
217A Game of Competitive Investment
Let us consider the total stage 1 capacity investment levels. By Equations
8.31 and 8.41, we can combine the competitive and rst-best cases to obtain
the following: for n = 1, 2,…,
zz
n
n
nL nH
*
(0)=
*
(0)=
(2 1)
2
2
2
−⋅
+
, (8.45)
and
zB n
LH LB
nL n
n
n
*
()=(21)
2
(16(
)
2
2
α−⋅
++ ⋅
()
⋅+ ,,
*
()=(21)
2
(16(
2
2
2
zB n
HL HB
nH n
n
n
α−⋅
++ ⋅
⋅+
22
).
(8.46)
We may dene
for n = 1,2,… as a ratio:
k
zz
n
nH n
nL n
*
=
*
(
*
)
*
(
*
)
0
0
.
(8.47)
It measures the condence a rm has in its acquired information about the
market outlook.
By Propositions 8.7 and 8.8 and Equations 8.45 through 8.47, we have, for
n = 1, 2,…,
AA C
KB