
end
-
to
-
en
d
qu
al
it
y
of
ser
vice
ca
n
express t
he
tra
ns
m
issi
o
n
en
d
-
to
-
e
nd d
el
ay
, t
he
e
nd
-
to
-
en
d
t
hro
ughput,
t
he e
nd
-
to
-
en
d
l
os
s
p
r
obabili
ty
o
r
any
com
bin
at
ion
of m
any q
ualit
y of ser
vice in
di
cat
or
s.
Lat
er,
we
will
be
lim
it
ed
to
c
ertai
n
sp
eci
al
cases
wh
e
re
the
end
-
to
-
en
d
qu
al
it
y
of
serv
ic
e
is
si
m
ple
enou
gh (
e
g, th
e en
d
-
to
-
e
nd del
ay
is the su
m
of
delay
s expe
rience
d on bot
h
li
nks E
U
-
ISP
and
IS
P
-
CP
).
2.2.
Dem
an
d
Model
We
c
on
si
der
t
ha
t
the
dem
and
functi
on
Di
(:)
for
the
ISP
ser
vices
is
li
near
with
re
sp
ect
to
pr
ic
e
(p
i
)
fixe
d
by
the
ISPi
and
prom
ise
d
e2e
Q
oS
,
see
[10].
T
h
is
de
m
and
al
so
de
pe
nds
on
pr
ic
e
p
i
an
d
e
2e
Q
oS
of
com
petit
or
s,
nam
el
y,
the
de
m
and
functi
on
de
pe
nd
s
on
p
an
d
q~.
Nat
ural
ly
,
the
dem
and
f
unct
ion
Di
is
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168
decr
easi
ng
w.r.
t
pi
and
increas
ed
w.r.t
p
i,
w
hi
le
i
t
is
increasing
w.
r
.t
q~i
an
d
it
is
decr
easi
ng,
w.r.t
q~
i.
We
consi
der that
t
he dem
and
fu
nc
ti
on
s
w.r.t the
I
SPi
ser
vice c
an be
wr
it
te
n
a
s foll
ow
s:
wh
e
re
α
ⅈ
is a
posit
ive c
on
sta
nt
u
se
d
to
en
s
ur
e the
non
-
ne
ga
ti
vity
o
f
the
d
e
m
and
s
on the
fe
asi
ble r
e
gion.
The
as
su
m
ption
1
is
reali
sti
c
and
ha
s
no
im
pact
on
the
fie
ld
of
a
ppli
cabil
it
y
of
this
w
ork.
I
nd
ee
d,
consi
der
i
ng
t
ha
t
the
influ
e
nc
e
of
e
2e
Q
oS
prom
ise
d
by
the
IS
Pi
on
it
s
gai
ns
m
or
e
weig
ht
relat
ive
to
the
su
m
of
th
e
infl
uen
c
es
of
prom
ise
d
e2e
Q
oS
by
I
SPs
com
petit
or
s
on
I
SPi
gains.
T
his
co
ndit
ion
c
ou
l
d
t
he
n
ta
ke
into
acco
unt
the
prese
nce
of
loya
lt
ie
s
of
custom
ers
and
/
or
par
ti
al
knowle
dge
of
e2e
QoS
of
com
petit
or
s.
More
ov
e
r,
this
assum
ption
is
a
reasonable
c
onditi
on
wh
ic
h
gu
a
ran
te
es
s
uperm
odularit
y
of
the
gam
e
an
d
So
the uniq
ue
ness
of Nash
equil
ibri
um
.
Con
si
der
i
ng
th
e
desire
of
pay
ing
c
us
tom
ers,
it
beco
m
es
pla
us
ible
to
c
on
si
der
that
the
t
otal
dem
an
d
is
in
-
creasi
ng
de
pendin
g
on
in
div
id
ual
e2e
Q
oS
fixe
d
by
I
SP
i.
W
he
n
the
I
SPi
decide
s
to
decr
ease
it
s
qu
al
ity
of
se
r
vice,
at
ta
ched
c
us
t
ome
rs
w
ould
be
m
igrated
an
d
s
ub
sc
ribe
with
it
s
com
petit
or
s
or
dec
ide
t
o
un
s
ubscri
be.
I
n
oth
e
r
wor
ds
,
this
ass
um
pti
on
say
s
t
hat
th
e
effe
ct
of
t
he
e2e
Q
oS
in
di
vidual
is
sti
ll
highe
r
than
the
overal
l
per
cei
ve
d
in
f
luence
from
c
om
petit
or
s.
A
n
i
m
po
rtant
c
ha
racteri
sti
c
is
that
the
var
ia
ti
on
of
the
total
dem
and,
com
par
e
d
to
in
div
i
dual
e2e
Q
oS
i
s
ver
y
lo
w,
because
fe
w
custom
ers
dec
ide
to
un
s
ubscri
be
c
om
ple
te
ly
.
The
num
ber
of
com
petit
or
s
c
an
in
flue
nce
t
he
dem
and
for
a
par
ti
c
ular
ISP
i
in
a
rem
ark
abl
e
m
ann
er
wh
e
n
t
he
nu
m
ber
beco
m
es
bigger
an
d
vi
ce
ver
sa
,
i.e.
of
the
s
um
of
t
he
m
utu
al
sensiti
viti
es
to
it
s
com
petit
or
s
qu
al
it
y
of
serv
ic
e
beco
m
e
ver
y
cl
os
e
to
that
of
the
I
SP
i
,
so
t
hat
de
fer
e
nce
sensiti
viti
es
can
be
bounde
d by th
e inv
e
rse o
f
the
total
num
ber
of these
co
m
petit
or
s.
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Th
e C
ompeti
ti
on Betw
een
I
SP
s in Pre
se
nce
o
f t
he
Net
Neu
trali
ty
(
Mohamed El A
mr
ani
)
169
2.3.
Ut
il
it
y M
od
el
We
tur
n
now
to
ta
ke
the
util
it
y
fu
nctio
n
of
each
I
SP
s
and
the
sin
gle
CP
.
Let
qi
(en
d
-
to
-
e
nd
qu
al
it
y
of
s
er
vi
ce)
the
real
qual
it
y
per
cei
ve
d
by
the
EUs
of
ISPi
,
(
In
t
his
case
q~i
is
the
QoS
pr
om
i
sed
/
adv
e
rtise
d
by
t
he
I
SPi
for
e
nd
us
ers
).
The
net
re
venue
of
ISPi
is
exactl
y
the
dif
fer
e
nc
e
betwee
n
it
s
t
otal
rev
e
nue
a
nd
it
s
ex
penses.
Th
ese
la
tt
er
co
rr
e
sp
on
d
to
the
s
um
of
the
c
os
t
s
to
c
ov
e
r
th
e
costs
of
ba
ndw
idth
i
and a ce
rtai
n p
enalt
y i
f
it
d
oe
s
not m
eet
p
rom
ise
d
qual
it
y
q
i
. T
hus, net
re
venue is
g
i
ven
by as
fo
ll
owin
g:
2.4.
Gam
e
Analysis
In
the
re
st
of
this
wor
k,
we
w
il
l
analy
ze
the
gam
e
that
arises
in
bo
th
th
e
est
ablishm
ent
of
neu
t
rali
ty
and
no
n
-
ne
utra
li
ty
.
The
play
e
rs
a
re
the
I
SP
s
that
m
us
t
to
def
i
ne
thei
r
str
at
egies
f
or
the
pri
ce
(
pi)
and
the
prom
ise
d
qu
al
it
y
of
serv
ic
e
(q
i
)
.
The
con
ce
pt
of
ne
utrali
ty
is
con
side
re
d
ass
um
ing
that
the
CP
distribu
te
s it
s
band
width
as
t
he
pro
-
c
esso
r
sh
ari
ng
pri
nci
ple.
In
an
ot
her
ha
nd,
t
he
non
-
ne
utrali
ty
scen
ari
o
is
ta
ken
int
o
account
by
ass
um
ing
that
there
is
one
(m
or
e
)
sp
eci
fic
IS
P
(
s)
(n
a
m
el
y
IS
P
1
)
who
sig
ne
d
a
con
t
ract
with
the
CP
,
in
ord
er
t
o
r
eser
ve
him
a
am
ou
nt
of
ba
ndwidt
h
to
en
s
ur
e
the
prom
is
ed
qu
al
it
y
of
s
erv
ic
e
(
q~
1)
.
I
n
this
con
te
xt,
the
co
m
pet
it
o
rs
of
I
SP
1
e
qu
al
ly
s
har
e
the
rem
ain
in
g
band
widt
h
as
i
f
we
have
ne
utrali
ty
case
by
ta
kin
g i
nto acc
ount the
to
po
l
ogy w
he
n we
do not h
a
ve
t
he
I
SP
1.
w
he
n
t
he vect
or
of
pri
ce pa
ra
m
et
ers,
p
,
of al
l pro
vid
er
s is
fixed to a
certai
n p
red
et
erm
ined
point.
Be
low,
we
a
na
ly
ze
the
co
m
petit
ive
qu
al
it
ie
s
of
ser
vice
f
or
N
IS
Ps
that
m
a
xim
iz
e
their
util
ities.
To
do
s
o,
we
de
m
on
strat
e
the
existe
nce
a
nd
un
i
qu
e
ness
of
the
gam
e
equ
il
ibriu
m
between
N
ISPs,
aft
er
w
e
cal
culat
e
the
equ
il
ib
rium
po
int.
To
a
naly
ze
equ
il
ib
rium
of
the
gam
e,
w
e
need
t
o
fin
d
prop
e
rtie
s
on
the
util
it
y fu
nctio
n w
hich re
qu
ire
that we
desc
rib
e the e
xpressi
on in
both
cases
.
2.5.
Le
arnin
g Na
s
h eq
uil
ibri
um
In
[
8,
3,
7,
10
]
,
the
m
ai
n
con
cer
n
was
the
searc
h
f
or
the
eq
uili
br
ium
sit
uations
(
nam
e
ly
Nash).
Lat
el
y
research
ers
a
re
quest
ion
i
ng
the
nee
d
fo
r
c
onve
rg
e
nc
e
of
a
le
arn
i
ng
al
gorithm
to
a
Nash
e
qu
il
ib
rium
,
there
a
re
se
veral
reasons
for
this.
First,
t
here
m
a
y
the
m
ulti
ple
equ
il
ib
ria
in
a
gam
e,
an
d
it
can
no
t
a
ny
m
et
ho
d f
or
c
oo
rd
i
nating ch
oic
e of a
gen
t.
Lear
ni
ng
al
go
r
it
h
m
s
rese
m
ble
the
beh
a
vior
of
com
petit
or
s
in
m
any
nat
ur
al
ly
arisi
ng
gam
es,
and
thu
s
res
ults,
on
the
co
nver
gen
ce
or
no
n
-
co
nver
gen
ce
pro
per
ti
es
of
su
c
h
dynam
ics
m
ay
info
rm
our
unde
rstan
ding
of
the
a
ppli
cab
il
ity
of
Nas
h
e
qu
il
ib
ria
as
a
pl
ausible
so
l
utio
n
co
nce
pt
in
som
e
set
t
ing
s.
In
the
reali
ty
,
wh
en
e
ver
y
I
SP
trie
s
to
m
axi
m
iz
e
its
rev
e
nu
e
,
it
is
the
m
os
t
natur
al
to
acce
pt
N
ash
eq
uili
br
i
um
as
the
opti
m
al
so
luti
on
c
on
ce
pt.
In
Nas
h
eq
uili
br
i
um
,
each
ISP
’s
strat
egy
is
the
best
res
pons
e
t
o
the
oth
e
r
IS
P
s’s
strat
e
gies.
Th
us
no
I
SP
ca
n gain
from
u
ni
la
te
ral d
eviat
ion.
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ber
201
7
:
166
–
178
170
3.
NEUT
RA
L
N
ET
WORKS
Rem
e
m
ber
that
for
the
s
ha
rin
g
ca
pab
il
it
y
of
ISP
s
under
th
e
Process
Sh
a
r
ing
(
P
S
)
pri
nc
iples,
ɸⅈ
is
giv
e
n by com
bin
ing b
oth t
he
expressi
on of
Delay
in
the
li
nk
s
bet
wee
n
I
S
Pi an
d
E
Us (L.
K
le
in
ro
c
k [11
]
)
Th
us
:
wh
e
re
ci
is t
he e
xp
ect
e
d delay
in
the
li
nk
between
I
SPi
a
nd
CP
.
The
e
nd
-
to
-
e
nd
delay
(
deno
te
d
)
ex
pe
rien
ced
by
e
nd
use
rs
of
the
I
SP
i
,
nam
el
y,
the
cum
ulati
ve
delay
on
both
li
nks
EU
-
I
SPi
a
nd
I
SPi
-
CP
,
de
pends
on:
the
total
dem
and
f
or
ser
vices
of
,
the
dem
and
f
or
se
rv
ic
es
tra
nspor
te
d
by
,
the
ba
ndwidt
h
al
loca
te
d
by
the
the
band
width al
lo
cat
ed
by
I
SPi
t
o
it
s c
us
tom
ers:
The
quest
io
n
is,
unde
r
gener
al
assum
ption
s,
wh
e
n
can
we
gu
ara
ntee
the
existe
nce
an
d
un
i
qu
e
ne
s
s
of
t
he
eq
uili
br
i
um
du
e
thr
ough
the
ISP
s
?
We
co
ns
i
der
t
hat
the
qu
al
it
y
of
se
r
vice
is
the
only
pa
ram
et
er
of
the
gam
e
(7
)
wh
ic
h
ar
os
e
w
hen
the
pr
ic
e
of
al
l
ISP
s
i
s
fixed.
Th
us
,
unde
r
the
assum
ption
1
a
nd
acc
ordi
ng
to
the
rem
ark
1,
we
ha
ve
the
fo
ll
owin
g
ge
ne
ral
resu
lt
on
un
i
qu
e
ness
of
qu
al
it
y
of
se
rvi
ce
based
on
Nas
h
equ
il
ib
rium
f
or all
N
ISP
s.
Le
mma
1
(Exi
stence)
Co
ns
i
derin
g
t
he
game
of
le
vel
s
of
qualit
y
of
se
rvi
ce
which
ar
os
e
w
hen
the
pr
ic
e
vect
or
is
fi
xed
for
all
I
SP
s
,
t
here
exi
sts
i
n
l
ess
one
qualit
y
of
servi
ce
bas
ed
N
as
h
eq
uili
br
iu
m
q~
*
,
of
I
SP
s’s game.
Le
mma
2
(Un
iqueness)
O
n
the
ass
um
ption
1
an
d
acco
r
ding
to
the
rem
ark
1,
the
eq
uili
bri
um
po
int
q~
*
,
of
th
e g
am
e o
f
I
S
P s,
w
hich
aris
es whe
n
the
price
v
ect
or is
fix
ed
to
all
I
SP
s
, i
s uniq
ue.
unde
r
le
m
m
as (
1,
2)
,
w
e
d
e
du
ce the
fo
ll
owin
g
the
orem
:
Theorem
1
(e
xistence
and
uniquenes
s)
C
on
si
der
t
he
ga
m
e
of
le
vels
of
qual
it
y
of
ser
vice(
7)
wh
ic
h
aro
s
e
wh
e
n
t
he
pr
ic
e
vect
or
is
fi
xed
to
al
l
ISP
s,
unde
r
t
he
ass
umpti
ons
1,
3
an
d
acco
rd
i
ng
to
the
rem
ark
2,
t
he
r
e
is
on
ly
on
e
le
ve
l
of
qual
it
y
of
serv
ic
e
base
d
Nash
e
qu
il
ib
rium
q~
of
the
IS
P
s’s
gam
e.
(the
pro
of
is
gi
ve
n
by
app
e
ndic
es
A
a
nd B)
4.
NON
-
NEUT
R
AL N
ET
W
O
RKS
As
we
m
entione
d
in
sect
io
n
2
,
in
no
n
-
neu
t
ra
l
networks
we
assum
e
that
there
is
a
sp
eci
fi
c
IS
P
(i.e.
IS
P
1
)
w
ho
si
gned
a
s
pecial
con
t
ract
with
CP
,
to
reserve
f
or
him
a
qu
ant
it
y
of
bandw
i
dt
h
to
guara
ntee
the
prom
ise
d
qu
al
i
ty
of
se
r
vice
q~1
.
U
nd
e
r
a
non
-
neu
tral
sys
tem
,
the
I
SP
1
will
gu
a
ra
ntee
the
pr
om
ise
d
QoS
,
and
the
re
fore,
the
expressi
on
of
the
value
of
IS
P
1
bec
om
es
si
m
pler
since
q~i
=
qi
i.e
.
no
pe
nalty
do
es
no
t
app
ea
r
i
n
the
fun
ct
io
n uti
li
ty
o
f
the
ISP1
:
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
ICT
IS
S
N:
22
52
-
8776
Th
e C
ompeti
ti
on Betw
een
I
SP
s in Pre
se
nce
o
f t
he
Net
Neu
trali
ty
(
Mohamed El A
mr
ani
)
171
In
t
his
co
ntext,
the
com
petit
or
s
of
t
he
ISP1
,
e
qu
al
ly
sh
a
re
th
e
rem
ai
nin
g
ba
ndwidt
h.
In
t
he
abse
nce
of
the
ISP1
,
th
e
net
work
behaves
a
s
a
ne
utr
al
netw
ork
w
he
re
oth
e
r
IS
P
s
are
com
peting
over
the
com
m
on
band
width.
T
he
util
it
y
fu
nction
of
ot
her
i
ntern
et
se
rv
ic
e
pro
vid
e
rs
(
ISP1
com
petit
or
s)
is
giv
e
n
by
eq
ua
ti
on
(11).
The
or
em
2
(e
xi
ste
nce
an
d
un
iqu
e
ness
)
Co
nsi
der
t
he
gam
e
of
qual
it
y
le
ve
ls
for
se
rv
ic
e
s
(
7)
t
hat
arises
with
ou
t
net
neu
t
rali
ty
.
Unde
r
the
assu
m
pt
ion
1
an
d
accor
ding
to
the
rem
ark
1,
there
is
one
le
ve
l
of
Nash
e
quil
ibri
um
qu
al
it
y
of
serv
ic
e
there
fore
th
e
util
it
y
fu
nctio
n
of
IS
P
s
sat
isfie
s
the
prop
e
rt
ie
s
of
con
ca
vity
and
un
i
qu
e
ness
. (t
he
proof i
s
giv
e
n by ap
pe
nd
i
x C
)
5.
NUMER
IC
A
L RES
ULTS
We
tu
rn
now
to
disc
us
s
ho
w
to
ta
ke
a
dv
antage
of
our
analy
ti
cal
resul
ts.
W
e
pro
pos
e
to
stu
dy
nu
m
erical
ly
the
m
ark
et
sh
a
re
gam
e
ta
kin
g
a
ccount
of
previ
ou
s
ex
pressi
on
s
of
dem
and
f
unct
ions
a
nd
uti
li
ty
of
the
I
SP
s.
To
il
lustrate
,
we
co
ns
ide
r
two
ho
m
og
e
ne
ou
s
IS
P
s
lo
okin
g
to
m
axi
m
iz
e
their
res
pecti
ve
payo
ff
s
.
I
n
pa
r
ti
cular,
we
dis
cuss
t
he
i
nf
lue
nce
of
the
pe
na
lt
y
factor
i
a
nd
the
band
widt
h
of
the
C
P
in
cases
of
neu
t
rali
ty
and
no
n
-
neu
t
rali
ty
.
The
fi
gures
2
an
d
3
re
pr
ese
nt
res
pecti
vely
the
curves
of
t
he
co
nver
ge
nc
e
to
Nash
e
qu
il
ib
rium
e2e
Q
oS
in
bo
t
h
ne
utral
an
d
non
-
ne
ut
ral
net
wor
k,
it
is
cl
ear
t
hat
the
be
st
res
po
ns
e
dynam
ic
al
go
rithm
1
converg
ence
to
t
he
uni
qu
e
Nas
h
e
qu
i
li
br
ium
e2e
Q
oS
,
i
n
bo
t
h
ca
ses,
we
al
so
noti
ce
the
co
nv
e
rgenc
e
sp
eed
is
r
el
at
ively
fast
(6
it
erati
on
s
for
the
neu
t
ral
case
an
d
5
it
erati
ons
f
or
the
non
-
ne
ut
ral
case).
S
o
this
si
m
ulati
on
of
th
e
al
go
rithm
1
i
s
able
to
eff
ic
ie
ntly
con
ve
r
ge
the
Nash
e
qu
il
ibriu
m
e2e
QoS
in
neu
t
ral an
d n
on
-
ne
utral n
et
w
ork.
5.1.
I
mp
act o
f the
QoS pe
na
l
ity fa
c
t
or
The
fig
ures
4
and
5
represe
nt
the
var
ia
ti
on
of
the
e2e
QoS
at
equ
il
ibrium
and
par
ti
ti
on
in
g
of
t
he
total
dem
and
a
t
equ
il
ib
rium
po
i
nts
w
.r.t
pe
nalty
factor
,
we
no
te
f
or
nu
ll
values
pe
nalty
factor
,
al
l
I
SP
s
,
ov
e
r
ne
utrali
ty
or
non
-
ne
utral
it
y
cases,
ha
ve
the
sam
e
resu
lt
s
of
e
2e
QoS
(resp.
of
the
de
m
and
par
ti
ti
oning).
And
as w
e
see
,
the
cha
nges
in
the
e2e
Q
oS
is
si
m
il
ar
to
tho
s
e
of
d
em
and
parti
ti
on
in
g,
w
hi
ch
is
norm
al
since
the
dem
and
Di(:)
of
IS
Pi
is
propo
rtion
al
to
it
s
e2e
QoS
(q
~i
).
H
ow
e
ve
r
the
increased
penal
ty
factor
reduces
the
e2e
Q
oS
(
Re
sp
.
dem
and
par
ti
ti
on
i
ng)
w
hich
is
norm
al
,
by
that
t
he
i
nc
rease
of
this
fa
ct
or
push
e
s
I
S
P
s
i
n
a
neu
t
ral
netw
ork
to
m
ini
m
ize
the
dif
fer
e
nc
e
betwee
n
pr
om
ise
d
QoS
an
d
real
Qo
S
,
un
ti
l
that
IS
P
s
in
this
reg
im
e
hav
e
fo
r
s
ub
sc
ribe
rs
that
these
fait
hful
EUs
(a=
500)
f
or
sm
al
l
value
of
e2e
QoS.
Th
us
f
or
non
-
pr
i
vileged
ISP
2,
t
he
inc
reasi
ng
of
this
fact
or
has
m
or
e
i
m
pact
on
this
IS
P
c
om
par
ed
to
I
SP
s
of
ne
utral
netw
ork,
t
he
i
nc
rease
of
t
his
f
act
or
m
ay
even
pu
s
h
t
he
E
U
s
of
this
IS
P
to
m
igrate
to
a
no
ther
IS
P
offe
ring
a
sign
ific
a
nt
e2e
Qo
S
or
to
unsu
bsc
ri
be
com
plete
ly
.
These
i
m
pacts
of
the
increas
e
d
pe
na
lt
y
factor
for
the
non
-
pri
vilege
d
ISP2
ha
ve
a
n
inv
e
rse
im
pact
f
or
t
he
pr
i
vileged
I
SP
1,
w
hich
al
lo
ws
it
t
o
offe
r
a
sig
nificant
e2e
QoS a
nd get
a larg
e
m
ark
et
sh
are
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2252
-
8776
IJECE
Vol.
6
,
No.
3
,
Decem
ber
201
7
:
166
–
178
172
5.2.
I
mp
act o
f the
availa
ble
ba
n
dwi
dt
h
ɸ
c
The
m
ai
n
te
xt
form
at
con
sist
The
fi
gure
6
re
pr
ese
nts
the
e
2e
QoS
va
riat
io
n
w.r.t
the
bandw
i
dth
ɸc
,
we
no
te
t
hat
f
or
sm
all
band
width
val
ues
betwee
n
(16
00
-
3000)
,
I
SP
s
in
a
ne
utral
netw
ork
or
a
non
-
pr
i
vileged
ISP
2
can
not
choos
e
la
rg
e
e2e
QoS,
H
oweve
r,
th
e
CP
do
es
no
t
hav
e
a
la
r
ge
ba
ndwidt
h
to
en
sur
e
e2e
Q
oS
pr
om
i
sed
by
t
he
pri
vi
le
ged
I
SP
1
,
e
ve
n
-
if
it
ch
ooses
e2e
Q
oS
as
m
uch
a
s
possible
accor
ding
to
t
he
c
band
width
ar
ri
ving
t
o
c
hoos
e
q
~
m
ax
,
and
f
or
ba
ndwi
dth
va
lues
(b
et
ween
3000
a
nd
78000),
the
I
SP
s
of
a
neu
t
ral
netw
ork
are
incr
easi
n
g
their
e2e
QoS
in
a
rem
ark
able
m
ann
er
with
resp
ect
to
t
he
I
SP
2
non
-
ne
utra
l
netw
ork u
ntil
all
ISP
s c
hoos
e
q
~
m
ax
, Th
is i
s the case
where
the
band
width r
ang
e
s fr
om
(
78000
-
2000
00).
F
igure
7
sho
w
s
the
dem
and
pa
rtit
ion
in
g
bet
ween
I
SP
s
w.r
.t
the
ba
ndwidt
h
c
,
we
no
te
th
at
for
I
SP
s
in
a
neu
t
ral
ne
twork
ha
ve
th
e
sam
e
de
m
and
s
a
nd
pro
porti
on
al
ly
inc
rease
with
c
unti
l
7800,
a
nd
dem
and
is
const
ant
f
or
al
l
ISP
s.
F
or
no
n
-
ne
utral
net
w
ork,
a
nd
f
or
s
m
al
l
ban
dw
i
dt
h
val
ues
(
betw
een
16
00
a
nd
3000)
,
ISP
s
in
a
neu
t
ral
net
w
ork
or
non
-
pri
vilege
d
ISP
2
ca
n
no
t
c
hoos
e
great
val
ues
of
the
e
2e
QoS
,
ho
wev
e
r,
th
e
CP
does
not
ha
ve
a
la
rg
e
ba
ndwidt
h
to
e
nsure
prom
ise
d
e
2e
QoS
of
the
pr
i
vileged
I
SP
1
,
eve
n
-
if
t
his
l
at
ter
choose
a
la
r
ge
st
e2e
QoS
po
ssible
w
.r
.t
ba
ndwidt
h,
getti
ng
to
c
hoo
se
q
~
m
ax
,
and
f
or
ba
ndwidt
h
va
lues
(b
et
ween
3000
an
d
78
000),
t
he
I
SP
s
of
a
neu
t
ral
net
wor
k
are
incre
asi
ng
their
e2e
Q
oS
in
a
rem
ark
a
ble
m
ann
er
w.r.t
the
I
SP
2
in
no
n
-
ne
utral
netw
ork
unti
l
al
l
ISP
s
ch
oose
q
~
m
ax
,
i
t
is
the
case
of
a
band
widt
h
betwee
n 780
00
an
d 200
000.
Figure 6
. I
m
pact
of
t
he
a
vaila
ble
ba
ndwi
dth
ɸc
on
equ
il
ib
rium
Q
oS
Figure
7.
Im
pact
of
the
avai
la
ble
ba
ndwidt
h
ɸc
of the CP
on p
arti
ti
on
in
g dem
and
F
igure
8
re
pre
sents
the
net
re
venue
of
the
I
SP
s
w.r.t
the
c
ba
ndwidt
h,
i
n
the
ne
utral
ne
twork
,
the
IS
P
s
e
quit
abl
y
sh
ar
e
the
ne
t
re
venue
bet
w
een
t
hem
.
Howev
e
r,
the
pri
vileged
I
SP
1
(i
f
the
no
n
-
ne
utrali
ty
)
at
tract
s a larg
e
m
ark
et
sh
a
re
w
hich
im
po
ve
ris
hed
t
he net re
ve
nu
e
of the
ISP
2
. W
e
rem
ark
that ther
e
are
t
hree
reg
im
es
m
a
inly
du
e
to
the
va
riat
ion
of
the
e
2e
Q
oS
,
well
,
us
ua
ll
y
wh
en
t
he
I
SP
s
ch
oos
e
q
~
m
a
x
,
we
no
t
e
that
there
is
a
ce
rtai
n
dif
fer
e
nce
in
net
re
ve
nue
du
e
to
the
ab
sence
of
pe
nalty
on
qu
al
it
y
of
se
r
vice,
but
this
diff
e
re
nce
will
disa
pp
ea
r
wh
e
n
band
width
c
te
nd
s
to
gr
eat
values
.
Com
par
ed
with
the
re
su
lt
s
of
net
re
ve
nue
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
ICT
IS
S
N:
22
52
-
8776
Th
e C
ompeti
ti
on Betw
een
I
SP
s in Pre
se
nce
o
f t
he
Net
Neu
trali
ty
(
Mohamed El A
mr
ani
)
173
wh
e
n
pri
ce
ch
ang
e
s
with
fi
xe
d
e2e
QoS
,
th
e
resu
lt
s
of
our
stud
y
will
al
low
I
SP
s
to
ach
ie
ve
sign
i
fican
t
net
rev
e
nue.
Figure
8. Im
pact o
f
the a
vaila
ble b
a
ndwi
dth
ɸc
of the C
P
on the
n
et
re
venue
5.2.1.
Neu
tr
al
setup V
S. no
n
-
neu
tra
l
setu
p
To
giv
e
pr
i
or
it
y
to
it
s
con
te
nt
s
ov
e
r
that
of
the
I
SP
2
,
T
he
I
SP
1
sig
ne
d
a
s
pecial
co
ntract
with
the
con
te
nt
pro
vide
r.
T
his
co
ntra
ct
can
be
c
onsi
der
e
d
as
ro
a
db
locks
or
sho
rtcuts
de
fine
d
by
the
CP
to
disc
er
n
the
con
te
nt
of
the
ISP
1
.
Fig
ures
6
an
d
7
il
lustrate
resp
ect
iv
el
y,
the
change
in
e2e
QoS
,
a
nd
the
dem
ands
at
the
Nas
h
e
quil
ibriu
m
,
by
va
r
yi
ng
the
qual
it
y
of
c
ba
ndwi
dth
offere
d
by
CP
.
We
no
te
that
the
e
qu
il
ib
rium
e2e
Q
oS
for
al
l
ISP
s
in
a
n
e
utral
netw
ork
and
a
no
n
-
ne
utral
netw
ork
in
crease
with
c.
A
sp
eci
al
featu
re
is
that
the
e2e
Q
oS
at
equ
il
ibri
um
of
non
-
ne
utr
al
it
y
are
m
or
e
im
po
rtant
than
the
e2e
Q
oS
i
n
a
neu
tral
netw
ork.
This
enc
oura
ge
s
custom
ers
t
o
purc
hase
ser
vices,
w
hich
e
xp
la
in
s
the
in
c
rease
in
total
de
m
and
in
non
-
neu
t
ral
netw
orks.
Ot
he
rw
ise
,
the
ISP
1
has
m
or
e
pow
er and bec
om
e
s the m
ast
er o
f t
he
m
ark
et
, g
iv
ing
it
the a
bili
ty
to
offer
ser
vices
with
bette
r
qu
al
it
y.
This
causes
at
tract
new
su
bs
c
ribe
rs,
r
edu
ci
ng
dem
a
nd
f
or
the
ISP
2
and
even
it
s
tur
nover.
Wh
en
c
is
relat
ively
lo
w
an
d
not
su
f
fici
ent
to
ans
wer
to
the
tot
al
de
m
and
,
th
e
ISP
2
without
pri
vileged
c
ontract
m
akes
le
ss
than
it
s
com
petito
r,
this
c
om
e
s
from
a
la
ck
of
ba
ndwi
dth
wa
s
consum
ed
by
t
he
I
SP
1
.
We
note
that
w
he
n
t
he
c
on
te
nt
pro
vid
e
r
m
anag
es
an
e
norm
ou
s
ba
ndwidt
h
to
a
nswer
the
total
de
m
a
nd,
the
m
easur
es
of
ne
utrali
ty
m
ee
t
the
m
e
asur
e
s
of
non
-
neu
t
rali
ty
.
Thus,
the
ISP
1
ha
d
no
reason
to
in
ves
t
in
the
sign
in
g
of
a
pri
vilege
d
co
ntract
sinc
e
the
two
re
gi
m
es
(n
eutral
a
nd
non
-
ne
utral
)
give
the sam
e resu
lt
.
5.2.2.
N
on
-
ne
ut
r
ality
sus
ta
i
ns m
onop
olist
ic
a
nd
unfair
compe
titio
n
The
fig
ur
e
8
r
epr
ese
nts
t
he
ne
t
rev
e
nue
of
t
he
bo
t
h
inter
ne
t
serv
ic
e
pro
vi
der
s
for
t
he
ne
utral
case
and
t
he
no
n
-
ne
utral
case.
Du
e
to
the
abse
nce
of
pen
al
ty
on
the
qual
it
y
of
serv
ic
e
(
Q
oS
s
ince
an
nounce
d
is
encou
ntere
d
in
non
-
ne
utral
co
nd
it
io
ns
)
,
the
I
SP
1
at
tract
s
a
hi
gh
e
r
m
ark
et
sh
are
.
Cl
early
t
his
sit
uation
-
w
here
the
ISP
1
has
a
dvanta
ges
ove
r
the
I
SP
2
is com
plete
ly
u
nf
ai
r
. In fact
, th
i
s in
duces a k
i
nd
of
m
on
opoly po
si
ti
on
a
m
on
g
I
SP
s
.
Howe
ver,
this
m
on
opoly
sit
uation
im
plicit
ly
pr
ohi
bits
th
e
com
petit
or
s
from
entering
the
m
ark
et
b
y
us
in
g unfair c
om
petit
ive p
racti
ces
arisi
ng fro
m
it
s inf
l
uen
ce
on t
he
m
ark
et
as a
pr
i
vileged
I
SP
.
6.
IMP
AC
T
OF
COMPE
TIT
I
ON
6.1.
Pri
ce
of
anarch
y
The
c
on
ce
pt
of
the
so
ci
al
s
urplus
[12]
or
tot
al
cost
[
13
]
,
is
def
i
ned
a
s
the
m
axi
m
u
m
of
the
s
um
of
util
it
ie
s
of
al
l
agen
ts
in
th
e
syst
e
m
s
(i.e.
Pr
ov
i
der
s
).
It
is
well
known
in
gam
e
theor
y
that
sel
fishn
ess
of
th
e
agen
t
,
as
i
n
a
Nash
e
quil
ibri
um
,
ty
pically
do
e
s
not
le
ad
to
a
so
ci
al
ly
eff
ect
ive
sit
uatio
n.
A
s
a
m
easu
re
of
eff
ic
ie
ncy
l
os
s
du
e
to
div
e
r
ge
nce
of
i
nterests
of
use
rs
,
we
use
the
pr
ic
e
of
anar
c
hy
P
oA
[
14
]
,
t
his
la
tt
er
is
a
m
easur
e
of
the
loss
of
eff
ic
ie
ncy
due
to
the
sel
fishn
e
ss
of
the
act
or
s
.
Th
is
loss
was
defi
ned
in
[14]
as
the
rati
o
of
the
w
or
st
com
par
in
g
the
m
easur
e
of
the
overall
eff
ic
ie
ncy
(to
be
sel
ect
ed)
at
the
end
of
non
-
coope
rati
ve
ga
m
e
play
ed
bet
ween
the
act
or
s,
to
t
he
opti
m
um
value
of
thi
s
m
easur
e
eff
i
c
ie
ncy.
A
P o
A
cl
os
e
to
1
in
dicat
es
that
the
e
qu
il
ib
rium
is
abo
ut
s
ocial
ly
op
ti
m
a
l
,
an
d
the
n
the
conseq
ue
nces
of
sel
fish
beh
a
vi
or
are
relat
ively
ben
i
gn.
The
te
rm
pr
ic
e
of
an
arch
y
was
us
e
d
by
K
outso
upia
s
and
Pa
pad
i
m
it
riou
[14].
As
in
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IS
S
N
:
2252
-
8776
IJECE
Vol.
6
,
No.
3
,
Decem
ber
201
7
:
166
–
178
174
[15],
m
easur
in
g
t
he
lo
s
s
of
eff
ic
ie
ncy
due
to
t
he
sel
fishness
of
the
ac
tors
as
th
e
quotient
of
the
s
ocial
welfare
obtai
ne
d
at
the
N
a
sh
equ
il
ib
rium
an
d
the
m
axi
m
um
v
al
ue
of so
ci
al
w
el
far
e:
We
represe
nt
the
var
ia
ti
on
in
the
pr
ic
e
of
an
arch
y
if
the
pr
i
ce
payable
by
ISP
s
is
fixed
(
Figure
9).
The
first
rem
ark
is
t
hat
the
pri
ce
of
a
nar
c
hy
e
xceeds
0.5,
it
m
eans
that
t
he
equ
il
ib
rium
is
so
ci
al
ly
acce
pt
able
for
any
val
ue
of
ba
ndwidt
h,
but
the
pri
ce
of
anar
c
hy
va
ries
accor
ding
to
th
ree
sit
uations.
The
fir
st
when
w
e
hav
e
no
e
no
ug
h
band
width,
t
he
I
SP
s
do
no
t
express
t
heir
sel
fish
beh
a
vi
or.
T
he
sec
ond
sit
uation
wher
e
the
CP
has
a
band
width
m
edium
,
the
ISP
s
are
beco
m
ing
m
or
e
and
m
or
e
sel
fish,
a
nd
the
t
hir
d
one
wh
e
r
e
we
hav
e
a
gr
eat
va
lue
of
t
he
ba
ndwidt
h
c,
the
sel
fish
be
ha
vio
r
w
ea
ke
ns
.
B
ut
ge
ne
rall
y,
ne
utrali
ty
is
so
c
ia
ll
y
good
for
ISP
s
w
hen
the
ba
ndwi
dth
c
is
lo
w,
by
c
ons,
w
hen
c
is
im
po
r
ta
nt,
the
pri
ce
of
ana
rch
y
of
a
non
-
neu
t
ral
net
wor
k
is
higher
co
m
par
ed
to
t
hat
of
the
ne
utral
netw
ork.
Th
us
wh
e
n
c
te
nds
t
o
gr
eat
values
,
each
case o
f neut
rali
ty
b
ecom
e so
ci
al
ly
r
esponsi
ble.
Figure
9
.
I
m
pact o
f
the a
vaila
ble b
a
ndwi
dth
ɸc of t
he
C
P
on the
pri
ce
of
a
nar
c
hy
7.
CONCL
US
I
O
N
We
pr
ese
nte
d
i
n
this
w
ork
a
non
-
c
ooper
at
iv
e
gam
e
m
ark
et
sh
are
.
Eac
h
ISP
re
ports
s
om
e
e2e
Q
oS
ref
e
ren
ce
it
cl
aim
s
to
guara
ntee
to
it
s
s
ubscri
ber
s
.
T
he
n,
eac
h
I
SP
,
ta
king
int
o
a
ccount
the
de
m
an
d
gen
e
rated
,
determ
ines
the
be
st
e2e
Q
oS
m
axi
m
iz
es
it
s
net
rev
e
nue.
I
n
a
dd
it
io
n,
both
ne
utral
(
no
discrim
inati
on
on
t
he
data
flo
wing
th
rou
gh
t
he
net
wor
k)
a
nd
non
-
ne
utral
wh
e
n
s
om
e
sp
eci
fic
ISP
si
gn
ed
a
sp
eci
al
con
t
rac
t
with
the
co
nt
ent
prov
i
der
t
o
f
ocus
it
s
con
-
te
nt.
Ba
sed
on
t
he
Rose
n’s
Superm
odularit
y
conditi
on,
we
pro
ved
t
he
e
xistence
a
nd
uniqu
e
ness
of
a
Nash
eq
uili
br
i
um
fo
r
both
ca
ses.
We
hav
e
s
ho
w
n
nu
m
eri
cal
ly
that
the
non
-
ne
utral
re
gim
e
i
s
ben
e
fici
al
for
EU
s
beca
use
it
inv
olv
es
at
gr
eat
rates
an
d
i
m
pr
oved
qu
al
it
y
of
serv
ic
e.
Howev
e
r,
it
can
sup
port
th
e
m
on
op
olist
ic
and
unfair
co
m
pet
it
ion
betwe
e
n
internet se
r
vice pro
vid
e
rs.
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IJ
-
ICT
IS
S
N:
22
52
-
8776
Th
e C
ompeti
ti
on Betw
een
I
SP
s in Pre
se
nce
o
f t
he
Net
Neu
trali
ty
(
Mohamed El A
mr
ani
)
175
APPE
ND
I
CE
S
a
.
Existence
o
f
T
he Nash
Equil
ibri
um
e
2e
Q
o
S
i
n
Neutral
N
etwork
Pr
oo
f
1
E
qu
at
i
on
(14)
represe
nt
the
seco
nd
de
rivati
ve
of
the
util
ity
fu
nctio
n
11
w.r.t
the
qu
al
it
y
of
serv
ic
e:
The
sec
ond
de
rivati
ve
of
t
he
util
it
y
fu
nction
is
neg
at
ive
,
th
en
the
util
it
y
fu
nctio
n
is
c
on
c
ave,
hence
the ex
ist
e
nce
of the
N
as
h
e
quil
ibriu
m
e2
e Qo
S foll
ows,
[
16
]
B
.
Un
ique
ness
o
f
t
he
Nash
Equ
il
ibri
um
e
2e Qo
S
i
n
Neu
tr
al N
e
twor
k
Pr
oo
f
2
T
he
uniq
uen
e
ss
of
the
e
qu
il
ib
rium
point
is
guara
nteed
i
f
the
uti
li
ty
fu
nctio
n
s
at
isfie
s
th
e
co
ndit
ions
of
Rosen
[
16
]
,
M
ou
li
n
[
17
]
,
de
rive
d
f
ro
m
the
superm
odularit
y
conditi
on
,
wh
ic
h
is
a
nothe
r
al
te
rn
at
ive to
s
at
isfy t
he
co
nd
it
ion
s
of
R
os
e
n:
Th
e
Nas
h
e
quil
ibriu
m
p
oin
t i
s uniq
ue
if:
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