September 2009
Intermediate to advanced
336 pages
9h 37m
English
Content preview from Auction Theory, 2nd Edition
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136 Efficiency and the English Auction
e
2
Single
e
3
e
1
S
2
S
1
S
3
e
2
Average
e
3
e
1
A
2
A
1
A
3
FIGURE 9.3 A comparison of the crossing conditions.
common value component—that is, for all i, v
i
(x) =u
i
(
x
i
)
+w(x), where u
i
> 0,
then the average crossing conditions is satisfied. To see this, note first that with
separability, for all i,j ∈A and i =j,
∂
v
A
∂x
j
(
x
)
=
1
#A
u
j
x
j
+
∂w
∂x
j
(
x
)
>
∂w
∂x
j
(
x
)
=
∂v
i
∂x
j
(
x
)
The additively separable specification is commonly employed in empirical work.
9.5 PROOF OF PROPOSITION 9.2
In an English auction, a strategy for bidder i determines the price at which
he would drop out given his private information and given the history of who
dropped out at what
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