Tests of Revenue Equivalence in
Internet Magic Auctions
David Lucking-Reiley
“I have never considered the lab to be a substitute
for field empirical work.” - Vernon Smith, 1996
Why study revenue equivalence
between auction formats?
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Equivalence between formats is one of the oldest
predictions of auction theory (Vickrey, 1961).
Previous experiments have found interesting
violations of the theory.
I have a unique opportunity for studying bidding
behavior in a preexisting auction market. My field
experiments were designed to see whether previous
laboratory results hold up in a field environment.
There are two kinds of revenue
equivalence across formats.
 Strategic
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The Dutch and first-price auctions are strategically
isomorphic, because they both involve the same
(lack of) relevant information available to bidders.
The English and second-price auctions are
strategically isomorphic under private values,
because both are dominant-strategy mechanisms
for truthful revelation of valuations.
 General
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equivalence is a strong prediction.
revenue equivalence is weaker.
The equivalence of all four auction formats
requires IPV and risk neutrality.
Laboratory experiments have found
violations of the theory.
 Cox
et al (1982, 83): First-price auctions raise
more revenue than Dutch auctions.
 Kagel et al (1987, 93): With private values,
subjects consistently overbid in second-price
auctions, yielding higher revenue than in
English auctions.
 The above studies consistently demonstrate
first/Dutch revenues higher than
English/second revenues. (Risk aversion?)
This research project involves the use of
field experiments.
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Advantages:
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As in a traditional field study, my research involves auctions for
real goods by people already accustomed to bidding for such
goods.
As in a laboratory experiment, I can run a treatment versus a
control (in this case, a pair of different auction formats for the same
auctioned good with the same bidders).
Disadvantages:
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As in a field study, I cannot induce (or even observe) the valuations
or the risk preferences of the subjects.
Magic: the Gathering is an interesting
economic phenomenon in itself.
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The product:
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First sold in July 1993, with a first printing of 10 million cards.
To date, well over 1 billion cards have been printed.
Estimated 1995 wholesale revenues: over $100 million
Cards come in random assortments, which generates a large
aftermarket:
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The <rec.games.deckmaster.marketplace> newsgroup gets traffic of
over 20,000 messages per month.
A variety of market institutions exist, but: a large number of them
are auctions.
This is a real-world laboratory!
I ran four pairs of auctions designed
for within-card comparisons.
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I auctioned the same set of cards twice, with dozens
of cards per set. The only change between auctions is
the format.
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First-price or second-price: bidders have one week to submit their
bids via email.
English: Bidders can send in bids at any time; they receive a daily
update of the current high bids via email. After three days without
a bid raise, the card is declared sold. (Going, going, gone!) This is
the most popular format used by other auctioneers in this market.
Dutch: Prices start out at some high level, then decrease by 5% to
10% each day, as announced in daily email updates.
To control for order effects, I ran each experiment
twice: FD, DF, ES, SE.
Result 1. Card-level data violates
Dutch/first revenue equivalence.
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The FD and DF experiments had a total of 173
matched pairs of cards.
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122 yielded higher revenue in the Dutch format
34 yielded higher revenue in the first-price format
On average, cards yielded $0.32 more in the Dutch
auction, or 24% of card value. These differences are
highly significant, according to a signed-rank test.
There was no qualitative difference between the FD
results and the DF results.
This is the opposite of the violation found by Cox et al
(1982, 83) !
Result 2. Bid-level data weakly support a
violation of this strategic equivalence.
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The idea: compare the two bids by the same bidder in
the two different auctions.
Data censoring prevents observation of most of the
bid strategies in the Dutch auction, so comparisons
are not possible for every bidder participating in both
auctions.
Of 38 observations where bids were observed both in
the Dutch and the matching first-price auction:
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30 favored the Dutch, with a mean difference of $2.52.
4 favored the first-price, with a mean difference of -$0.50.
Result 3. The English auction seems
to produce slightly more revenue
than the second-price auction.
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Card-level data: 164 observations
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Bid-level data: 112 matched bid pairs
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English auction produces 1.8% more revenue overall than
the second-price auction, but this difference is not
statistically significant.
Cannot reject revenue equivalence with this data.
75 cases had higher bids in English
29 cases had higher bids in second-price
On average, English bid levels were 3% higher.
This finding is opposite to Kagel et al (1987, 93).
Result 4. Dutch/first auctions yield
more revenue than English/second.
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I use “Cloister price” as a reference price for each good, and see
how the auction revenues deviate from this reference price.
Pool together Dutch/first data, as well as English/second,
obtain a total of 370 observations.
On average, DF auctions raise at least 12% more revenue than
ES auctions. This difference is statistically significant, at least at
the 90% level.
The difference is lower for the higher-priced cards (it goes to
zero at a price of about $13.00).
Could this be risk aversion? If so, why is the effect smaller for
higher-priced cards?
Conclusions
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My revenue ranking:
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Dutch > first-price > English > second-price
With field data, I get opposite violations of the FD and ES
strategic isomorphisms from those found in laboratory
experiments.
I find the same FD > ES effect as laboratory experiments.
What causes my results to be different from those in the
laboratory?
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Real goods versus cash payoffs?
Simultaneous versus sequential?
Clock speed?