Copyright © 1996, Agorics, Inc.

Auction Strategies

-by Kate Reynolds

One in a Series of Articles from Agorics, Inc.

The truth is that the entire subject of auction strategy is numbingly complex with numerous variables coming into play. Is a bidder risk-averse or risk-neutral? Is the auction for one item or multiple units? Do you plan to resell the acquired object or use it yourself? If you plan to resell it, are the other bidders symmetric? That is, do they use the same measurements to estimate their valuations? Do you have secret information about the object? Might others have secret information?

All of these factors play a part in auction strategy, and so this section can only provide an overview with a few assorted general ideas. Those readers wishing to know more are invited to read the bibliography which contains excellent references, and those references in turn point to other more technical papers.

It is safe to make a few general remarks.

Buyers really do bid differently depending upon the rules of an auction, and it is worth understanding the rules of an auction thoroughly. In fact, the one piece of information available to all is the rules.

Economists use a framework called game theory to think about auction behavior. Using game theory economists examine rational behavior and decisions made in varying conditions.

A seller, on the one hand, is faced with choosing an auction type, and so he must predict the behavior of bidders. On the other hand, a bidder tries to predict the behavior of the other bidders. Each bidder makes an estimate of his own value of the object and also an estimate of what others will bid on it. Good bidding is often the result of correct predictions about the behavior of others and sometimes that means guessing the extent of someone else's information correctly. [Mester]

Economists try to devise sets of rules to determine dominant strategies under a huge array of variables. Bidders, of course, tend to worry more about their bids than their strategy.

From a Seller's Perspective

In any auction a seller can influence results by revealing information about the object. Intuitively, a bidder's profits rise when he can exploit information asymmetries (when the bidder has information not available to others). In general, the more information a bidder has, the more the price-dampening effect of winner's curse is lessened. So a seller's optimal strategy is to reveal information and to link the final price to outside indicators of value (an authoritative evaluation). It is also a good idea because if a seller seems reluctant to disclose something, a buyer always assumes the hidden information must be unfavorable.

SidebarRevealing information removes uncertainty.

Theoretical literature demonstrates that, under assumption of private value, all four basic auction types can be shown to yield the same expected price and revenue to the seller when bidders are risk neutral and symmetric. This implies that auction choice is not crucial because each format yields on average the same payoff.

But revenue equivalence does not hold true under common value assumption (when bidders have similar evaluations). It has been shown that the four auction types can be ranked from highest to lowest as follows: English ascending-price; the second-price, sealed bid auction; Dutch (descending) auctions and first-price, sealed bid auctions tied. The rankings illustrate advantages of increased information. Remember that an English auction reveals information about rival bidder valuations and permits dynamic updating of personal valuation (which leads to more aggressive bidding). In comparison, bidders, recognizing winner's curse, bidding in first-price auctions bid less aggressively and shade their bids. Similar reasoning applies to Dutch (descending) auctions. In contrast, in second-price sealed-bid format, the winner pays the bid of the next highest so bidders raise bids, secure that they will not be disadvantaged if rival bids are lower.

In Dutch and first-price auctions, bidders behave in the same way, and so, it does not matter which of these auctions a seller chooses nor does it matter whether the bidders have private values or common values. The reason that a bidder behaves the same in both kinds of auction is that he makes the same decision and this decision is based upon the same information. In both auctions a bidder knows that if he wins he must pay exactly what he bid. He knows also that he only wins if his bid is higher than that of everyone else. He must also decide upon his bid without knowing what others will do.

There is disagreement over this. Paul Milgrom [Milgrom (3)] argues that in general an English auction generates more money in more environments than the Dutch or sealed bid auction types (on average), and this probably helps explain its popularity.

In the case of choosing between a second-price and an English auction, however, the decision must be based upon whether bidders know their private valuations or whether they are uncertain about the single common value of the item for sale. In an auction wherein bidders have independent private values, the auctions both yield the same.

However, in a common value auction the English and second-price auctions do not yield the same revenue. Remember that in an English auction a bidder can gain useful information by observing other bidders. He can watch to see how many bidders drop out of the auction (they value the object less) and he can see also exactly when they dropped out (how high was their last bid?). If lots of bidders remain in an auction this gives a bidder confidence that a high valuation was correct, and so he tends to bid higher.

Expected Revenue

(This chart taken from "Going, Going, Gone", by Loretta J. Mester) [Mester]

But the risk characteristics of a bidder are important too. A bidder who is risk averse (meaning he absolutely requires the item being auctioned) tends to bid higher so that he will have a greater chance of victory. A risk neutral bidder does not.

In the independent value behavior when all bidders are risk neutral, a seller receives the same revenue from both the English and second-price auction.

However, if the bidders are risk averse, then the first-price (and also the Dutch) yields greater revenue than English and second-price auctions.

Expected Revenues

(This chart taken from "Going, Going Gone", by Loretta J. Mester) [Mester]

From a Bidder's Perspective

Theoretical literature assumes that auction participants are homogeneous (risk neutral and symmetric--they use the same distribution function to estimate valuations). It assumes bidders all focus on maximizing profits and that only one item is being auctioned.

Paul Milgrom [Milgrom (1)] describes a strategy for contract bidding. "To make money in competitive bidding, you will need to mark up your bids twice: once to correct for the underestimation of costs on the projects you win and a second time to include a margin for profit. Don't let the presence of several competing bidders push you into making too aggressive a bid. The markup to adjust for underestimation will have to be larger the larger the number of your competitors and the more you respect the accuracy of their cost estimation; you may, however, want to make the profit markup smaller when there are more competitors."

Students point out that you can't make money if you are too cautious. Milgrom [Milgrom (1)] says in response, "The most important lessons to be learned from both the theory and the experiments are that the returns in bidding come from cost and information advantages, that naive bidding strategies can squander these advantages, and that bidders without some advantage have little hope of earning much profit, but could with a little bit of carelessness suffer large losses."

What about irrationality amongst bidders? What if Louise, a bidder, understands winner's curse, but her opponents, Ellen and Sam do not? What should Louise do? She knows that her rivals will overbid. Answer: she should scale down her bid even further because winner's curse is intensified against over-optimistic rivals. If Louise wins against a rival who commonly overbids, Louise has probably erred in her valuation.

A bidder uses the same strategy in both Dutch and first-price sealed auctions because the same information is available in each. In a Dutch auction, a bidder considers and selects a cutoff price. He will claim the object if no one has claimed it before. In a sealed-bid first price, the decision is exactly the same. All bidders have the same strategies for these auctions--shade bids down slightly so as not to be caught by winner's curse.

English Strategy

In a private-value English auction, a player's best strategy is to bid a small amount more than the previous high bid until he reaches his valuation and then stop. This is optimal because he always wants to buy an object if the price is less than its value to him, but he wants to pay the lowest possible price. Bidding always ends when the price reaches the valuation of the player with the second-highest valuation.

An advantage to English auctions is that a bidder gains information. He can observe and see not only that other players drop out, but also the price at which the competition abandons the bidding. That tells a bidder a great deal about the valuations of others and allows a bidder to revise his valuation on the fly.

A player's strategy is his series of bids as a function of (1) his value, (2) his prior estimate of the other players' valuations, and (3) the past bids of other players. His bid can be updated as information changes.

If you attend an auction in person, it is good to remember that auctioneers sometime appreciate the first bid on an item because it helps get the auction started. Sometimes they show their appreciation by giving a first bidder what is called a "fast knock". From the point of view of the auctioneer, a fast knock is a calculated sacrifice, something akin to a loss-leader in a department store sale.

Another point to remember is that some people are intimidated by rings, but you can always outbid a ring. Their strategy has to be based upon buying an item at a low enough price to make a profit.

Dutch Strategy

The problem for the bidder in a Dutch auction is exactly the same as that facing a bidder in a sealed-bid auction. At some point in advance, the bidder must decide the maximum amount he will bid. He must decide when to stop the auction based upon his own valuation of the object and his prior beliefs about the valuations of other bidders.

This auction type is strategically equivalent to first-price sealed auction because no relevant information is disclosed in the course of the auction, only at the end when it is too late.

First-Price, Sealed Bid Strategy

It is difficult to specify a single strategy because a profit-maximizing bid depends upon the actions of others. The tradeoff is between bidding high and winning more often, and bidding low and benefiting more if the bid wins (bigger profit margin).

Most bidders attempt to shade their bids to move closer to market consensus. This also helps to avoid winner's curse.

Vickrey Strategy

Paul Milgrom [Milgrom (1)] suggests that the dominant strategy for a bidder in a Vickrey (second-price) auction is to submit a bid equal to his true reservation price because he then accepts all offers below his reservation bid and none that are above. A participant who bids less is more likely to lose the auction and all that strategy accomplishes is to lower the chance of victory. Bidding high carries the risk of winner's curse. Neither affects the price paid if he wins.

When each bidder adopts a strategy of bidding his true price, the outcome is that the item is awarded to the bidder with the highest valuation at a price equal to the second highest valuation. The existence of a dominant strategy means that bidder can determine his own sealed bid without regard for the actions of others. So a second-price auction duplicates the principal characteristics of an English auction. It should be noted that a second-price auction participant chooses a strategy without regard for the actions of others.

A potential drawback is that this system requires total honesty from the auctioneer (s). If the auctioneer is not trustworthy, he could open the bids, find the winner and insert a new bid just barely under that to ensure higher revenues.

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Work presented here is copyrighted material belonging to Agorics, Inc. (Copyright © 1996, Agorics, Inc.) Agorics, Inc. reserves all copyrights. Agorics disclaims any warranty as to the utility, accuracy or effectiveness of the information contained in this document and specifically disclaims any liability for consequential damages that may result directly or indirectly from use of the information in this document.