## 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?