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http://find/http://goback/
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2/30
http://find/
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http://find/
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http://find/
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(yi)
(y
+y
)
http://goforward/http://find/http://goback/
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7/22/2019 Econ2101 2210 Oligopoly Game Theory
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y
y
(y
; y
) =p(y
+y
)y
c
(y
)
y
F.O.C.
(y
;y
)y
= = y =y (y )
y
y
(y
; y
) =p(y
+y
)y
c
(y
)
y
F.O.C (y ;y )y
= = y
=y
(y
)
y
(y
) y
(y
)
http://find/
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7/22/2019 Econ2101 2210 Oligopoly Game Theory
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(y
, y
)
y
=R
(y
)
y
=R
(y
)
p(yT) = yT
yT =y +y c (y ) =y
c
(y
) = y
+y
maxy
(y
; y
) = ( y
y
)y
y
F.O.C.
y
=
y
y
y
=
y y =R (y )=
y
http://find/
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y2
Firm 1s reaction curve
60 y R y y1 1 2 2154
( ) .
y115
http://find/
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7/22/2019 Econ2101 2210 Oligopoly Game Theory
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maxy
(y
; y
) = (
y
y
)y
y
y
F.O.C.
y
= y
y
y
=
y
y
=R
(y
) = y
y2
y R y
y2 2 1
145
4 ( ) .
45/4
y145
http://find/
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7/22/2019 Econ2101 2210 Oligopoly Game Theory
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y
=R
(y
) =
y
y
=R
(y
) = y
y2Firm 1s reaction curve
1
Firm 2s reaction curve60
y y y1 1 2 2
4
.
y R y y
2 2 1145
4 ( ) .
45/4
y115 45
http://find/
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y
=
( y
) y
=
y
=
=
(y
, y
) = ( , )y2
Firm 1s reaction curve1
Firm 2s reaction curve
60 y y y1 1 2 2
4 .
y R y y
2 2 1145
4 ( ) .
8
Cournot-Nash equil ibrium
y y 13 8* *, , .y14813
http://find/
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http://find/
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http://find/
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y
y
=R
(y
)
S
(y
) =p(y
+y
)y
c
(y
)
y
y
S
(y
) =p(y
+R
(y
))y
c
(y
)
yS
F.O.C
http://find/
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7/22/2019 Econ2101 2210 Oligopoly Game Theory
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maxy
(y
; y
) = ( y
y
)y
y
y
y
y
=R
(y
) = y
y
S
(y
) = ( y
R
(y
))y
y
y
S
(y
) =
y
y
F.O.C.
=
y
= yS
= .
yS
= .
=
.
http://goforward/http://find/http://goback/
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(y
, y
) = ( , )
http://find/
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p
S(p) =y (p)
http://find/
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7/22/2019 Econ2101 2210 Oligopoly Game Theory
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D(p)
p
L(p) =D(p) S(p)
pL(p) =p(D(p) S(p)) cL(D(p) S(p))
y
py
y
y
F.O.C= y
= p
y
= p y
= .
.
p
pp( . . p) ( . . p)
http://find/
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7/22/2019 Econ2101 2210 Oligopoly Game Theory
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y
y
y
,y
p(y
+y
)[y
+y
] c
(y
) c
(y
)
F.O.C. p(y
+y
) + pY
(y
+y
) =MC
(y
)
p(y
+y
) + p
Y(y
+y
) =MC
(y
)
http://find/
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y
y
y
,y
p(y
+y
)[y
+y
] c
(y
) c
(y
)
F.O.C. p(y
+y
) + pY
(y
+y
) =MC
(y
)
p(y
+y
) + p
Y(y
+y
) =MC
(y
)
y
y
p
Revenue
Revenue
profit
profit
http://find/
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7/22/2019 Econ2101 2210 Oligopoly Game Theory
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i
y
=p(y
+y
)y
c
(y
)
F.O.C d
dy
=p(y
+y
) + p
Yy
MC
(y
) =
http://find/
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p(y
+y
) + p
Y(y
+y
) =MC
(y
)
p(y
+y
) + p
Yy
MC
(y
) = p
Yy
>
d
dy >
http://find/
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http://find/
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7/22/2019 Econ2101 2210 Oligopoly Game Theory
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ayer
L R
This is theames
U (3,9) (1,8)
payoff matrix.
D (0,0) (2,1)
Player As payoff is shown first.P ayer B s payo is s own secon
.
http://find/
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rm
Advertise Dont advertise
Advertise 10, 5 15, 0
Dont advertise 6, 8 10, 2
http://find/
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rm
Advertise Dont advertise
Advertise 10, 5 15, 0
Dont advertise 6, 8 10, 2
http://find/
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L R
ayer
U (3,9) (1,8)
D (0,0) (2,1)
(U, L) (D,R)
http://find/
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Player B
L R
(1,2) (0,4)U
(0,5) (3,2)D
http://find/
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Prisoner B
Confess Dont confess
Prisoner AConfess 5, 5 1, 10
Dont confess 10, 1 2, 2
http://find/
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Prisoner B
Confess Dont confess
Prisoner AConfess 5, 5 1, 10
Dont confess 10, 1 2, 2
