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Dutch Auction and First-Price Sealed-Bid Auction

Theoretical Prediction

In a Dutch auction, The first bidder who calls out that he will accept the current price wins the object at that price. In the first-price sealed-bid auction, a bidder wins the auction and pays her own bid if she submits the highest bid. Therefore in both Dutch and first-price sealed-bid auctions, bidders are making tradeoffs between the probability of having the higest bid and the amount they pay if they have the highest bid.

The set of strategies available to a bidder is the same in the Dutch auction (descending auction) as in the first-price sealed-bid auction, and therefore the Bayesian Nash Equilibrium bid functions are the same. Therefore, the Dutch auction is strategically equivalent to the first-price sealed-bid auction. This is why the descending bid auction is sometimes referred to as an open first-price auction.

Experimental Design

Cox, Roberson and Smith (1982) experimentally investigate whether the Dutch auction and the first-price sealed-bid auction are stretigically equivalant in practice. Their experimental design includes several treatments like the following:

1. All recruited market participants are buyers. The computer serves as an "auctioneer," and generates buyers' resale values randomly. Every buyer has an equally likely chance of receiving any resale value from \$0.10,\$0.50,..., and \$16.90 inclusive. The buyers are privately informed of their resale values. The unit of divisibility for bids is the same as for resale values: \$0.40
2. In a Dutch auction, the clock starts from \$17.70, and decreases by \$0.40 every 2 seconds. When the first person pushes the button to signal purchase, the clock will stop at a "buy price." Then that person will get the item, and her profit will be her resale value minus the buy price.
3. In a first price sealed-bid auction, every buyer submits a bid. The person who bids highest will get the item, and her profit will be her resale value minus her bid.

Experimental Results

The experiment results show that prices in first-price sealed-bid auctions are significantly higher than Dutch auction prices, which contradicts the theoretical predction that the first-price auction and the Dutch auction are strategically equivalent.

Possible Explainations for the Experimental Results

There are two possible explainations for this behavioral difference between first-price sealed-bid and Dutch auctions.

1. After the experiments, some subjects reported that they enjoyed the Dutch "clock" experiment much more because of the "suspense of waiting." Therefore, trading between the monetary payoff and the nonmonetary utility of playing the "waiting game" might be a reason why in practice prices in Dutch auctions are lower than in the first-price sealed bid auctions.
2. Another explaination is that bidders systematically violate Bayes rule and hence miscalculate the probability of winning in Dutch auctions.

To test these two hypotheses, one can design an experiment by keeping all the parameters the same but tripling the monetary payoff. If the model of the "waiting game" is correct, then tripling the reward should reduce the price difference observed in Dutch and first-price auctions. If the model of miscalculation is correct, the price gap between the two auction systems will be maintained. The subsequent experiments by Cox, Smith and Walker (1983) show that there is no significant difference in auction prices from tripling the monetary payoff. Therefore, the model of miscalculation is supported.

Experimental Design

Lucking-Reily(1999) examines whether the Dutch auction and first-price sealed-bid auction are strategically equivalent. His experimental design included the following:

1. \$1600 worth of Magic cards were purchased in order to resell in auctions on the Internet.
2. To compare the revenues directly, the same cards in double copies were sold under two different auction formats.
3. Bidders were invited by posting advertisements on newsgroups related to magic cards and by email invitations.
4. Paired experiments were conducted: A first price auction followed by a Dutch auction with matched pair of cards for sale. The experiment was also run reversing the time order of the auctions, with a different set of matched cards.

Experimental Results

The experiment results show that prices in the first-price sealed-bid auction are significantly lower than Dutch auction prices, which contradicts the theoretical prediction that the first-price auction and the Dutch auction are strategically equivalent.

The price comparison reported by Lucking-Reily(1999) is the opposite of that reported by Cox,Roberson and Smith(1982)

Possible resolution of the Inconsistent Results

The key to resolving this apparent inconsistency in results seems to be the variation in speed of the Dutch clock and a theory involving impatient bidders. Kwasnica and Katok (2003) found that variations in the speed of the Dutch clock significantly change the auctioneer's revenue in these two auction formats. While fast Dutch auction clock speeds generated revenues that were significantly below that in the sealed-bid auctions (similar to Cox et.al), a slower clock generated significantly more revenues than the sealed bid auctions (consistent with Lucking-Reily 1999).

References

• Cox, J., B. Roberson and V. Smith, 1982. "Theory and Behavior of Single Object Auctions," in V. Smith ed., Research in Experimental Economics Vol. 2, Greenwich: JAI press.

• Kwasnica A., Elena Katok (2003). "Time is Money: The Effect of Clock Speed on Seller's Revenue in Dutch Auctions," Penn State University working paper.

• Lucking-Reily,D.,1999. "Using Field Experiments to Test Equivalence Between Auction Formats: Magic on the Internet." American Economic Review,89:1063-1080.