Center for the Study of Rationality
The Hebrew University of Jerusalem
Herodotus of Ancient Greece 500 BC
Women are sold for marriage by their families through
auctions (they used Dutch Auctions).
Auctions are held as mandatory for selling women into
Rome 193 AD
Pertinax the Emperor is executed for the failing
economy in Rome.
The entire empire is sold by an auction to the highest
Julianus wins the auction and becomes the new
Auction vs. Bargaining
Auction: When the number of potential buyers is
large and the seller’s information about the buyers’
willingness to pay is limited.
Bargaining: Mainly in bilateral transactions or when
the good has better-defined market value.
In many cases one can combine an auction with
bargaining (there are downsides and upsides).
Common Value: All bidders have the same monetary
value for the object but this value is unknown.
Private Value: Different bidders have different values
for the object but each bidder is fully informed about
his own value (and is not informed about other
The Winner’s Curse
Popular Auction Mechanisms
First Price Sealed Bid: Bidders submit bids in sealed
envelopes. The highest bidder wins the object and pays
Second Price Sealed Bid: Like the first price sealed
bid, except that the winner pays the second highest
price instead of his own price.
English Auction: The auction involves ascending
prices. Bids are announced publicly and have to exceed
those currently in the system. The winner is the last to
Dutch Auction: A pointer points and there is a very
high price that gradually declines. The pointer stops
with the first “stop” call of a bidder. This bidder pays
the price at which the pointer stops.
Japanese Auction: The auction starts at a very low
price that gradually rises. People leave the room when
the price exceeds their willingness to pay. The last to
remain wins and pays the price at which the next to
last left the room.
Israeli Auction: Like first price sealed bid, except that
the winner is the cousin of the mayor and he pays 50%
of the lowest bid.
In the Second Price Sealed Bid auction, there is a
dominant strategy for each bidder, which is to bid the
true value of the object.
Proof: Denote by x the highest bid (apart from mine).
Assume that my value for the object is 1000 EUR.
If x < 1000, then any bid above x will make me the
winner and will make me pay x. Any bid below x will
make me lose. So saying 1000 is best.
If x > 1000, then bidding above x will make me win the
object but lose money, and bidding below x (regardless
of the bid and including 1000) will give me zero profit.
Proxy servers in Internet auctions create a second price
The Equivalence of Auction
First Price Sealed Bids and Dutch Auctions are
Second Price Sealed Bids and English Auctions are
The Revenue Equivalence Theorem (Vickery 1961;
Myerson 1980): All efficient auctions are revenue
The Analysis of First Price Auctions
v1 ,…vn (bidders’ valuations) are iid with the cumulative
b(v) is the bidding function of each player.
In equilibrium each player’s bidding function has to
maximize his expected profit, given the bidding
functions of the rest.
Expected profit of player i is given by
Ei(b)= P (player i has the highest bid) [v – b(v)].
P(i’s the highest bid) = P(bi(vi)) > bj(vj)) for all j ≠i) =
p(vi > vj for all j ≠i) = [F(vi)]n-1
Equilibrium Conditions: argmaxw[F(w)] n-1[v-b(w)]=v
(n-1)[F(w)] n-2F’(w)[v-b(w)]-b’(w)[F(w)] n-1|w=vi= 0
If vi ~ U[0,1] then b(v) =
First price auctions generate more revenue than Dutch
Average bids increase with the number of bidders in
The Cellular Auctions
From 1993 to 2001 governments in the world made a
revenue of 100 billion USD.
In 1994 the New York Times announced the British
Cellular Auction as the largest auction ever, totaling a
revenue of 34 billion USD.
Ken Binmore designed the auction and became Sir
The New Zealand Failure
The auction used was second price sealed bids.
On one batch of frequencies the highest bid was 7
million NZD, and the second highest bid only 5000
On another batch the highest bid was 100,000 and the
second highest only 6 NZD!!!
The FCC Auction in the US
The auction runs in stages.
At each stage each bidder can introduce new bids and
withdraw his existing bids.
New bids have to exceed those in the system.
Bids that are withdrawn incur a potential fine on the
bidder. The bidder has to pay the difference between
his withdrawn bid and the price at which the batch is
Auctions in Google
Any query in Google earns around 10 cents for the
The participating companies compete on the location
in the ad and bid on any query.
Google estimates the number of clicks per query for
each company and ranks pages to maximize revenue.
Large Auctions in Israel
In 2006 the government share in the national
telephone company was sold in an auction. The
highest bid was around 200m EUR.
After the auction ended the government requested an
additional 6m EUR and received it.
Is it a good strategy?
The country’s storage facilities for gas were sold in
2007. There were 3 sites.
The mechanism used was a combinatorial auction
(with ascending prices).
The government earned 350m EUR where expert
estimates were about 60m EUR.
The largest Israeli newspaper announced this auction
as the most successful one in the history of the
Legal Issues in Auctions
Collusion: Why is it banned by most governments?
Around 50% of the Anti-Trust cases in the US are on
collusion in auctions.
Sellers “hide” reservation prices and make bidders
believe that they will sell to the highest bidder at any
Sellers make fictitious bids to boost prices in auctions.
They inform one bidder of the price of another bidder
to get a higher price.
Why is it wrong to allow it?
Manipulation destroys the efficiency of the market
“Tacit” Collusion in Auctions
On batch no. 128 in the US FCC auction someone bids
The California Electricity Market: Tacit collusion
requires long term interactions between bidders.
Contracts in the electricity market in CA were too
short and facilitated long-term interactions (Repeated
Behavioral Aspects of Auctions
The Afternoon Effect