Questions

1. Consider that you are preparing to sell some antique
items at auction. How might you design the auction so
as to receive the highest possible sale price? What sorts
of behavioral anomalies will be important to consider?
What role will the number and experience of the bidders
play in the auction?
2. Consider now that you are preparing to purchase an item
at auction for your personal use. What factors should
you consider in forming your bid? What behavioral
tendencies should you try to avoid? What if you were
purchasing the item for resale at a later date instead?
3. Building contractors bidding on a building project
often calculate their anticipated costs, add some percentage
for profit, and then double this number and
submit it as a bid. Similar rules of thumb have been
reported in other auction arenas. Why do you think
such rules of thumb developed? What purpose do they
serve? In what ways might the contractors be worse off
for using this rule of thumb?
4. Suppose that two people are engaged in a Vickrey
auction for a good with two possible values: $10 or
$20. Further, suppose each bidder receives a signal of
the value, xn, where xn is equal to the true value with
probability 0.8, and equal to the other possible value
with probability 0.2. No information other than this
signal is available. Each player must select a bid based
on his own signal. What bidding strategy would be
suggested by the fully cursed equilibrium (e.g., what
should you bid if you receive a signal of $10 and what
should you bid if you receive a signal of $20)? Suppose
that players can only bid integer amounts, and
follow the example given in the text. Thus, if player 1
draws x1 =10, the mean value of winning the auction
is μ= 0.8 × 10+0.2 × 20 =12, the probability of
signals that player 2 might receive is (similar to
equation 5.14)
p x2 =
0.8 × 0.8+0.2 × 0.2=0.68 if x2 =10
0.8 × 0.2+0.2 × 0.8=0.32 if x2 =20.
If player 1 draws x1 =20, the expected value of winning
the auction is μ=0.8 × 20 +0.2 × 10= 18, and the
probability distribution of signals that player 2 might
receive is
p x2 =
0.8 × 0.8+ 0.2 × 0.2=0.68 if x2 =20
0.8 × 0.2+ 0.2 × 0.8=0.32 if x2 =10
Suppose that in the event of a tie, both players receive
the value of the object. First try the strategy in which
each player bids the expected value of the gamble
given the signal each has received. Show that this
constitutes a cursed equilibrium. What is the expected
profit in this case (the actual, not perceived)? Do these
strategies constitute a Bayesian Nash equilibrium? If
not, can you find the Bayesian Nash equilibrium?