6.
a.
With only two bidders,
n
= 2.
The lowest possible valuation is
L =
$1,000, and
your own valuation is
v =
$2,500.
Thus, your optimal sealed bid is
$2,500
$1,000
$2,500
$1,750
2
v
L
b
v
n


=

=

=
.
b. With ten bidders,
n =10
.
The lowest possible valuation is
L =
$1,000, and your
own valuation is
v =
$2,500.
Thus, your optimal sealed bid is
$2,500
$1,000
$2,500
$2,350
10
v
L
b
v
n


=

=

=
.
c.
With one hundred bidders,
n =100
.
The lowest possible valuation is
L =
$1,000,
and your own valuation is
v =
$2,500.
Thus, your optimal sealed bid is
$2,500
$1,000
$2,500
$2,485
100
v
L
b
v
n


=

=

=
.
7.
a.
With 5 bidders,
n = 5
.
The lowest possible valuation is
L =
$50,000, and your
own valuation is
v =
$75,000.
Thus, your optimal sealed bid is
$75,000
$50,000
$75,000
$70,000
5
v
L
b
v
n


=

=

=
.
b. A Dutch auction is strategically equivalent to a firstprice sealed bid auction (see
part (a)).
Thus, you should let the auctioneer continue to lower the price until it
reaches $70,000, and then yell “Mine!”
c.
$75,000, since it is a dominant strategy to bid your true valuation in a second
price, sealedbid auction.
d. Remain active until the price exceeds $75,000; then drop out.