Item to be bid: A $5 bill

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Rules for Auction 1
Item to be bid A 5 bill Starting bid 2. Bid
increments 25 cents. Winning bid is the highest
bid.
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Rules for Auction 2
Item to be bid A 5 bill. Starting bid 1. Bid
increments 50 cents. Winning bid is the highest
bid. However, the top two bidders must pay what
they bid.
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Some lessons
The rules of the game matter.
Some rules work better than others. Some
different rules may induce equivalent behavior.
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Questions from auctions we held touch on the most
fundamental concerns of economists

• When people make choices in different settings,
  can we predict what choices they will make, and
  what choices they should make?
• Can we devise ground rules that help people
  make choices leading to the best possible
  outcomes for themselves, or the best possible
  outcomes for society?
• ? If we change the ground rules, how will this
  affect the choices they do, or should, make?

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Types of auctions
Private-value auctions Individuals know what the
value of the item is to them, but the item has a
different value to each potential buyer.
Common-value auctions Individuals would all
have the same valuation of the item were they to
obtain it, but they do not know in advance
exactly what the value of the item is.
Oral auctions Everyones bid is visible to
everyone else. Sealed-bid auctions Every bid
is secret. Bids are opened at the same time and
the winner is announced.
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Two types of oral auctions
English oral auction The auctioneer begins with
a low asking price, and continues to raise it
until no one offers to beat the last bid. The
last bidder wins the item at the price she last
offered. Dutch oral auction The auctioneer
begins with a high price, and then gradually
drops it until someone offers to take the item at
that price. Dutch auctions can be very fast. The
price declines are called out rapidly until
someone calls out Mine! If youre not on the
ball, you miss out.
Two types of sealed-bid auctions
First-price sealed-bid auction A single, secret
bid is made by each participant. The item for
sale goes to whoever submitted the highest
bid. Second-price sealed-bid auction A single,
secret bid is made by each participant. The item
for sale goes to whoever submitted the highest
bid. However, the winner only pays the value of
the second-highest bid. Also known as Vickrey
auctions.
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Valuable properties of Vickrey auctions
In the Vickrey auction, the rational strategy is
to bid exactly what the item is worth to you. Put
another way, bidding honestly is at least as
good as any other strategy in any scenario, and
it is strictly better in some scenarios.
Proof Let v be the value of the object to
Mariela, Let b be the highest bid any of her
opponents makes. If Mariela wins the bid, she
makes a net gain of v-b (could be negative). If
she doesnt win, then she receives 0.
Three scenarios (i) bgtv. (ii) bltv. (iii)
bv.
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(No Transcript)
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Weakly dominant strategy a strategy that is at
least as good as any other strategy under all
possible scenarios
Strictly dominant strategy A strategy is
strictly better than any other under all possible
scenarios.
Thus, bidding ones true valuation for an item in
a Vickrey auction is a weakly dominant strategy.
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A Vickrey auction with multiple items for sale.
Suppose a seller has 10 identical items he wants
to sell. How can we devise an auction so that all
10 items are sold? Hold a modified Vickrey
auction
Deliver all the supply to the highest bidders and
make everyone pay the price that is paid by the
bidder who just failed top get an one of the
units (i.e. the 11th-highest bidder). This type
of auction gets everyone to bid their true
values, so it guarantees that everyone with the
highest valuations for the items will get them.
The auction system will enable the seller to
get rid of his stock of goods. This seems a
good way to run an auction. (Google did it in
2004).
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The Great Arizona State Office Auction
New building with 6 departments to move. Some
offices had windows, others did not.
Management, Marketing, Accounting assigned
offices by seniority. Finance chair did a
surprise post-up sheet. Statistics rolled
dice. Economics held a first-price auction.
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An Example
The seller has five units to sell. Mara values
the item at 14 and wants only one. John values
two at 10 each, Abu wants one for a value of 8,
Fred values one at 4, Juan one at 3, and Eli
one at 2. The seller ranks the bidders in
order of the bids (which are the same as their
true valuations). She then finds that she can get
rid of all of her five units by charging 3. Juan
and Eli dont get any, because their valuations
are too low.
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Consumer Surplus
Mara earns a valuation of 14 put pays only 3.
Her net gain is 11. Johns net gain is 14
two units at 7 each. Abus is 5, and Freds
is . Juan and Eli have net gains of zero they
get none of the good, but they also dont pay
anything. If we add together each individuals
net gains -- 11 (Mara) 14 (John) 5 (Abu)
1 (Fred) 31, we get a measure of how well off
they are from participating in this auction.
The excess of a persons valuation of a good over
and above what they pay for it is called her
consumer surplus.
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Graphically, total consumer surplus is given by
the shaded area of the graph that lies above the
price line.
The seller sells 5 units at 3 each, so her
revenues are 15. Revenues to the seller are
given by the shaded area that lies below the
price line. Revenues may not be all profit, of
course.
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Producer surplus, profits, costs and revenues
Profits are the excess of revenues from selling
goods over the cost of making them available for
sale. Profits are often referred to in economics
as the producer surplus.
Example Imagine that the seller has five units
of the item in question, and they are worth 2
each to her if she consumes them instead of
selling them. This 2 per unit is her cost of
selling the items. As she can sell each unit for
3, she is happy to sell, and she makes profit of
5.
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The Vickrey auction maximizes the sum of producer
and consumer surplus.
There is no way to change the price, or the
allocation of the goods among the bidders, to
make them better off as a whole.
If we take a unit of the good away from any of
those who have them, and give it to either Juan
or Eli, who dont, consumer surplus must fall at
the current price. If we keep the allocations
among bidders unchanged but lower the price, we
can raise consumer surplus. However, the seller
is made worse off by exactly the same amount.
Moreover, Juan might now want one because the
price falls and we may have to devise some new
rule to explain why he cant have one. If we
raise the price we make the seller better off,
but only by reducing consumer surplus by the same
amount. Moreover, Fred will no longer want to buy
his unit, so we would have to force consumption
on him.
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In summary, a Vickrey auction has several
attractive features.
At the price that enables the seller to offload
all her goods

• Everyone that buys the good finds it worthwhile
  to do so because their valuation exceeds the
  price.
• Everyone that doesnt buy the good finds it
  optimal not to do so, because the price exceeds
  their valuation.
• At this price, the sum of the welfare of
  consumers (measured by consumer surplus) and the
  welfare of the seller (measured by producer
  surplus) is maximized.
• There is no alternative allocation scheme that
  makes society better off.

Thus, the rules of the game in a Vickrey auction
make for a desirable outcome.
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Private value auctions
In a Vickrey auction, consumer surplus is
maximized. But this was a special type of
Vickrey auction a private-value auction -- in
which all consumers knew exactly what the item
was worth to them. Knowing exactly what the item
is worth enables consumers to bid exactly their
valuations. Bidding exactly their valuations
enables the auction scheme to allocate the items
to all the participants with the highest
valuations. This in turn maximizes the sum of
consumer surplus and seller profits, which we can
use as a measure of the well-being of society
But there is another type of auction a common
value auction. In common value auctions, no rules
of the game work quite as well.
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Common-value auctions and the winners curse
There are 9 bidders and 5 units for sale. The
true valuation of the good in question is the
same for everyone 9. Three bidders think the
item is worth only 8, Three think it worth 10,
Three think it worth 12. If everyone follows
the strategy of bidding what they think the item
is worth, everyone pays the lowest bid that
clears the market -- 10.
But the successful bidders will be disappointed.
They paid 10, only to discover, after all, that
the items is only worth 9. This disappointment
is know as the winners curse. The winners in an
auction are those who made the biggest
overestimates of the true value of the good.
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The term winners curse was introduced to the
profession by Capen, Clapp and Campbell (1971),
who studied bidding behavior in the oil industry.
In the 1950s, firms were competing in auctions
to win oil-drilling rights in the Gulf of Mexico.
But every time a winning firm started drilling,
they ended up losing money.
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The winners curse another example
There are five units for sale.
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The winners curse another example
There are five units for sale.
Winners
Winners curse
Abu should have got one instead of Juan
This misallocation from Abu to Juan reduces
consumer surplus by 5.
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When participants are imperfectly informed about
the value of the goods, the Vickrey auction may
not maximize consumer surplus. A Vickrey
auction will make society as well off as possible
only under the assumption that participants in
the market have perfect information. When that
assumption is violated, the very same market no
longer guarantees society will be made as well
off as possible. Economists refer to this
inability of the market to work as well as we
would like as a market failure.
What can people do to avoid or reduce the problem
of the winners curse?
If you know that mistakes in valuation are
possible, you should bid less than your guess.
How much less is a complicated question. Or as
policymakers, we might try and change the rules
of the game.
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Vickrey auctions are much like many markets we
see all around us.
Of course, we dont submit sealed bids at the
grocery store and wait to see if we get what we
bid on. Instead, the grocery store posts the
price at which it will sell its stock, and we
will only buy a good if the posted price is less
than our valuation. The person with the lowest
valuation that actually buys the good has a
valuation just equal to the posted price.
People who dont buy the good have a lower
valuation than the posted price. If the grocery
store can guess the right price, it will be able
to sell all the units it has for sale.
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The details of the grocery stores problem is
different, but the outcome is the same. Thus,
many markets have the same desirable features as
Vickrey auctions. If the market is working well,
we will prefer to leave it alone and let it
function. But if a market failure stops the
Vickrey auction from having desirable properties,
these same problems will stop other markets from
having desirable features. In these cases we
might prefer to devise a policy to change the
outcomes of the market.
Some markets may not take the form of a Vickrey
auction at all. It is then reasonable to assume
that they will often not have the desirable
features we are looking for. In such cases we
might again want to devise a policy to change the
way the market work.