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B
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[
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T
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ati
v
e
w
ater
-
f
il
lin
g
"
t
y
p
e,
to
s
elec
t
th
eir
p
o
w
er
allo
ca
tio
n
b
et
w
ee
n
th
e
av
ailab
le
ch
a
n
n
els
to
m
a
x
i
m
iz
e
th
eir
i
n
d
iv
id
u
al
tr
an
s
m
is
s
io
n
r
ate
[
5
]
.
T
h
e
id
ea
o
f
th
is
p
o
w
er
eliti
s
t
allo
ca
ti
o
n
alg
o
r
ith
m
is
th
a
t
th
e
e
m
itter
s
u
p
d
ate
th
eir
allo
ca
tio
n
p
o
licy
in
t
u
r
n
b
y
o
b
s
er
v
in
g
w
h
at
t
h
e
o
th
er
tr
an
s
m
i
tter
s
h
a
v
e
ch
o
s
e
n
(
in
f
ac
t,
o
b
s
er
v
in
g
a
n
ag
g
r
eg
ate
s
i
g
n
a
l
o
f
t
y
p
e
s
ig
n
al
-
to
-
n
o
is
e
r
atio
is
e
n
o
u
g
h
to
i
m
p
le
m
en
t
t
h
e
al
g
o
r
ith
m
)
.
U
n
d
er
ce
r
tain
co
n
d
itio
n
s
,
th
i
s
iter
ativ
e
a
lg
o
r
it
h
m
co
n
v
er
g
e
s
an
d
w
h
e
n
it
d
o
es,
it
co
n
v
er
g
e
s
to
Nas
h
eq
u
ilib
r
i
u
m
o
f
a
ce
r
tai
n
s
et
[
6
]
.
W
h
eth
e
r
th
e
co
n
tr
o
ller
t
y
p
e
u
n
co
o
r
d
in
ated
ap
p
r
o
ac
h
o
r
th
e
co
o
r
d
in
ated
ap
p
r
o
ac
h
o
f
d
is
tr
ib
u
ted
o
p
ti
m
izatio
n
,
w
e
s
ee
th
at,
u
n
d
er
ce
r
tain
co
n
d
itio
n
s
to
b
e
s
p
ec
i
f
ied
,
t
h
e
Na
s
h
eq
u
ilib
r
i
u
m
ap
p
ea
r
s
,
th
u
s
s
h
o
w
in
g
t
h
e
n
at
u
r
al
l
in
k
b
et
w
ee
n
t
h
es
e
ap
p
r
o
ac
h
es
is
i
m
p
o
r
tan
t
f
o
r
c
o
g
n
iti
v
e
r
ad
io
an
d
g
a
m
e
t
h
eo
r
y
.
C
o
r
r
esp
o
n
d
in
g
l
y
th
e
o
b
s
er
v
atio
n
s
m
ad
e
ab
o
v
e,
th
is
ar
ticle
i
s
o
r
g
an
ized
as
f
o
llo
w
s
.
First,
w
e
d
ef
i
n
e
m
at
h
e
m
a
ticall
y
,
an
d
w
e
p
r
o
p
o
s
e
a
s
i
m
p
lifie
d
class
i
f
icatio
n
o
f
g
a
m
es
t
y
p
e
s
.
T
h
en
w
e
d
escr
ib
e
an
i
m
p
o
r
ta
n
t
s
o
l
u
tio
n
co
n
ce
p
t
o
f
a
g
a
m
e
,
Nash
eq
u
ilib
r
i
u
m
.
Fin
all
y
,
w
e
p
r
ese
n
t
t
w
o
alg
o
r
ith
m
s
t
h
at
h
av
e
b
ee
n
u
s
ed
i
n
th
e
liter
atu
r
e
o
f
co
g
n
iti
v
e
r
ad
io
at
lar
g
e
an
d
co
n
v
er
g
in
g
to
w
ar
d
s
a
b
alan
c
e.
T
h
e
ar
ticle
co
n
clu
d
ed
w
it
h
an
e
x
a
m
p
le
t
h
at
o
f
t
h
e
all
o
ca
tio
n
p
r
o
b
lem
f
o
r
d
is
tr
ib
u
ted
p
o
w
er
co
m
m
u
n
i
ca
tio
n
s
s
ce
n
ar
io
s
m
o
d
eled
b
y
a
m
u
l
tip
le
ac
ce
s
s
ch
a
n
n
el
w
it
h
s
ev
er
al
o
r
th
o
g
o
n
al
s
u
b
ch
a
n
n
els.
2.
M
AT
H
E
M
AT
I
CAL RE
P
R
E
SE
N
T
AT
I
O
N
O
F
T
H
E
G
A
M
E
AND
CL
ASS
I
F
I
CA
T
I
O
N
O
F
T
H
E
M
AIN T
YP
E
S O
F
G
AM
E
S
T
h
er
e
ar
e
th
r
ee
ca
teg
o
r
ies
o
f
g
a
m
e
s
th
a
t
ca
n
b
e
d
is
tin
g
u
is
h
ed
in
th
r
ee
ca
teg
o
r
ies:
(
i)
th
e
ab
ilit
y
o
f
p
lay
er
s
to
f
o
r
m
al
l
y
co
m
m
it
t
h
e
m
s
el
v
es
to
t
h
eir
f
u
t
u
r
e
d
ec
i
s
io
n
s
,
(
ii)
t
h
e
n
atu
r
e
o
f
th
e
in
f
o
r
m
atio
n
,
a
n
d
(
iii)
th
e
s
tatic
o
r
d
y
n
a
m
ics
o
f
t
h
e
g
a
m
e.
T
h
is
clas
s
i
f
icatio
n
is
n
ec
ess
ar
y
b
ec
a
u
s
e,
d
ep
en
d
i
n
g
o
n
th
e
t
y
p
e
o
f
g
a
m
e
w
e
ar
e
f
ac
in
g
,
w
e
d
o
n
o
t u
s
e
(
n
ec
es
s
ar
il
y
)
t
h
e
s
a
m
e
to
o
ls
to
s
o
lv
e
it.
T
h
e
f
i
n
al
cr
iter
io
n
is
s
i
m
p
le.
T
h
u
s
,
it
w
ill
b
e
s
aid
o
f
a
g
a
m
e
th
a
t
it
is
d
y
n
a
m
ic
i
f
t
h
e
co
u
r
s
e
o
f
t
h
e
g
a
m
e
p
r
o
v
id
es
in
f
o
r
m
at
io
n
to
at
least
o
n
e
p
la
y
er
;
o
th
er
w
is
e
it
is
s
tatic.
T
h
e
f
ir
s
t
cr
it
er
io
n
r
ef
er
s
to
t
w
o
m
aj
o
r
ap
p
r
o
ac
h
es,
co
o
p
er
ativ
e
v
er
s
u
s
n
o
n
-
co
o
p
er
ativ
e,
ar
o
u
n
d
w
h
ic
h
is
h
is
to
r
icall
y
c
o
n
s
tr
u
cted
t
h
e
g
a
m
e
th
eo
r
y
.
E
s
s
e
n
tiall
y
,
th
e
co
o
p
er
ativ
e
ap
p
r
o
ac
h
is
in
ter
ested
in
co
llectiv
e
d
ec
is
io
n
m
a
k
i
n
g
th
at
is
to
s
a
y
to
s
it
u
atio
n
s
wh
er
e
o
n
e
m
u
s
t
d
ec
id
e
in
co
m
m
o
n
w
h
at
is
to
b
e
d
o
n
e
[
7
]
.
T
h
u
s
,
th
er
e
i
s
a
n
e
g
o
tiatio
n
p
h
ase
b
e
f
o
r
e
th
e
s
tar
t
o
f
th
e
g
a
m
e,
th
e
lat
ter
lead
in
g
to
th
e
s
i
g
n
in
g
o
f
a
b
in
d
in
g
co
n
tr
ac
t
(
i.e
.
w
h
ich
h
as
th
e
f
o
r
ce
o
f
la
w
)
an
d
w
h
ic
h
th
e
p
la
y
er
s
ag
r
ee
o
n
ac
tio
n
s
t
h
at
s
h
o
u
ld
b
e
tak
e
n
d
u
r
in
g
t
h
e
g
a
m
e.
T
h
e
n
o
n
-
co
o
p
er
ativ
e
ap
p
r
o
ac
h
f
o
c
u
s
es
o
n
p
r
ed
ictin
g
w
h
at
w
ill
b
e
s
p
o
n
ta
n
eo
u
s
l
y
p
la
y
ed
b
y
p
lay
er
s
w
h
o
ar
e
co
m
p
letel
y
f
r
ee
to
m
a
k
e
d
ec
is
io
n
s
a
s
th
e
y
m
ak
e
th
eir
c
h
o
ices.
T
h
e
p
o
in
t
is
th
at
it
ca
n
t
h
e
n
b
e
o
r
n
o
t
a
n
eg
o
tiatio
n
p
h
a
s
e
b
ef
o
r
e
th
e
s
tar
t
o
f
t
h
e
g
a
m
e,
i
n
o
r
d
er
to
co
o
r
d
in
ate,
f
o
r
ex
am
p
le,
b
u
t
if
t
h
er
e
is
n
eg
o
tiat
io
n
,
a
g
r
ee
m
e
n
ts
w
h
ic
h
ar
e
li
k
el
y
to
b
e
p
ass
ed
ar
e
n
o
t
th
e
f
o
r
ce
o
f
la
w
(
f
o
r
ex
a
m
p
le,
b
ec
au
s
e
t
h
e
y
ar
e
illeg
al)
.
A
s
s
u
c
h
,
p
la
y
er
s
,
i
f
t
h
e
y
h
o
n
o
r
th
e
co
m
m
it
m
e
n
ts
t
h
e
y
m
ig
h
t
h
av
e
ta
k
e
n
d
u
r
in
g
t
h
is
n
eg
o
tiatio
n
p
h
ase,
n
o
t
d
o
it b
ec
au
s
e
th
e
y
ar
e
r
eq
u
ir
ed
to
d
o
s
o
b
u
t
b
ec
au
s
e
it
s
er
v
es
th
e
ir
in
ter
est
s
[
8
]
.
T
h
e
cr
it
er
io
n
o
f
th
e
n
at
u
r
e
o
f
th
e
i
n
f
o
r
m
atio
n
is
th
e
m
o
s
t
co
m
p
lex
.
I
n
p
ar
ticu
lar
,
we
d
is
tin
g
u
is
h
b
et
w
ee
n
(
i)
p
er
f
ec
t
v
s
i
m
p
er
f
ec
t
i
n
f
o
r
m
atio
n
,
(
ii)
co
m
p
le
te
v
s
in
co
m
p
lete
i
n
f
o
r
m
atio
n
,
a
n
d
(
iii)
s
y
m
m
etr
ic
v
s
a
s
y
m
m
etr
ic
i
n
f
o
r
m
atio
n
ac
co
r
d
in
g
to
Fig
u
r
e
1
.
Fig
u
r
e
1
.
Dif
f
er
en
t i
n
f
o
r
m
atio
n
co
n
ce
p
ts
Gen
er
icall
y
,
th
e
d
is
tin
c
tio
n
b
et
w
ee
n
p
er
f
ec
t
an
d
i
m
p
er
f
e
ct
in
f
o
r
m
atio
n
is
s
i
m
p
le.
T
h
u
s
,
p
er
f
ec
t
in
f
o
r
m
atio
n
,
"
w
e
k
n
o
w
all"
o
r
,
m
o
r
e
ac
cu
r
atel
y
,
"
w
e
k
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o
w
t
h
at
w
e
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o
w
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h
at
it
w
ill
b
e
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s
ef
u
l
to
k
n
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w
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is
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n
"
.
On
th
e
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er
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a
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d
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in
i
m
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er
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t
in
f
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e
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s
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leas
t
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n
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t
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t
h
at
is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
Ga
me
th
eo
r
y
fo
r
r
eso
u
r
ce
s
h
a
r
in
g
in
la
r
g
e
d
is
tr
ib
u
ted
s
ystems
(
S
a
r
a
R
ia
h
i
)
1251
r
elev
an
t
f
o
r
d
ec
is
io
n
-
m
a
k
in
g
th
at
i
s
u
n
k
n
o
w
n
(
al
w
a
y
s
at
th
e
m
o
m
e
n
t
w
h
e
n
a
d
ec
is
io
n
h
a
s
to
b
e
m
ad
e)
.
T
h
u
s
,
p
la
y
er
s
w
h
o
ta
k
e
t
u
r
n
s
o
b
s
er
v
in
g
w
h
at
h
a
s
b
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p
la
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ed
b
y
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th
er
s
,
s
u
ch
as
ch
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s
s
,
f
o
r
ex
a
m
p
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ev
o
l
v
e
i
n
a
co
n
te
x
t o
f
p
er
f
ec
t
i
n
f
o
r
m
atio
n
.
O
n
t
h
e
o
th
er
h
a
n
d
,
if
t
h
e
y
d
o
n
o
t
k
n
o
w
w
h
a
t
h
as
b
ee
n
p
la
y
ed
b
ef
o
r
e,
s
u
c
h
a
s
in
a
s
ea
led
au
ctio
n
f
o
r
th
e
a
war
d
o
f
a
p
u
b
lic
co
n
tr
ac
t
f
o
r
ex
a
m
p
le,
th
e
i
n
f
o
r
m
atio
n
i
s
i
m
p
er
f
ec
t
[
6
]
.
L
ater
,
it
tu
r
n
s
o
u
t
t
h
at
t
h
i
s
f
ir
s
t
d
i
s
ti
n
ctio
n
i
s
n
o
t
s
u
f
f
ic
ien
t,
an
d
it
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s
o
n
ec
e
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s
ar
y
to
k
n
o
w
w
h
e
n
i
n
f
o
r
m
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n
is
i
m
p
er
f
ec
t,
if
p
la
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s
k
n
o
w
w
i
th
ce
r
tai
n
t
y
t
h
e
r
u
le
s
,
t
h
e
latt
er
in
cl
u
d
in
g
all
p
la
y
er
s
(
w
h
o
p
lay
s
?
)
,
th
e
s
et
s
o
f
ac
tio
n
s
(
w
h
at
ca
n
t
h
e
p
la
y
er
s
d
o
?
)
an
d
f
u
n
ctio
n
s
r
eg
u
lat
io
n
s
(
h
o
w
th
e
p
la
y
er
s
g
et?
)
.
I
f
th
at
i
s
t
h
e
ca
s
e,
t
h
e
in
f
o
r
m
atio
n
i
s
co
m
p
lete;
o
th
e
r
w
i
s
e
,
it
is
in
co
m
p
le
te,
an
d
it
b
ec
o
m
es
u
n
b
ala
n
ce
d
if
s
o
m
e
ar
e
m
o
r
e
f
a
m
iliar
w
it
h
t
h
e
r
u
les,
u
s
u
all
y
s
ettl
e
m
en
t
f
u
n
ctio
n
s
,
t
h
an
o
th
er
s
.
No
te
th
at
co
m
p
lete
i
n
f
o
r
m
atio
n
is
a
s
tr
o
n
g
h
y
p
o
t
h
esi
s
i
n
s
o
m
e
co
n
tex
ts
(
as
i
n
a
u
ctio
n
s
f
o
r
ex
a
m
p
le
b
e
ca
u
s
e
it
as
s
u
m
e
s
t
h
at
ev
er
y
o
n
e
k
n
o
w
s
t
h
e
r
e
s
er
v
e
p
r
ices
o
f
all)
a
n
d
r
ea
s
o
n
ab
le
i
n
o
th
er
s
(
s
u
ch
as
f
ail
u
r
es,
f
o
r
ex
a
m
p
le)
[
4
]
.
On
th
e
o
th
er
h
a
n
d
,
ag
e
n
c
y
m
o
d
els,
an
ti
-
s
elec
t
io
n
a
n
d
s
i
g
n
a
ls
,
d
e
v
elo
p
ed
in
co
n
tr
ac
t
th
eo
r
y
an
d
w
id
el
y
u
s
ed
i
n
th
e
f
ield
s
o
f
lab
o
r
ec
o
n
o
m
ic
s
,
co
r
p
o
r
ate
f
in
a
n
ce
,
in
s
u
r
a
n
ce
,
t
ax
atio
n
ar
e
as
y
m
m
e
tr
ic
in
f
o
r
m
atio
n
g
a
m
es.
2
.
1
.
Str
a
t
eg
ic
f
o
r
m
o
f
a
g
a
m
e
T
h
er
e
ar
e
th
r
ee
d
o
m
i
n
a
n
t
m
at
h
e
m
a
tical
r
ep
r
esen
tatio
n
s
o
f
a
g
a
m
e:
t
h
e
n
o
r
m
al
o
r
s
tr
ateg
ic
f
o
r
m
,
th
e
ex
ten
s
i
v
e
f
o
r
m
an
d
t
h
e
co
alit
io
n
f
o
r
m
.
W
e
d
escr
ib
e
th
e
f
ir
s
t
o
f
t
h
ese
f
o
r
m
s
,
s
tr
ate
g
ic
f
o
r
m
b
ein
g
t
h
e
m
o
s
t
u
s
ed
i
n
th
e
liter
at
u
r
e
o
f
co
g
n
it
iv
e
r
ad
io
an
d
th
eo
r
y
o
f
n
o
n
-
co
o
p
er
ativ
e
g
a
m
es;
a
g
a
m
e
i
s
s
a
id
u
n
co
o
p
er
ativ
e
i
f
ea
ch
p
la
y
er
h
as
h
i
s
o
w
n
g
o
al,
also
ca
lled
co
s
t
f
u
n
ctio
n
o
r
in
d
iv
id
u
al
u
til
it
y
.
On
e
r
ea
s
o
n
f
o
r
th
is
d
o
m
i
n
an
ce
i
s
th
e
ea
s
e
o
f
u
s
e
o
f
th
e
s
tr
ate
g
i
c
f
o
r
m
.
Fo
r
m
o
r
e
d
etail
s
o
n
t
h
e
o
th
er
t
w
o
f
o
r
m
s
,
t
h
e
r
ea
d
e
r
m
a
y
f
o
r
ex
a
m
p
le
r
ef
er
to
[
4
]
.
A
s
tr
ateg
y
g
a
m
e
is
an
o
r
d
er
ed
tr
ip
let
th
at
i
n
clu
d
e
s
t
h
e
(
d
is
cr
ete
m
o
s
t
o
f
te
n
)
s
et
o
f
p
la
y
er
s
1
,
2
,
.
.
.
,
Kk
th
e
s
e
ts
o
f
s
tr
ate
g
ies
o
f
t
h
ese
,
k
kK
p
lay
er
s
an
d
t
h
e
u
tili
t
y
f
u
n
ct
io
n
s
o
f
ea
ch
o
f
t
h
ese
p
la
y
er
s
k
u
.
Ma
th
e
m
atica
ll
y
,
a
g
a
m
e
in
s
tr
ateg
ic
f
o
r
m
is
a
s
et
o
r
co
llectio
n
o
f
f
u
n
ctio
n
s
K
to
K
v
ar
iab
les
1
:
.
.
.
.
kK
u
I
R
[
9
]
.
I
n
co
g
n
iti
v
e
r
ad
io
,
u
s
u
al
l
y
p
la
y
er
s
ar
e
th
e
co
g
n
iti
v
e
r
ad
io
tr
an
s
m
itter
s
.
T
h
e
u
t
ilit
y
f
u
n
ctio
n
s
ar
e
th
e
is
s
u
er
s
o
f
p
er
f
o
r
m
an
ce
cr
iter
ia.
I
t
m
a
y
b
e,
f
o
r
ex
a
m
p
le,
a
co
m
m
u
n
ica
tio
n
r
ate,
an
en
er
g
y
ef
f
icien
c
y
to
b
e
m
a
x
i
m
ized
o
r
a
d
elay
,
en
er
g
y
to
b
e
m
i
n
i
m
i
ze
d
.
A
s
i
m
p
le
s
et
o
f
s
tr
ateg
ie
s
co
u
ld
b
e
th
e
s
et
o
f
p
o
w
er
lev
els t
h
at
a
tr
a
n
s
m
itter
ca
n
u
s
e
[
1
0
]
.
2
.
2
.
A
s
i
m
pli
f
ie
d c
la
s
s
if
ica
t
i
o
n o
f
t
y
pes
o
f
g
a
m
e
s
I
n
th
e
p
r
ec
ed
in
g
p
ar
ag
r
ap
h
s
we
h
av
e
m
e
n
tio
n
ed
t
h
e
n
o
n
-
co
o
p
er
ativ
e
g
a
m
es
w
h
ic
h
ar
e
th
e
s
u
b
j
ec
t
o
f
th
is
ar
ticle.
Fo
r
t
h
e
s
e
g
a
m
e
s
,
ea
ch
p
la
y
er
h
as
h
i
s
i
n
d
iv
id
u
al
g
o
al.
I
n
co
o
p
er
ativ
e
g
a
m
e
s
,
th
er
e
ar
e
s
et
s
o
f
p
lay
er
s
w
h
o
h
av
e
t
h
e
s
a
m
e
g
o
al.
T
h
e
d
o
m
i
n
a
n
t
t
y
p
e
o
f
co
o
p
er
ativ
e
g
a
m
es
is
g
iv
e
n
b
y
c
o
alitio
n
s
g
a
m
e
s
[
6
]
w
h
er
e
q
u
esti
o
n
s
ar
e
m
ad
e
co
n
ce
r
n
i
n
g
w
h
ic
h
co
alitio
n
w
ill
f
o
r
m
,
h
o
w
w
ill
b
e
d
is
tr
ib
u
te
d
co
o
p
er
ativ
e
g
ai
n
s
,
etc.
An
o
t
h
er
w
a
y
to
d
is
ti
n
g
u
i
s
h
a
g
a
m
e
m
o
d
el
i
s
to
ca
ll
it
a
s
tatic
(
o
n
e
-
s
h
o
t)
g
a
m
e
o
r
a
d
y
n
a
m
ic
g
a
m
e.
I
n
a
s
tatic
g
a
m
e,
ea
ch
p
la
y
er
m
u
s
t
m
ak
e
a
d
ec
is
io
n
,
ch
o
o
s
e
a
s
tr
a
teg
y
o
n
ce
a
n
d
f
o
r
all.
A
d
y
n
a
m
ic
g
a
m
e
is
p
la
y
ed
s
ev
er
al
ti
m
es,
p
la
y
er
s
m
ak
e
o
b
s
er
v
atio
n
s
d
u
r
in
g
th
e
g
a
m
e
,
s
u
c
h
ac
tio
n
s
p
er
f
o
r
m
ed
b
y
o
th
er
s
tates
a
n
d
th
e
g
a
m
e,
an
d
u
s
e
th
e
m
to
tak
e
ac
tio
n
.
I
f
o
n
e
r
ef
er
s
to
th
e
s
tr
ateg
ic
f
o
r
m
g
iv
e
n
ab
o
v
e,
a
s
tr
ateg
y
i
n
a
s
tatic
g
a
m
e
is
a
s
i
m
p
le
ac
tio
n
,
s
u
c
h
as
s
elec
tin
g
a
tr
an
s
m
it
p
o
w
er
lev
el
[
11]
.
T
h
e
d
if
f
er
en
t
t
y
p
es
o
f
g
a
m
e
s
h
o
w
n
in
Fig
u
r
e
2
.
Fig
u
r
e
2
.
T
h
e
d
if
f
er
en
t t
y
p
e
s
o
f
g
a
m
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
9
,
No
.
2
,
A
p
r
il
2019
:
1
2
4
9
-
1257
1252
I
n
a
d
y
n
a
m
ic
g
a
m
e,
s
tr
ateg
y
i
s
a
m
o
r
e
co
m
p
lex
o
b
j
ec
t,
it
m
a
y
b
e
f
o
r
ex
a
m
p
le
a
s
eq
u
en
ce
o
f
ca
u
s
al
f
u
n
ctio
n
s
to
g
en
er
ate,
f
r
o
m
it
s
i
n
f
o
r
m
atio
n
a
l
ar
g
u
m
e
n
ts
(
k
n
o
w
led
g
e,
o
b
s
er
v
a
tio
n
s
)
a
s
er
ies
o
f
ac
tio
n
s
a
s
a
s
eq
u
en
ce
o
f
lev
el
s
p
o
w
er
.
T
h
er
e
ar
e
o
th
er
w
a
y
s
to
ch
ar
ac
ter
i
ze
a
g
a
m
e.
Fo
r
ex
a
m
p
le,
o
n
e
ca
n
d
is
t
in
g
u
is
h
t
h
e
ze
r
o
-
s
u
m
g
a
m
es
(
t
h
e
s
u
m
o
f
u
tili
tie
s
is
ze
r
o
)
g
a
m
e
s
at
n
o
n
-
ze
r
o
-
s
u
m
g
a
m
e
s
w
it
h
p
er
f
ec
t
in
f
o
r
m
atio
n
(
th
e
h
i
s
to
r
y
o
f
th
e
g
a
m
e
is
o
b
s
er
v
ed
b
y
all
p
la
y
er
s
)
,
g
a
m
es
w
it
h
co
m
p
le
te
in
f
o
r
m
at
io
n
(
ea
ch
p
la
y
er
h
a
s
t
h
e
k
n
o
w
led
g
e
o
f
all
t
h
e
g
a
m
e
s
et
tin
g
s
)
,
etc.
Fo
r
m
o
r
e
d
etail
s
,
th
e
r
ea
d
er
ca
n
r
ef
er
to
[
1
2
]
.
I
n
co
g
n
iti
v
e
r
ad
io
,
th
e
m
o
s
t
u
s
ed
m
o
d
el
s
ee
m
s
to
b
e
th
e
s
tatic
a
n
d
n
o
n
-
co
o
p
er
ativ
e
g
a
m
e
m
o
d
el.
T
h
is
m
o
d
el
m
ak
es
it
p
o
s
s
ib
le
to
s
tu
d
y
t
h
e
p
o
in
t
s
o
f
co
n
v
er
g
e
n
ce
o
f
iter
ati
v
e
p
r
o
ce
d
u
r
es
s
u
ch
as
th
o
s
e
d
escr
ib
ed
in
f
o
r
m
all
y
i
n
th
e
p
r
e
v
io
u
s
s
ec
tio
n
a
n
d
w
h
ic
h
w
e
w
ill d
es
cr
ib
e
m
o
r
e
p
r
ec
is
el
y
later
.
2
.
3
.
G
a
m
e
ex
a
m
p
le
C
o
n
s
id
er
t
w
o
tr
an
s
m
itter
s
i
n
co
n
n
ec
tio
n
w
it
h
t
h
eir
r
e
s
p
ec
tiv
e
r
ec
ei
v
er
s
an
d
a
s
s
u
m
e
th
at
b
o
t
h
co
m
m
u
n
icatio
n
s
i
n
ter
f
er
e.
A
s
s
u
m
e
th
at
ea
ch
tr
a
n
s
m
itter
h
a
s
t
w
o
ac
tio
n
s
,
ch
o
ice
s
,
co
n
f
i
g
u
r
atio
n
s
o
r
o
p
tio
n
s
:
is
s
u
e
w
ith
a
n
ar
r
o
w
f
r
eq
u
en
c
y
b
an
d
o
r
tr
an
s
m
it
w
it
h
a
w
id
e
f
r
eq
u
en
c
y
b
an
d
.
Fo
u
r
ca
s
es
th
en
ap
p
ea
r
k
n
o
w
i
n
g
th
e
q
u
a
n
titati
v
e
tr
an
s
latio
n
f
o
r
ea
ch
tr
an
s
m
it
ter
[
1
3
]
.
T
h
e
co
u
p
le
o
f
c
h
o
ices
(
r
o
w
,
c
o
lu
m
n
)
lead
s
to
to
r
q
u
e
r
ate
s
.
T
h
is
g
a
m
e
ill
u
s
tr
ates
a
p
ar
ad
o
x
k
n
o
w
n
i
n
g
a
m
e
th
eo
r
y
.
I
f
th
e
t
w
o
tr
a
n
s
m
itter
s
ca
n
s
e
n
d
in
n
ar
r
o
w
b
a
n
d
(
o
n
e
o
p
tio
n
)
th
e
y
g
et
b
o
th
a
r
ate
g
r
ea
ter
th
an
t
h
at
o
b
tain
ed
b
y
ad
d
in
g
th
e
o
p
p
o
r
tu
n
it
y
to
i
s
s
u
e
b
r
o
ad
b
an
d
i.e
.
,
h
a
v
i
n
g
a
s
et
o
f
lar
g
er
o
p
ti
m
i
za
tio
n
s
o
f
th
e
f
o
u
r
p
o
s
s
ib
le
s
ce
n
ar
io
s
,
th
i
s
g
a
m
e
ca
n
b
e
r
ep
r
esen
ted
i
n
s
tr
ate
g
ic
f
o
r
m
u
s
i
n
g
T
ab
le
1
.
I
n
th
e
e
x
a
m
p
le
ab
o
v
e,
th
e
s
et
o
f
p
la
y
er
s
is
t
h
e
s
et
o
f
tr
an
s
m
itter
s
,
t
h
e
s
et
o
f
s
tr
ateg
i
es
o
f
a
p
lay
er
i
s
th
e
(
b
r
o
ad
b
an
d
,
n
ar
r
o
w
b
a
n
d
)
s
et
an
d
th
e
u
ti
liti
es
a
s
s
o
ciate
d
w
i
th
th
e
p
o
s
s
ib
le
s
tr
ate
g
y
v
ec
to
r
s
ar
e
th
e
co
m
p
o
n
e
n
t
s
o
f
th
e
t
o
r
q
u
es
in
d
icate
d
in
th
e
tab
le
[
1
4
]
.
P
lay
er
1
c
h
o
o
s
es
t
h
e
li
n
e,
p
la
y
er
2
ch
o
o
s
e
s
t
h
e
co
l
u
m
n
a
n
d
t
h
e
u
til
it
y
o
f
p
la
y
er
1
(
r
esp
.
2
)
i
s
th
e
co
m
p
o
n
en
t
1
(
2
)
o
f
th
e
p
air
.
T
h
e
u
tili
t
y
ca
n
f
o
r
ex
a
m
p
le
b
e
a
r
ate
in
Mb
it
/
s
.
I
n
t
h
is
g
a
m
e,
w
e
o
b
s
er
v
e
t
h
at
a
s
elf
i
s
h
e
m
it
ter
h
as
a
n
i
n
ter
est
in
u
s
i
n
g
t
h
e
b
r
o
ad
b
an
d
a
ctio
n
b
ec
au
s
e
1
>0
an
d
4
>3
.
T
h
is
lead
s
to
th
e
o
u
tco
m
e
o
f
t
h
e
g
a
m
e
(
1
,
1
)
is
th
e
u
n
iq
u
e
Na
s
h
eq
u
il
ib
r
iu
m
o
f
t
h
e
g
a
m
e.
T
h
i
s
co
n
ce
p
t
i
s
d
is
c
u
s
s
ed
i
n
t
h
e
f
o
llo
w
in
g
s
ec
t
io
n
.
T
ab
le
1
.
E
x
am
p
le
o
f
a
S
tr
ateg
i
c
Ga
m
e
;
T
h
e
tr
an
s
m
itter
1
(
r
es
p
.
2
)
Sel
ec
ts
t
h
e
L
i
n
e
L
ea
d
s
to
a
C
o
u
p
le
(
r
esp
.
C
o
lu
m
n
)
B
r
o
a
d
b
a
n
d
N
a
r
r
o
w
b
a
n
d
B
r
o
a
d
b
a
n
d
(
1
,
1
)
(
4
,
0
)
N
a
r
r
o
w
b
a
n
d
(
0
,
4
)
(
3
,
3
)
3.
B
ASI
C
G
AM
E
SO
L
UT
I
O
N
CO
NCEPT
:
NA
SH
E
Q
UI
L
I
B
RIUM
:
I
n
class
ical
o
p
ti
m
izatio
n
,
t
h
e
n
o
tio
n
s
o
f
m
aj
o
r
an
t,
m
i
n
i
m
u
m
,
m
i
n
o
r
an
t
a
n
d
m
ax
i
m
u
m
ar
e
p
er
f
ec
tl
y
d
ef
in
ed
.
I
n
t
h
e
t
h
eo
r
y
o
f
n
o
n
-
co
o
p
er
ativ
e
g
a
m
e
s
,
it
is
n
ec
es
s
ar
y
to
d
ef
i
n
e
t
h
e
co
n
ce
p
t
o
f
s
o
lu
tio
n
o
f
th
e
g
a
m
e
b
ef
o
r
e
s
o
lv
i
n
g
th
e
g
a
m
e,
t
h
at
is
to
s
a
y
,
co
n
d
u
c
t
t
h
e
an
a
l
y
s
is
o
f
t
h
is
s
o
lu
tio
n
(
th
e
ex
i
s
t
en
ce
f
o
r
ex
a
m
p
le)
.
I
n
d
ee
d
,
in
a
n
o
n
-
co
o
p
er
ativ
e
g
a
m
e,
a
p
la
y
er
co
n
tr
o
ls
o
n
l
y
o
n
e
o
f
th
e
v
ar
iab
le
s
(
s
tr
at
eg
y
o
r
ac
tio
n
)
t
h
a
t
d
eter
m
in
e
it
s
u
til
it
y
f
u
n
ct
io
n
.
T
h
e
co
n
ce
p
t
o
f
o
p
tim
al
d
ec
is
i
o
n
is
th
er
e
f
o
r
e
a
p
r
io
r
i
n
o
t
c
lear
s
in
ce
th
e
d
eg
r
ee
o
f
o
p
ti
m
ali
t
y
d
ep
en
d
s
o
n
th
e
s
tr
ateg
ie
s
a
n
d
ac
tio
n
s
c
h
o
s
en
b
y
o
th
er
p
la
y
er
s
.
W
e
m
u
s
t
t
h
er
ef
o
r
e
d
ef
i
n
e
th
e
s
o
lu
tio
n
o
f
th
e
p
r
o
b
lem
b
ef
o
r
e
s
o
lv
in
g
it
[
1
2
]
.
On
e
o
f
th
e
m
aj
o
r
co
n
ce
p
ts
o
f
g
a
m
e
s
o
lu
tio
n
s
is
th
e
Na
s
h
eq
u
ilib
r
iu
m
.
An
eq
u
ilib
r
i
u
m
o
r
Nash
p
o
in
t
is
a
v
ec
to
r
o
f
s
tr
ateg
ies
s
u
c
h
th
at
i
f
o
n
e
ev
alu
a
tes
th
e
u
tili
t
y
f
u
n
ctio
n
o
f
an
y
p
la
y
er
kK
b
y
ch
an
g
i
n
g
o
n
l
y
th
e
v
ar
iab
le
kk
sS
th
e
n
th
e
v
alu
e
o
f
th
e
u
tili
t
y
o
f
t
h
is
p
lay
er
is
at
m
o
s
t
eq
u
al
to
t
h
at
o
b
tain
ed
f
o
r
th
e
s
o
-
ca
lled
eq
u
ilib
r
iu
m
v
ec
to
r
.
T
h
is
is
ex
p
r
ess
ed
m
at
h
e
m
atica
ll
y
b
y
t
h
e
f
o
llo
w
in
g
i
n
eq
u
alit
y
.
T
h
e
s
tr
ateg
y
v
ec
to
r
1
(
,
.
.
.
.
,
)
K
ss
is
a
Na
s
h
p
o
in
t
(
i
n
p
u
r
e
s
tr
ate
g
ies)
o
f
th
e
co
llectio
n
o
f
f
u
n
ctio
n
s
k
u
,
kK
if
an
d
o
n
l
y
i
f
:
'
'
,
kk
k
K
s
S
'
'
(
,
)
(
,
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k
k
k
k
k
k
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s
s
u
s
s
w
h
er
e
th
e
n
o
tatio
n
k
s
in
d
icate
s
th
e
s
tr
ate
g
ies
o
f
th
e
p
la
y
er
s
o
th
er
th
a
n
t
h
e
p
la
y
er
kK
[
1
0
]
.
T
h
e
Nash
eq
u
ilib
r
iu
m
co
n
ce
p
t
is
a
co
r
n
er
s
to
n
e
o
f
th
e
g
a
m
e
t
h
eo
r
y
.
Na
s
h
eq
u
ilib
r
iu
m
h
as
t
h
r
ee
s
u
c
h
o
u
ts
tan
d
i
n
g
f
ea
t
u
r
es.
B
y
d
ef
i
n
itio
n
,
a
s
y
s
te
m
o
p
er
atin
g
at
an
eq
u
ilib
r
i
u
m
p
o
in
t
h
as
a
f
o
r
m
o
f
s
tab
ilit
y
:
a
n
y
u
n
i
later
al
d
ev
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n
i
s
n
o
t
p
r
o
f
itab
le
to
th
e
d
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ter
.
I
n
a
s
y
s
te
m
i
n
v
o
lv
i
n
g
h
ete
r
o
g
en
eo
u
s
co
m
m
u
n
icati
n
g
o
b
j
ec
ts
d
esig
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ed
b
y
v
ar
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u
s
en
titi
es,
t
h
is
en
s
u
r
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s
th
at
n
o
co
o
r
d
in
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a
m
o
n
g
p
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tiall
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s
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f
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s
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e
n
titi
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s
,
a
n
y
e
n
tit
y
d
e
v
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th
e
eq
u
ilib
r
iu
m
p
o
in
t (
t
h
i
n
k
o
f
a
r
ec
o
m
m
e
n
d
atio
n
o
n
h
o
w
to
u
s
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th
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s
p
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m
)
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A
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d
f
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d
a
m
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is
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Si
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w
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[
8
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[
1
1
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.
Fo
r
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le,
w
e
ca
n
u
s
e
th
e
co
n
ce
p
t
o
f
s
tr
o
n
g
eq
u
ilib
r
iu
m
,
p
r
o
v
id
ed
th
at
it
is
r
eg
ar
d
ed
in
th
e
g
a
m
e
[
1
5
]
.
I
f
th
e
o
b
j
ec
tiv
e
o
f
a
p
lay
er
is
n
o
t
to
m
ax
i
m
ize
h
is
u
tili
t
y
b
u
t
to
r
ea
ch
a
m
in
i
m
u
m
t
h
r
es
h
o
ld
v
alu
e,
o
n
e
ca
n
ex
p
lo
it
t
h
e
n
o
tio
n
o
f
g
e
n
er
alize
d
Nash
eq
u
ilib
r
iu
m
o
r
s
atis
f
ac
ti
o
n
eq
u
ilib
r
iu
m
[
1
6
]
.
T
h
er
e
ar
e
s
o
m
a
n
y
o
th
er
co
n
ce
p
ts
o
f
s
o
lu
tio
n
s
th
at
ca
n
b
e
ex
p
lo
ited
in
th
e
co
n
tex
t o
f
co
g
n
iti
v
e
r
ad
io
,
m
a
n
y
o
f
t
h
e
m
b
u
i
lt o
n
th
e
Na
s
h
eq
u
ilib
r
iu
m
.
4.
AL
G
O
RI
T
H
M
S CO
NVERG
E
T
O
WAR
DS E
Q
U
I
L
I
B
R
I
UM
T
h
er
e
ar
e
en
o
u
g
h
s
i
m
p
le
co
n
d
itio
n
s
u
n
d
er
w
h
ic
h
iter
ati
v
e
alg
o
r
ith
m
s
,
s
u
c
h
as
lear
n
i
n
g
a
lg
o
r
ith
m
s
,
co
n
v
er
g
e
to
w
ar
d
Nas
h
eq
u
il
ib
r
iu
m
.
O
n
e
o
f
t
h
e
b
est
k
n
o
w
n
i
s
t
h
e
p
r
o
p
er
t
y
p
o
ten
tia
l
o
f
a
g
a
m
e
[
1
7
]
.
T
h
e
co
llectio
n
o
f
f
u
n
ctio
n
s
k
u
,
kK
h
a
s
th
e
e
x
ac
t p
o
ten
tial p
r
o
p
er
ty
i
f
th
er
e
e
x
is
t
s
a
f
u
n
ctio
n
s
u
c
h
t
h
at:
'
'
'
''
,
,
(
,
)
(
,
)
(
,
)
(
,
)
k
k
k
k
k
k
k
k
k
k
k
k
k
K
s
S
u
s
s
u
s
s
s
s
s
s
(
1
)
T
h
e
i
m
p
o
r
tan
t
p
o
in
t
to
n
o
te
is
t
h
at
t
h
is
f
u
n
ctio
n
ϕ
ca
l
l
ed
an
ex
ac
t
p
o
te
n
tial
o
f
t
h
e
g
a
m
e,
is
in
d
ep
en
d
en
t
o
f
t
h
e
i
n
d
ex
o
f
t
h
e
p
la
y
er
s
.
I
t
is
th
u
s
p
o
s
s
ib
le
to
ev
al
u
ate
t
h
e
v
ar
iatio
n
i
n
u
tili
t
y
o
f
a
g
i
v
e
n
p
la
y
er
f
r
o
m
t
h
is
f
u
n
ct
io
n
.
W
h
e
n
a
g
a
m
e
is
to
co
r
r
ec
t p
o
ten
tial,
th
e
ex
is
te
n
ce
o
f
Na
s
h
eq
u
ilib
r
iu
m
in
p
u
r
e
s
tr
ate
g
ies i
s
ass
u
r
ed
.
T
h
e
co
n
v
er
g
en
ce
o
f
m
a
n
y
s
tr
ateg
i
e
s
f
o
r
u
p
d
atin
g
s
tr
ateg
ie
s
i
s
al
s
o
e
n
s
u
r
ed
[
1
8
]
.
T
w
o
i
m
p
o
r
tan
t
alg
o
r
ith
m
s
t
h
at
co
n
v
er
g
e
to
Nash
eq
u
i
lib
r
iu
m
in
a
n
ex
ac
t p
o
ten
tial
g
a
m
e.
4
.
1
.
A
r
einf
o
rc
e
m
e
nt
lea
rning
a
lg
o
rit
h
m
Su
p
p
o
s
e
th
at
th
e
s
e
t
o
f
s
tr
ate
g
ies
o
r
co
n
f
i
g
u
r
atio
n
o
f
th
e
t
r
an
s
m
itter
kK
is
d
is
cr
ete
an
d
f
i
n
i
te
1
,
.
.
.
.
,
kN
S
s
s
.
Ass
u
m
e
t
h
at
t
h
e
co
n
tr
o
ller
th
at
i
m
p
le
m
e
n
ts
th
e
u
p
d
ate
alg
o
r
ith
m
o
f
t
h
e
s
tr
ateg
y
o
f
co
g
n
iti
v
e
tr
an
s
m
itter
h
a
s
p
er
io
d
ic
ac
ce
s
s
to
ac
h
iev
e
it
s
u
s
e
f
u
l
f
u
n
c
tio
n
,
t
h
e
u
til
it
y
f
u
n
c
ti
o
n
is
ass
u
m
ed
to
b
e
u
n
k
n
o
w
n
[
1
9
]
.
T
h
e
f
o
llo
w
in
g
r
u
le
u
p
d
ates t
h
e
p
r
o
b
ab
ilit
y
th
at
th
e
s
e
n
d
er
k
ass
o
ciate
s
w
it
h
t
h
e
n
S
s
tr
ateg
y
o
r
co
n
f
i
g
u
r
atio
n
.
,
,
,
,
(
)
,
(
1
)
(
)
(
)
(
)
1
(
)
n
k
n
k
n
k
n
k
k
n
t
S
k
n
x
t
x
t
t
u
t
s
x
t
(
2
)
C
o
n
v
er
g
es
to
Nas
h
eq
u
ilib
r
iu
m
o
f
t
h
e
co
llectio
n
o
f
f
u
n
c
tio
n
s
k
u,
kK
,
w
h
e
n
it
h
as
a
n
ex
ac
t
p
o
ten
tial
.
Sev
er
al
co
m
m
e
n
t
s
m
u
s
t b
e
m
ad
e.
T
im
e
i
s
s
u
p
p
o
s
ed
to
b
e
d
is
cr
ete
h
er
e:
t
.
T
h
e
v
ec
to
r
1
(
(
)
,
.
.
.
.
,
(
)
)
k
k
N
x
t
x
t
r
ep
r
esen
ts
t
h
e
p
r
o
b
ab
ilit
y
d
is
tr
ib
u
tio
n
t
h
at
th
e
tr
an
s
m
itter
k
u
s
e
s
t
o
s
elec
t
(
r
an
d
o
m
l
y
)
it
s
co
n
f
i
g
u
r
atio
n
o
r
s
tr
ateg
y
=
u
n
n
ec
e
s
s
ar
y
h
er
e
at
ti
m
e
t.
T
h
e
p
ar
a
m
ete
r
k
,
n
(
t)
h
as
t
h
e
s
a
m
e
r
o
le
as
t
h
e
s
tep
i
n
a
g
r
ad
ien
t
al
g
o
r
ith
m
.
T
h
e
q
u
a
n
ti
t
y
k
u
(
t)
r
ep
r
esen
ts
t
h
e
v
al
u
e
o
f
t
h
e
u
tili
t
y
o
f
t
h
e
tr
an
s
m
itter
k
at
th
e
i
n
s
ta
n
t
t
an
d
th
e
f
u
n
ctio
n
C
1
is
th
e
i
n
d
icato
r
f
u
n
c
tio
n
(
h
e
n
ce
1
if
an
d
o
n
l
y
i
f
th
e
co
n
d
itio
n
C
is
tr
u
e)
[
2
0
]
.
I
n
a
p
o
ten
tial
g
a
m
e
i
f
th
e
y
u
p
d
ate
th
eir
s
tr
ate
g
y
in
t
u
r
n
m
a
x
i
m
izi
n
g
th
eir
u
til
it
y
k
n
o
w
i
n
g
th
e
s
tr
ateg
y
o
f
t
h
e
o
th
er
,
th
e
n
t
h
e
y
h
ea
d
to
Nash
eq
u
il
ib
r
iu
m
.
4
.
2
.
T
he
s
e
qu
en
t
ia
l dy
na
m
ic
s
o
f
bet
t
er
a
ns
w
er
s
I
n
its
m
o
s
t
clas
s
ic
v
er
s
io
n
,
th
i
s
d
y
n
a
m
ic
m
ak
e
s
it
p
o
s
s
ib
le
t
o
u
p
d
ate
s
tr
ateg
y
o
r
ac
tio
n
d
ir
ec
tl
y
;
t
h
er
e
ar
e
v
er
s
io
n
s
w
h
er
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as
i
n
t
h
e
p
r
ev
io
u
s
al
g
o
r
ith
m
,
a
d
is
tr
ib
u
ti
o
n
is
u
p
d
ated
[
2
1
]
.
A
t
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m
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u
p
d
ates
its
s
tr
ate
g
y
b
y
m
ax
i
m
izin
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its
u
ti
lit
y
,
a
n
d
th
en
t
h
e
tr
an
s
m
itter
2
u
p
d
ates
it,
an
d
s
o
o
n
.
T
h
is
ca
u
s
es
th
e
f
o
llo
w
in
g
s
eq
u
en
ce
[
2
2
]
:
1
1
1
1
(
1
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a
r
g
m
a
x
u
(
(
0
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,
(
0
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S
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2
2
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S
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a
r
g
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Fig
u
r
e
3
illu
s
tr
ate
s
th
i
s
p
r
o
ce
s
s
f
o
r
a
ca
s
e
in
v
o
lv
i
n
g
t
w
o
p
lay
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s
c
h
o
o
s
in
g
th
e
ir
ac
tio
n
in
IR
.
T
h
e
cu
r
v
e
in
r
ed
/d
ash
ed
(
r
esp
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B
lu
e/
s
o
lid
lin
e)
s
h
o
w
s
t
h
e
b
est
ac
tio
n
o
f
p
la
y
er
2
(
r
esp
.
1
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ac
co
r
d
in
g
to
th
e
ac
tio
n
p
er
f
o
r
m
ed
b
y
t
h
e
p
la
y
e
r
1
(
r
esp
.
2
)
,
th
er
ef
o
r
e
it is
ca
ll
ed
th
e
b
est r
esp
o
n
s
e
c
u
r
v
e
(
B
R
)
.
T
h
e
in
ter
s
ec
tio
n
o
f
t
h
ese
c
u
r
v
e
s
i
s
Na
s
h
eq
u
ilib
r
iu
m
.
I
n
a
p
o
te
n
t
ial
g
a
m
e,
th
e
s
eq
u
e
n
tial
d
y
n
a
m
ics
b
etter
an
s
w
er
s
ar
e
g
u
ar
a
n
teed
to
co
n
v
er
g
e
to
o
n
e
o
f
th
e
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o
in
ts
o
f
in
ter
s
ec
tio
n
o
f
th
e
s
e
b
est an
s
w
er
s
[
1
8
]
.
Fig
u
r
e
3
.
C
o
n
v
er
g
en
ce
o
f
th
e
s
eq
u
en
tial d
y
n
a
m
ics o
f
b
est r
e
s
p
o
n
s
es
f
o
r
a
s
ce
n
ar
io
w
it
h
t
wo
tr
an
s
m
i
tter
s
5.
T
H
E
P
O
W
E
R
A
L
L
O
C
A
T
I
O
N
I
N
M
UL
T
I
P
L
E
ACCES
S
CH
ANN
E
L
S
I
N
SE
V
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RA
L
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RT
H
O
G
O
NA
L
CH
ANN
E
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S
C
o
n
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id
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K
co
g
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iti
v
e
tr
a
n
s
m
itter
s
th
a
t
ca
n
u
s
e
M
b
an
d
s
o
f
f
r
eq
u
en
cie
s
t
h
at
d
o
n
o
t
o
v
er
l
ap
(
w
e
s
p
ea
k
o
f
o
r
th
o
g
o
n
al
o
r
p
ar
allel
c
h
an
n
els).
E
ac
h
tr
an
s
m
itter
m
u
s
t
d
ec
id
e
it
s
el
f
h
o
w
to
al
lo
ca
te
it
s
tr
an
s
m
is
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n
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et
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M
av
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d
s
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d
t
h
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s
in
o
r
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to
m
ax
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m
ize
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d
iv
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al
p
er
f
o
r
m
an
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cr
iter
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at
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e
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s
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m
e
a
b
it
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ate
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Ma
x
i
m
izi
n
g
t
h
e
SIN
R
p
o
w
er
allo
ca
ted
s
h
o
w
n
in
Fi
g
u
r
e
4
.
Fig
u
r
e
4
.
Qu
an
t
it
y
o
f
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
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&
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g
,
Vo
l.
9
,
No
.
2
,
A
p
r
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2019
:
1
2
4
9
-
1257
1256
RE
F
E
R
E
NC
E
S
[1
]
S
a
ra
Riah
i,
A
li
El
Ho
re
,
Ja
m
a
l
El
Ka
f
i,
"
A
n
a
l
y
sis
a
n
d
S
i
m
u
latio
n
o
f
OFDM
”,
IJ
S
R
,
IS
S
N
On
li
n
e
:
2
3
1
9
-
7
0
6
4
,
v
o
lu
m
e
3
,
Iss
u
e
3
,
P
a
g
e
No
(
4
0
5
-
4
0
9
),
M
a
rc
h
2
0
1
4
.
[2
]
S
a
ra
Ria
h
i,
A
li
El
Ho
re
,
Ja
m
a
l
El
Ka
f
i,
"
S
tu
d
y
a
n
d
A
n
a
l
y
sis
o
f
a
No
isy
S
ig
n
a
l
b
y
V
it
e
rb
i
D
e
c
o
d
in
g
"
,
IJ
S
R
,
IS
S
N
On
li
n
e
:
2
3
1
9
-
7
0
6
4
,
V
o
l
u
m
e
3
Iss
u
e
1
0
,
P
a
g
e
No
(3
9
2
-
3
9
8
),
Oc
to
b
e
r
2
0
1
4
.
[3
]
S
a
ra
Riah
i,
A
li
El
Ho
re
,
J
a
m
a
l
El
Ka
f
i,
"
P
e
rf
o
r
m
a
n
c
e
St
u
d
y
o
f
th
e
OFDM
M
o
d
u
latio
n
f
o
r
th
e
u
se
in
W
irele
s
s
Co
m
m
u
n
ica
ti
o
n
S
y
ste
m
s o
f
th
e
4
G
"
, e
-
IS
S
N:
2
3
9
5
-
0
0
5
6
,
p
-
IS
S
N:
2
3
9
5
-
0
0
7
2
,
Vo
lu
m
e
:
0
2
Iss
u
e
:
0
6
,
P
a
g
e
No
(1
2
1
9
-
1
2
2
7
),
S
e
p
-
2
0
1
5
.
[4
]
S
a
ra
Riah
i,
A
li
El
Ho
re
,
Ja
m
a
l
El
Ka
f
i,
"
Op
ti
m
iza
ti
o
n
o
f
R
e
so
u
rc
e
A
ll
o
c
a
ti
o
n
in
W
irele
ss
S
y
ste
m
s
Ba
se
d
o
n
G
a
m
e
T
h
e
o
r
y
,
"
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
Co
mp
u
ter
S
c
ien
c
e
s
a
n
d
En
g
in
e
e
rin
g
,
V
o
l.
-
4
(1
)
,
P
P
(0
1
-
1
3
)
Ja
n
2
0
1
6
,
E
-
IS
S
N:
2
3
4
7
-
2
6
9
3
.
[5
]
A
z
z
e
d
d
in
e
Riah
i
,
S
a
ra
Riah
i
,
"
S
t
u
d
y
o
f
Di
ff
e
re
n
t
Ty
p
e
s
o
f
No
ise
a
n
d
T
h
e
ir
Ef
f
e
c
ts
o
n
Dig
it
a
l
Co
m
m
u
n
ica
ti
o
n
s
,
"
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ter
n
a
t
io
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a
l
J
o
u
r
n
a
l
o
f
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v
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n
c
e
d
Res
e
a
rc
h
in
Co
mp
u
ter
a
n
d
Co
mm
u
n
ica
ti
o
n
E
n
g
i
n
e
e
rin
g
,
IJ
AR
CCE
,
2
0
1
5
.
4
9
6
8
,
V
o
l
.
4
,
Iss
u
e
9
,
S
e
p
tem
b
e
r
2
0
1
5
.
[6
]
S
a
ra
Riah
i,
"
P
e
rf
o
rm
a
n
c
e
Op
ti
m
i
z
a
ti
o
n
o
f
A
W
irele
ss
M
u
lt
im
e
d
ia
T
ra
n
s
m
issio
n
S
y
ste
m
B
a
se
d
On
t
h
e
Re
d
u
c
ti
o
n
o
f
P
A
P
R
,
"
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
En
g
i
n
e
e
rin
g
a
n
d
T
e
c
h
n
i
q
u
e
s
-
V
o
lu
m
e
3
Iss
u
e
4
,
Ju
ly
-
A
u
g
2017.
[7
]
S
.
N.
Ra
u
t,
R.
M
.
Ja
ln
e
k
a
r
,
“
P
e
rf
o
r
m
a
n
c
e
En
h
a
n
c
e
m
e
n
t
in
S
U
a
n
d
M
U
M
IM
O
-
OFDM
T
e
c
h
n
i
q
u
e
f
o
r
W
irel
e
ss
Co
m
m
u
n
ica
ti
o
n
:
A
Re
v
ie
w
,
”
In
te
rn
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
En
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
V
o
l.
7
,
No
.
5
,
Oc
to
b
e
r,
p
p
.
2
4
5
9
~
2
4
6
7
,
2
0
1
7
.
D
OI:
1
0
.
1
1
5
9
1
/i
jec
e
.
v
7
i
5
.
p
p
2
4
5
9
-
2
4
6
7
.
[8
]
S
a
n
g
so
o
n
L
im
,
“
G
a
m
e
T
h
e
o
re
ti
c
Ch
a
n
n
e
l
A
ll
o
c
a
ti
o
n
i
n
C
o
g
n
it
i
v
e
Ra
d
io
Ne
tw
o
rk
s
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
a
n
d
Co
mp
u
ter
E
n
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
V
o
l
.
7
,
No
.
2
,
p
p
.
9
8
6
~
9
9
1
,
A
p
ril
2
0
1
7
.
I
S
S
N:
2
0
8
8
-
8
7
0
8
,
DO
I:
1
0
.
1
1
5
9
1
/i
jec
e
.
v
7
i2
.
p
p
9
8
6
-
9
9
1
.
[9
]
I.
F
.
Ak
y
il
d
iz,
W
.
S
u
,
Y.
S
a
n
k
a
ra
su
b
ra
m
a
n
ia
m
,
E.
Ca
y
ir
c
i,
“
Wi
re
les
s
S
e
n
so
r
Ne
t
w
o
rk
s:
A
S
u
rv
e
y
,
”
Co
mp
u
ter
Ne
two
rk
s:
T
h
e
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Co
m
p
u
ter
a
n
d
T
e
lec
o
mm
u
n
ica
ti
o
n
s
Ne
two
rk
in
g
,
v
.
3
8
n
.
4
,
p
.
3
9
3
-
4
2
2
,
1
5
M
a
rc
h
2
0
0
2
.
[1
0
]
J
ia
Z,
Ch
u
n
d
i
M
,
Jia
n
b
in
H.
“
G
a
m
e
T
h
e
o
re
ti
c
En
e
rg
y
Ba
lan
c
e
Ro
u
ti
n
g
in
W
irele
ss
S
e
n
so
r
Ne
t
w
o
r
k
s
,
”
In
:
Ch
in
e
se
c
o
n
tro
l
c
o
n
fer
e
n
c
e
,
2
0
0
7
.
CCC 2
0
0
7
.
Hu
n
a
n
Pr
o
v
in
c
e
,
Ch
i
n
a
:
IE
EE
;
2
0
0
7
.
p
.
4
2
0
-
4.
[1
1
]
X
in
A
i,
V
.
S
r
in
iv
a
sa
n
,
Ch
e
n
-
k
h
o
n
g
T
h
a
m
,
"
Op
ti
m
a
li
t
y
a
n
d
Co
m
p
lex
it
y
o
f
P
u
re
Na
sh
Eq
u
il
i
b
ria
in
th
e
Co
v
e
ra
g
e
G
a
m
e
,
"
IEE
E
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