English Auction and Second-Price Sealed-Bid Auction

Theoretical Prediction

In an English auction, an individual bidder will obtain a positive income from participating if and only if she can win the auction with a bid that is less than her valuation of the object. Therefore, a bidder drops out only when the bid "on the floor" exeeds her valuation. Therefore, the bidder with the highest valuation wins the auction and pays an amount slightly higher than the value of the second highest bidder.

In a second-price sealed-bid private-values auction the person with the highest bid will win at a price equal to the second-highest bid. It is a dominant strategy for a bidder to bid her true value. Therefore, the bidder with the highest valuation wins the object and pays an amount equal to the value of the second highest bidder.

This is why the English auction is sometimes referred to as an open second-price auction. However, this equivalence applies only for private values, or if there are just two bidders. With any common components to valuations and more than two bidders, players revise their estimates of the unknown common value where other bidders with different estimates quit an ascending bid auction and condition their behavior on this information.

Experimental Design

Kagel, Harstad and Levin (1987) conduct experiments to test whether the prices in second-price auctions are the same as the prices in English clock auctions (note: English clock auction is a variation of the English Auction. Please see English Auction for details.)

1. In second-price auction experiments, the bidder who bids highest wins the item and pays the second-high-bid price. After all bids are collected, bids are posted on the blackboard in descending order. The highest bid is marked, and the experimenter calculates and posts profits of the high bidder.
2. In English clock auction experiments, the price of the item increases by small increments at every fixed time interval. Bidders must signal whether to drop out. Once withdrawn, bidders cannot re-enter the market. The number of active bidders is stated during the whole experiment, with the last bidder receiving the item at the price on the clock when the next-to-last bidder dropped out of the bidding.

Experimental Results

 The experimental results show the failure of strategic equivalence in second-price and English auctions. The prices in second-price auctions are significantly higher than the prices in English auctions. These results are replicated in later experiments, with experienced and inexperienced bidders (Kagel and Levin 1993).

Possible Explanations for the Experimental Results

The result is attributed to differential information flows inherent in the structure of the two auctions.

In the second price auction, bidding in excess of bidder's own value is probably based on the illusion that it improves the likelihood of winning with no real cost since the winner is paying the second highest bid. The overbidding phenomenon is sustainable as far as bidders' average profits are positive. However, the structure of the English auction makes it clear to bidders that they don't want to bid above their own value. First, in English auctions, any time you win and bid above your own value you necessarily lose money. Second, the feature of "price increment" in English auctions gives bidders a chance to learn without losing money. By comparing the ongoing price with their private value, bidders are likely to see that they are going to lose money whenever the price exceeds their value.

Please see the section on revenue equivalence in auctions.

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.

Kagel, J. H., R. M. Harstad, and D. Levin, 1987. “Information Impact and Allocation Rules in Auctions with Affiliated Private Values: A Laboratory Study.” Econometrica 55: 1275-1304.

Kagel, J. H., and D. Levin, 1993. "Independent Private Value Auctions: Bidder Behavior in First, Second and Third Price Auctions with Varying Numbers of Bidders." Economic Journal, 103: 868-879.