Auctions
Ruth Tarrant
Classifying auctions
What is the nature of the
good being auctioned?
Private value
auction
Each bidder has a
potentially different
valuation of the
good owing to
tastes and
preferences e.g. fine
art
Common
value auction
The good has the
same value to
each bidder but
they may have
different
estimates of that
value e.g. offshore drilling
rights
What are the rules of
bidding?
English, Dutch, sealed-bid
or Vickrey?
Rules of bidding – private value
auctions (1)
• English auction (most common)
– Start with a ‘reserve price’ (the lowest that the seller
will accept)
– Bidders offer successively higher prices
– When no bidder is prepared to go higher the good is
awarded to the highest bidder
• Dutch auction
– Auctioneer starts with a high price and lowers it step
by step until someone is prepared to buy it
– Very rapid!
Rules of bidding – private value
auctions (2)
• Sealed-bid auction
– Each bidder writes their bid on paper and seals it
in an envelope, which are collected and opened,
and the good is awarded to the highest bidder (or
possibly lowest bidder depending on auction)
– Common for construction work and large projects
where the job will be awarded to the lowest bid
• Vickrey auction
– Like sealed bid but the good is awarded to the
highest bidder but at the second highest price
How do we choose the type of
auction? (1)
Two goals
Pareto efficiency
The good must be assigned to the person
with the highest value
(Alice values it higher than Bob – if Bob
receives it then you can make both better off
by Alice transferring the good to Bob and Bob
paying Alice some value between Alice’s value
and Bob’s value)
Profit maximisation
The good must be assigned to the person
with the highest value
How do we choose the type of
auction? (2)
• English auction
– Pareto efficiency: yes!
– Profit maximisation: difficult to say because the
winning bidder may have gone higher if he had
been pushed by other bidders
– Susceptible to collusion
How do we choose the type of
auction? (2)
• Dutch auction
– Pareto efficiency: no guarantee that the good will
go to the person with the highest valuation as
they may wait too long to bid
– The optimal bid depends on the highest bidder’s
beliefs about the values of other bidders
How do we choose the type of
auction? (3)
• Sealed-bid auction
– Similar to Dutch auction as the optimal bids by
each bidder depends on their beliefs about the
bids of others, so can’t guarantee Pareto efficiency
or profit maximisation
How do we choose the type of
auction? (4)
• Vickrey auction
– If everyone bids their ‘true’ value the bidder with
the highest valuation will receive the good (same
as the English auction)
– We can prove mathematically that bidders have
an incentive to bid truthfully in this type of
auction, so it’s the quickest and most likely to
achieve Pareto efficiency and profit maximisation
as a result
The Winner’s Curse – common value
auctions
• Assume that the rights or goods are given to
the highest bidder
• The winner will win only by being overly
optimistic!
Questions
1. Is an auction of antique quilts to collectors a
private-value or common-value auction?
2. Suppose there are 2 bidders with values of £8
and £10 for the item, with a bid increment of £1.
What is the profit maximising reservation price
for an English auction?
3. A teacher fills a jar with pennies and auctions it
off using an English auction. Is this a privatevalue or common-value auction? Will the
winning bidder usually make a profit?
Questions
4. Suppose there are 2 bidders for an item. The
seller believes the bidders have a value of
£10 or £100. Assume these two cases are
equally likely:
a. What is the expected revenue to the seller?
b. Is there any way the seller can do better than this?
Questions
5. A dealer decides to sell an antique car by
means of an English auction with a reservation
price of £900. There are 2 bidders. The dealer
believes that there are only 3 possible values
that each bidder’s valuation might take: £6300,
£2700 and £900, each with equal probability.
Assuming that the bidders bid rationally and
don’t collude, what is the dealer’s expected
revenue from selling the car?
Questions
6. A bank repossesses a house and sells it off at
auction. There are 3 bidders. The bank believes
that each of the bidders has a probability of 1/3
of valuing the house at £700,000, a probability
of 1/3 of valuing it at £500,000 and a 1/3
probability of a £200,00 valuation. These
probabilities are independent between buyers.
If the bank uses a Vickrey auction, what will the
bank’s expected revenue be from the sale?