Networks: Spring 2010
Homework 3
David Easley and Jon Kleinberg
Due February 26, 2010
As noted on the course home page, homework solutions must be submitted by upload to
the CMS site, at https://cms.csuglab.cornell.edu/. This means that you should write these
up in an electronic format (Word ﬁles, PDF ﬁles, and most other formats can be uploaded
to CMS). Homework will be due at the start of class on the due date, and the CMS site will
stop accepting homework uploads after this point. We cannot accept late homework except
for University-approved excuses (which include illness, a family emergency, or travel as part
of a University sports team or other University activity).
Reading:
The questions below are primarily based on the material in Chapters 9, 10
and 11 of the book.
(1)
In this problem we will examine a second-price, sealed-bid auction for a single item.
Assume that there are three bidders who have independent, private values
v
i
; each is a
random number independently and uniformly distributed on the interval [0
,
1], and each
bidder knows his or her own value, but not the other values.
You are bidder 1. You know that bidders 2 and 3 bid according to bidding rules in which
they bid below their true value by certain factors. Speciﬁcally, when bidder 2 has a true
value of
v
2
, she bids
c
2
v
2
, for a constant number
c
2
that is greater than 0 and less than 1.
Similarly, when bidder 3 has a true value of
v
3
, he bids
c
3
v
3
, for a constant number
c
3
that is
greater than 0 and less than 1. You know your own value
v
1
, and you know these multipliers
c
2
and
c
3
, but you do not know the true values
v
2
and
v
3
of the other bidders.
How much should you bid? Provide an explanation for your answer; a formal proof is
not necessary.
(2)
In this problem we will examine a second-price, sealed-bid auction for a single item.
We’ll consider a case in which true values for the item may diﬀer across bidders, and it
requires extensive research by a bidder to determine her own true value for an item —
maybe this is because the bidder needs to determine her ability to extract value from the
item after purchasing it (and this ability may diﬀer from bidder to bidder).
There are three bidders. Bidders 1 and 2 have values