1. 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

2. Why study revenue equivalence between auction formats? u Equivalence between formats is one of the oldest predictions of auction theory (Vickrey, 1961). u Previous experiments have found interesting violations of the theory. u 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.

3. There are two kinds of revenue equivalence across formats. u Strategic equivalence is a strong prediction. l The Dutch and first-price auctions are strategically isomorphic, because they both involve the same (lack of) relevant information available to bidders. l The English and second-price auctions are strategically isomorphic under private values, because both are dominant-strategy mechanisms for truthful revelation of valuations. u General revenue equivalence is weaker. l The equivalence of all four auction formats requires IPV and risk neutrality.

4. Laboratory experiments have found violations of the theory. u Cox et al (1982, 83): First-price auctions raise more revenue than Dutch auctions. u Kagel et al (1987, 93): With private values, subjects consistently overbid in second-price auctions, yielding higher revenue than in English auctions. u The above studies consistently demonstrate first/Dutch revenues higher than English/second revenues. (Risk aversion?)

5. This research project involves the use of field experiments. u Advantages: l As in a traditional field study, my research involves auctions for real goods by people already accustomed to bidding for such goods. l 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). u Disadvantages: l As in a field study, I cannot induce (or even observe) the valuations or the risk preferences of the subjects.

6. Magic: the Gathering is an interesting economic phenomenon in itself. u The product: l First sold in July 1993, with a first printing of 10 million cards. l To date, well over 1 billion cards have been printed. l Estimated 1995 wholesale revenues: over $100 million u Cards come in random assortments, which generates a large aftermarket: l The newsgroup gets traffic of over 20,000 messages per month. l A variety of market institutions exist, but: a large number of them are auctions. l This is a real-world laboratory!

7. I ran four pairs of auctions designed for within-card comparisons. u I auctioned the same set of cards twice, with dozens of cards per set. The only change between auctions is the format. l First-price or second-price: bidders have one week to submit their bids via email. l 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. l Dutch: Prices start out at some high level, then decrease by 5% to 10% each day, as announced in daily email updates. u To control for order effects, I ran each experiment twice: FD, DF, ES, SE.

8. Result 1. Card-level data violates Dutch/first revenue equivalence. u The FD and DF experiments had a total of 173 matched pairs of cards. l 122 yielded higher revenue in the Dutch format l 34 yielded higher revenue in the first-price format u 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. u There was no qualitative difference between the FD results and the DF results. u This is the opposite of the violation found by Cox et al (1982, 83) !

9. Result 2. Bid-level data weakly support a violation of this strategic equivalence. u The idea: compare the two bids by the same bidder in the two different auctions. u 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. u Of 38 observations where bids were observed both in the Dutch and the matching first-price auction: l 30 favored the Dutch, with a mean difference of $2.52. l 4 favored the first-price, with a mean difference of -$0.50.

10. Result 3. The English auction seems to produce slightly more revenue than the second-price auction. u Card-level data: 164 observations l English auction produces 1.8% more revenue overall than the second-price auction, but this difference is not statistically significant. l Cannot reject revenue equivalence with this data. u Bid-level data: 112 matched bid pairs l 75 cases had higher bids in English l 29 cases had higher bids in second-price l On average, English bid levels were 3% higher. u This finding is opposite to Kagel et al (1987, 93).

11. Result 4. Dutch/first auctions yield more revenue than English/second. u I use “Cloister price” as a reference price for each good, and see how the auction revenues deviate from this reference price. u Pool together Dutch/first data, as well as English/second, obtain a total of 370 observations. u On average, DF auctions raise at least 12% more revenue than ES auctions. This difference is statistically significant, at least at the 90% level. u The difference is lower for the higher-priced cards (it goes to zero at a price of about $13.00). u Could this be risk aversion? If so, why is the effect smaller for higher-priced cards?

12. Conclusions u My revenue ranking: l Dutch > first-price > English > second-price u With field data, I get opposite violations of the FD and ES strategic isomorphisms from those found in laboratory experiments. u I find the same FD > ES effect as laboratory experiments. u What causes my results to be different from those in the laboratory? l Real goods versus cash payoffs? l Simultaneous versus sequential? l Clock speed?