Bidding and Auction Design
Prelude
Auctions for selling goods and services date back to ancient Greece
and Rome – slaves
First formal analysis of auctions dates only to 1961 – the path-breaking
work of Nobel Prize winner William Vickrey
The term “auction” refers to any transaction where the final price of
the object for sale is arrived at by way of competitive bidding
We participate in online auctions, offline (unknowingly)
Your life is greatly influenced by them – auctions of 4G spectrum, Sir
India
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Prelude
From a strategic perspective, auctions have several characteristics of
interest.
1. Existence of asymmetric information between seller and bidders,
as well as among bidders. Thus, signaling and screening can be
important components of strategy for both bidders and sellers.
2. Optimal strategies for both bidders and sellers will depend on their
levels of aversion to risk.
3. Under some specific circumstances, expected payoffs to the seller as
well as to the winning bidder are the same across auction types
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Types of Auctions
Auctions differ in the methods used for the submission of bids and for
the determination of the final price paid by the winner.
These aspects of an auction, which are set in advance by the seller, are
known as auction rules.
In addition, auctions can be classified according to the type of object
being auctioned and how it is valued; this determines the auction
environment.
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Auction Rules
The seller generally determines the rules that will govern the auction.
She has to do this with only limited knowledge of the bidders’
willingness to pay.
The four major categories of auction rules –
1. Open Outcry: bidders call out or otherwise make their bids in
public. All bidders are able to observe bids as they are made. The
ascending, or English, version of an open-outcry auction
conforms feverish bidding – start with a low price and increase the
bid – auctioned (or sold) to highest bidder. Dutch, or descending,
auction – starts with a high price, then decreases the price until
someone accepts the price and makes the bid (not a feverish
bidding).
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Auction Rules
2. Sealed Bid Auction: bidding is done privately and bidders cannot
observe any of the bids made by others; in many cases, only the
winning bid is announced.You get only one chance to bid. No
auctioneer, only one observer who opens the bid and determines the
winner.
In a first-price, sealed-bid auction, the highest bidder wins the
item and pays a price equal to her bid.
In a second-price, sealed-bid auction, the highest bidder wins the
item but pays a price equal to the bid of the second-highest
bidder (Vickrey Auction).
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Auction Environment
There are a number of ways in which bidders may value an item up for
auction
The main distinction in such auction environments is based on the
difference between common and private-value objects
In a common-value, or objective-value auction, the value of
the object is the same for all the bidders, but each bidder generally
knows only an imprecise estimate of it. Oil exploration – same
revenue, but doesn’t have the exact estimate of the oil reserve. In such
auctions, signaling and screening can play an important role.
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Auction Environment
In a common-value auction, each bidder should be aware of the fact
that other bidders possess some (however sketchy) information about
an object’s value, and she should attempt to infer the contents of that
information from the actions of rival bidders.
In addition, she should be aware of how her own actions might
signal her private information to those rival bidders.
When bidders’ estimates of an object’s value are influenced by their
beliefs about other bidders’ estimates, we have an environment in
which bids are said to be correlated with each other.
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Auction Environment
In a private-value, or subjective-value auction, bidders each
determine their own individual value for an object. In this case,
bidders place different values on an object. For example, a gown
worn by Princess Diana.
Bidders know their own private valuations, doesn’t know others’,
seller does not know any of the bidders’ valuations. Bidders and sellers
may each be able to formulate rough estimates of others’ valuations
and can use signals and screens to attempt to improve their final
outcomes.
Information is very important - not only to bidding strategies but also
to the seller’s strategy in designing the form of auction to identify the
highest valuation and to extract the best price
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The Winner’s Curse
A standard but often ignored outcome arises in common-value
auctions. Recall that such auctions entail the sale of an object whose
value is fixed and identical for all bidders, although each bidder can
only estimate it. The winner’s curse is a warning to bidders that if
they win the object in the auction, they are likely to have paid more
than it is worth.
You are trying to bid for a company (Targetco); your experts valued it
in the range 0 to $10bn. The current management not revealing.
You believe that whatever Targetco is worth under existing
management, it will be worth 50% more under your control.
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The Winner’s Curse
What should you bid?
Say you believe the value is $5bn under current management and
$7.5bn under yours – then a bid somewhere between $5 billion and
$7.5 billion should be profitable
If Targetco is actually worth more than your bid, the current owners
are not going to accept the bid (You are going to get the company only
if its true worth is toward the lower end of the range)
Suppose you bid amount b. you can expect the company to be
currently worth b/2 if your bid is accepted – under your management,
the value will be 50% more or 0.75b < b.
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The Winner’s Curse
This is not a problem only when there is a single bidder.
Similar problems arise when you are competing with other bidders in
a common-value auction and all of you have separate estimates for the
object’s value
Consider a lease for the oil- or gas-drilling rights on a tract of land (or
sea). At the auction for this lease, you win only if your rivals make
estimates of the value of the lease that are lower than your estimate.
You should recognize this fact and try to learn from it.
Jar of coins, players...
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Bidding Strategies
English Auction
Highest bidder gets it
Your valuation is V
the rival bid is r
If V<r, you don’t bid
If V>r, you add the smallest amount (allowed by the auction house) to
r –say 1 cent
So you win but pay marginally higher than r
Your effective profit is (V-r)
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Bidding Strategies
First-Price, Sealed-Bid
Should you bid V?
If your bid is the highest, you win but pay V with zero effective profit
If you bid less than V, you might well not get it even if the highest bid is
less than V but greater than your bid
You have an incentive to shade(lowering your bid from V) your bid
Optimal shading: balances your advantage (increasing profit margin)
and disadvantage (lowering your chance of winning)
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Bidding Strategies
Dutch Auction
If the auctioneer quotes a price > V, you don’t bid
If no taker at that price, auctioneer quotes lower price, say V.
You can bid now and get zero profit or wait for the price to drop
lower
Just like sealed bid first price –incentive to shade
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Bidding Strategies
Second-Price, Sealed-Bid Auctions
Highest bidder gets at second highest price
The advantage gained from shading, the increase in your profit margin,
is zero in this auction.
You do not improve your profit by shading your bid, because your
profit is determined by the second-highest bid, not your own.
All else being equal, sellers would prefer bids that were not shaded
downward -induce bidders to reveal their true valuations with their
bids
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Vickrey’s Truth Serum
William Vickrey showed that truthful revelation of valuations from
bidders would arise if the seller of a private-value object used a
modified version of the standard, first-price, sealed-bid scheme –his
suggestion was to modify the sealed-bid auction so that it more
closely resembles open-outcry
The highest bidder should get the object for a price equal to the
second-highest bid—a second-price, sealed-bid auction
Vickrey showed that, with these rules, every bidder has a dominant
bidding strategy to bid her true valuation.
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Vickrey’sTruth Serum
Suppose your valuation is $3000; but you do not know the valuations
of the other bidders
Your bid b and the largest rival bid r. What would be the optimal value
of b?
What if b>3000; there can be 3 cases –
1. r<3000; you win and pay r; your profit is (3000-r) –same result if
you had a bid of $3000
2. 3000<r<b; you win but pay r; your loss is (r-3000) –you could have
done better by bidding at 3000
3. r>b; you don’t win the auction –same result if you had a bid of
$3000
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Vickrey’sTruth Serum
What about the possibility of shading your bid slightly and bidding
b<3,000?
Again, there can be 3 cases –
1. If r<b; you win and pay r –same result if you had a bid of $3000
2. b<r<3000; you loose –if you had made a bid of $3000, you have won
and made a profit of (3000-r)
3. 3000<r; your rival wins –quoting $3000 would not have changed
the result.
Bidding your true valuation is never worse, but better in some
situations –better bid your true valuation
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Selling at auction
Bidders are not the only auction participants
An auction is really a sequential-play game in which the first move is
the setting of the rules; bidding starts only in the second round of
moves
Rules are set by the seller
Seller is also trying to maximize her profit
One concern of many sellers is that an item will go to a bidder for a
price lower than the value that the seller places on the object.
To counter this concern, most sellers insist on setting a reserve
price for auctioned objects; they reserve the right to withdraw the
object from the sale if no bid higher than the reserve price is obtained.
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Selling at auction
Other than reserve price, following Vickrey the seller can opt for 2nd
price sealed bid auction
But does that maximize seller’s profit?
The seller is giving the bidder a profit margin to counter the
temptation to shade down the bid in the hope of a larger profit –this
reduces the seller’s revenue, just as shading does
Type of auction mechanism that is best for the seller depends on –
1. Bidder’s attitude towards risk and
2. Beliefs about the value of the object
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Risk-Neutral Bidders, Independent Estimates
Risk-neutral people care only about the expected monetary value of
their outcomes, regardless of the level of uncertainty associated with
those outcomes
Independence in estimates means that a bidder is not influenced by the
estimates of other bidders when determining how much an object is
worth to her
If these conditions for bidders hold, sellers can expect the same
average revenue (over a large number of trials) from any of the four
primary types of auction: English, Dutch, and first-and second-price
sealed-bid.
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Revenue Equivalence
This revenue equivalence result implies not that all of the auctions
will yield the same revenue for every item sold, but that the auctions
will yield the same selling price on average in the course of
numerous auctions.
2nd Price Auction: dominant strategy is bid true valuation, seller gets a
price equivalent to the 2nd highest bid
English Auction: Seller gets a cent (minimum allowed) more than the
2nd highest bid.
Same can be proved for Dutch and 1st Price auctions
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Revenue Equivalence
Intuition: In all four types of auctions, in the absence of any risk
aversion on the part of bidders, the highest-valuation bidder should
win the auction and pay on average a price equal to the second-highest
valuation.
Experimental evidences –
1. Dutch auction prices lower, on average, than first-price sealed-bid
auction prices
2. Over-bidding in 2nd price but not English auctions
Field (internet) evidences –
1. Dutch prices are 30% higher than 1st price auctions
2. No evidence for near revenue equivalence
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Risk-averse Bidders
Continue with uncorrelated beliefs
Risk-averse bidders –more concerned about losses due to
underbidding (and , hence, loosing the object) than by the costs
associated with bidding at or close to their true valuations
Implication for 1st price and 2nd price auctions?
1st price (like Dutch) auction -risk aversion leads bidders to bid earlier
rather than later -as the price drops to the bidder’s valuation and
beyond, there is greater and greater risk in waiting to bid –won’t wait
just a little bit longer in the hope of gaining those extra few pennies of
profit –lesser shading
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Risk-averse Bidders
2nd price auction -Bidders bid their true valuations but pay a price less
than that
Bids will be shaded somewhat, but the price ultimately paid in the 1st
price auction will probably exceed what would be paid in the 2nd price
auction
When bidders are risk averse, the seller then does better to choose
a first-price auction rather than a second-price auction.
The seller does better with the first-price auction in the presence of
risk aversion only in the sealed-bid case.
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Correlated Estimates
Common value auctions; Oil-field –your estimates are not really great
(say, V)
Concerned about your rivals’ estimates –are they similar (positively
correlated) –the likelihood that your rivals’ estimates also are
unfavorable may magnify the effect of your pessimism on your own
valuation
1st price auction: positively correlated estimates lead to higher
(pessimistic) or lower (optimistic) shading.
If estimates are positively (but only optimistic) correlated, 2ndprice
auction is better for seller.
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Correlated Estimates
If estimates are positively (but only pessimistic) correlated, 1st price
auction is not a good option for the seller.
An English auction will have the same ultimate outcome as the second-
price, sealed-bid auction, and a Dutch auction will have the same
outcome as a first-price, sealed-bid auction.
Thus, a seller facing bidders with correlated estimates of an object’s
value also should prefer the English to the Dutch version of the open-
outcry auction.
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Correlated Estimates
If you are bidding on the oil-land lease in an English auction and the
price is nearing your estimate of the lease’s value but your rivals are
still bidding feverishly, you can infer that their estimates are at least as
high as yours—perhaps significantly higher.
The information that you obtain from observing the bidding behavior
of your rivals may convince you that your estimate is too low.
You might even increase your own estimate of the land’s value as a
result of the bidding process.
Your continuing to bid may provide an impetus for further bidding by
other bidders, and the process may continue for a while.
The seller can expect a higher selling price in an English auction than
in a first-price, sealed-bid auction when bidder estimates are
correlated
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Correlated Estimates
If estimates are negatively correlated?
Seller can’t do good with English auction
Any seller facing a small number of bidders with potentially very
different valuations to choose a Dutch or first-price, sealed-bid
structure
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Extensions
Multiple Objects: Bidder may value a package more than the sum of
individual items; Land sale (small plots vs. entire)
Defeating the System: Collusion among bidders
2nd price auction –one large bid followed by small bids (1stprice
auctions are less vulnerable; collusion among bidders is vulnerable,
multi-person PD; sealed bid protect the cheater’s identity)
Shilling–planting false bidder on behalf of the seller
Information Disclosure: Private information with seller –best to
reveal it. Correct estimate to all, bidding up. If negative information,
then also reveal as signal of not disclosing may result in worse outcome
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Reference
A. Dixit, S. Skeath and DH Reiley (2010). Games of Strategy. Viva-
Norton [Chapter – 17]
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