Homework 4, Problems due November 8
Read this chapter
and Sections 13.1-13.4 of this book
(username:agt1user, password: camb2agt).
(You might also want to read this chapter as a warm-up.)
There are also
relevant sections in Chapter 10 of this book.
-
Consider a seller selling digital goods (i.e. items available in unlimited
supply) to a set of n agents, each with a private value for one of these goods.
The seller's goal is to make $1000 if possible and towards this end
he runs the following mechanism:
He asks players each to submit a sealed bid indicating
their value for one of these digital goods. Let k be
the largest number of players who submit a bid at or above $1000/k.
These players will receive a copy of the good and pay $1000/k for it.
If there is no such k, then no player wins.
For example, if the bids are 500, 300, 300, 250, 125, then k is 4 and the first
4 players receive a copy of the good and each pay $250 for it
If the bids are 500, 300, 300, 200, 125, then no player wins.
Prove that it is a dominant strategy in this mechanism to tell the truth.
(As usual, a player's utility is their value minus the payment if they
win and 0 otherwise.)
- Problem 6 on page 270 of this book.
- Show that a single-item auction in which the item is allocated to the second
highest bidder is not truthful no matter what payment rule is used.
- Additional Problems -- these are due by November 10.
- Extra Credit: Problem 2.2 in this chapter.