# first-price auction

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pages: 523 words: 143,139

Algorithms to Live By: The Computer Science of Human Decisions by Brian Christian, Tom Griffiths

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In a Vickrey auction, on the other hand, honesty is the dominant strategy. This is the mechanism designer’s holy grail. You do not need to strategize or recurse. Now, it seems like the Vickrey auction would cost the seller some money compared to the first-price auction, but this isn’t necessarily true. In a first-price auction, every bidder is shading their bid down to avoid overpaying; in the second-price Vickrey auction, there’s no need to—in a sense, the auction itself is optimally shading their bid for them. In fact, a game-theoretic principle called “revenue equivalence” establishes that over time, the average expected sale price in a first-price auction will converge to precisely the same as in a Vickrey auction. Thus the Vickrey equilibrium involves the same bidder winning the item for the same price—without any strategizing by any of the bidders whatsoever.

they’re shading their bids based on their prediction of yours!: The equilibrium strategy for a sealed-bid first-price auction with two players is to bid exactly half what you think the item is worth. More generally, in this auction format with n players, you should bid exactly (n−1)⁄n times what you think the item is worth. Note that this strategy is the Nash equilibrium but is not a dominant strategy; that is to say, nothing is better if everyone else is doing it, too, but isn’t necessarily optimal under all circumstances. Caveat emptor. Also, if you don’t know the number of bidders in the auction, the optimal strategy gets complicated in a hurry; see, for instance, An, Hu, and Shum, “Estimating First-Price Auctions with an Unknown Number of Bidders: A Misclassification Approach.” Actually, even the seemingly clean results—(n−1)⁄n—require some serious assumptions, namely that the bidders are “risk neutral” and that their different values for the item are distributed evenly across some given range.

Meanwhile, governments use auctions to sell rights to bands of the telecommunications spectrum (such as cell phone transmission frequencies), raising tens of billions of dollars in revenue. In fact, many global markets, in everything from homes to books to tulips, operate via auctions of various styles. One of the simplest auction formats has each participant write down their bid in secret, and the one whose bid is highest wins the item for whatever price they wrote down. This is known as a “sealed-bid first-price auction,” and from an algorithmic game theory perspective there’s a big problem with it—actually, several. For one thing, there’s a sense in which the winner always overpays: if you value an item at \$25 and I value it at \$10, and we both bid our true valuations (\$25 and \$10), then you end up buying it for \$25 when you could have had it for just a hair over \$10. This problem, in turn, leads to another one, which is that in order to bid properly—that is, in order not to overpay—you need to predict the true valuation of the other players in the auction and “shade” your bid accordingly.

pages: 252 words: 73,131

The Inner Lives of Markets: How People Shape Them—And They Shape Us by Tim Sullivan

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Thus, supposing either of these parties receives two bids on one lot of 20 and 25 cents apiece, they would start the lot at 21 cents, at which price it would be given to the person sending the 25 cent order, unless some one present advanced, when they would continue to bid, stopping at the limit of 25 cents . . . Persons sending bids should give the number of the lots and the highest price they are willing to give, when the lot will be bought for them as low as possible consistent with the representation of other bids. In a live (first-price) auction, a bidder keeps raising his paddle until the price goes above what he’s willing to pay for the lot that’s up for bid. And what price do we expect the winner to ultimately pay? If there are just two bidders who value the lot at 20 and 25 cents, respectively, the first will stay in the running until the price hits 21 cents, at which point the gavel will fall. The lot goes to the buyer who values it for more, who gets the lot for “close” to the runner-up’s walk-away price.

Consider how it would have simplified John Henry’s job in making an offer on Matsuzaka. Suppose, for the sake of argument, that Henry set the value of the right to negotiate with Matsuzaka at \$60 million. That is, for a price of \$60 million, he’d take it. If it were a dollar more, he’d walk away. (Of course, we’ll never know what his walk-away price was, beyond the fact that it was above \$51,111,111.11.) In a first-price auction, we’ve already seen that it’s not clear where Henry should set his bid—sure, it should be less than \$60 million, but how much less? For each dollar you drop your bid, you’re less and less likely to come out on top. But then again, you’re a dollar richer if you do. In a second-bid auction, there would’ve been no such uncertainty as to what Henry should’ve bid. Start by asking whether it could’ve made sense for Henry to bid more than \$60 million, just to make sure he won (and knowing he wouldn’t have had to pay the full amount anyway).

The Problems with Vickrey Auctions Vickrey probably wouldn’t have been troubled by the fact that online shoppers don’t care much for his auction; he was, after all, far more interested in allocation decisions of larger social consequence. But his design also sees scarce application in areas like government procurement, which had been Vickrey’s primary motivation for building something better than a first-price auction in the first place. Nor has the Vickrey auction seen much action in the sale of state assets, where it matters not just how much revenue is generated but also that the asset—whether an oil concession or wireless spectrum—goes to the bidder who values it the most (because, it is presumed, he will make the most productive use of it). This lack of use of the Vickrey auction was something of a puzzle to economists who were captivated by the way that, in its elegant simplicity, the mechanism helped magically cure the bidders’ headaches over strategizing and overpaying.

pages: 298 words: 43,745

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A Generalized Second Price auction achieves this stability by encouraging advertisers to not bid too high as an adversarial technique (i.e., there is no use in bidding extremely high to try and force a competitor to bid higher, to really “win” the top space, etc.). From an overall auction perspective, this has the advantage of keeping the auction stable, with few wide or wild price swings once the auction reaches a point of stability. This is especially true relative to a first-price auction [22] (i.e., you pay what you bid). The first-price auction has no point of equilibrium or stability, so the bids can constantly be in flux. However, stability is a range, not an exact point, and there can be situations in a sponsored-search auction where it may be advantageous to bid somewhat higher than optimal to hurt a competitor [c.f., 23]. However, this strategy has limitations and beyond a certain bid point it becomes counterproductive, returning the auction to equilibrium.

On February 21, 1998, GoTo.com launched a sponsored-search model in which the search engines ranked “Web sites based on how much the sites are willing to pay to be placed at the top of the search under a real-time competitive bidding process [2].” Advertisements for these Web sites appeared on the search engine results page, and the ad displayed based on the searcher was actively seeking at the time. The conceptualization was relatively straightforward, with a transparent ranking factor (i.e., money), advertisers bidding on exact phrases, and editors checking for relevance. This concept is a first-price auction, where the top bidder gets the top advertising position. GoTo.com also provided nonsponsored listings, provided by Inktomi.com. Potpourri: GoTo.com was the rebranded search engine, World-Wide Web Worm, which was the first Web search engine. Created in September 1993 by Oliver McBryan at the University of Colorado, the World-Wide Web Worm is the grandfather of all Web search engines. It started it all!

pages: 282 words: 80,907

Who Gets What — and Why: The New Economics of Matchmaking and Market Design by Alvin E. Roth

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In contrast, a sealed bid auction, in which you can’t see when the other bidders drop out, might make it risky to bid at all, since a company with an unrealistically high estimate of how much recoverable oil is in the ground might suffer the “winner’s curse”—that is, win the auction only because it overestimated the value of winning and paid too much. But first-price auctions, in which the winning bidder pays what she bids, have their own charms and exist in many varieties. One version of a first-price auction is used to sell cut flowers in bulk, in a “descending bid” auction. The auctioneer sets up a “clock” that has the current bid on it, starting with a very high bid and quickly descending, until some bidder stops the clock by offering the price it currently shows, which is higher than any of the other bidders have offered to pay, as they haven’t already stopped the clock.

Notice that while a second-price auction makes it safe for bidders to bid the true value to them, it doesn’t necessarily impose a cost on the seller, even though the seller receives only the amount of the second-highest bid. That’s because in a first-price sealed bid auction, for example, it isn’t safe for bidders to bid their true value; they have to bid less than that if they are going to make any profit, since if they win the auction, they will have to pay the full amount of their bid. So the seller in a first-price auction receives the amount of the highest bid, which is, however, less than the true value of the highest bidder. By comparison, in a second-price auction, the seller receives only the second-highest bid, but the bids are higher. That is, when the rules of the auction change, the bids change, too. In fact, there are reasons to think that these two effects balance out. The situation changes when you don’t know how much the object is worth to you.

pages: 324 words: 93,175

The Upside of Irrationality: The Unexpected Benefits of Defying Logic at Work and at Home by Dan Ariely

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Here is the logic: if the creators realized that they were uniquely overimpressed with their own frogs and cranes, they would bid more when using the second-price auction (when only their value matters) than when using the first-price auction (when they should also take into account the values of others). In contrast, if the creators did not realize that they were the only ones who overvalued their origami and they thought that others shared their perspective, they would bid a similarly high amount in both bidding procedures. So did the origami builders understand that others didn’t see their creations as they did? We found that creators bid the same amount when they considered only their own evaluation for the product (second-price auction) as when they also considered what noncreators would bid for it (first-price auction). The lack of difference between the two bidding approaches suggested not only that we overvalue our own creations but also that we are largely unaware of this tendency; we mistakenly think that others love our work as much as we do.

The Armchair Economist: Economics and Everyday Life by Steven E. Landsburg

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The answer is yes if there happen to be two high bidders in the audience and no if Cursed Winners and Glum Losers 177 there happens to be just one. Because bidders are unlikely to reveal their bidding strategies in advance of the auction, the seller can never know for certain on any given night whether an English auction is preferable to, say, a Dutch auction. Even to decide between a first-price and a second-price sealed bid auction can be difficult for the seller. On the one hand, in a first-price auction he collects the high bid, while in a second-price auction he collects only the amount of the second-highest bid. On the other hand, bidders generally submit higher bids in a second-price auction. They submit even higher bids in a third-price auction. Which is best for the seller? Again the answer depends on who shows up to bid, and what the bidders' strategies are. Given his limited information, the seller is in no position to choose the rule that will maximize the selling price at any one auction.

pages: 350 words: 103,988

Reinventing the Bazaar: A Natural History of Markets by John McMillan

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An alternative way of running the bidding is the Dutch auction, used to sell flowers at Aalsmeer, in which the price starts high and falls until a bidder claims the item. Another is the sealed-bid auction, in which there is a single round of sealed bids; the high bidder wins and pays his or her bid. Commercial real estate is sometimes sold this way. A variant is the second-price auction, in which there is a single round of bidding and the high bidder wins, but unlike first-price auctions, the price paid is the second-highest bid. Second-price auctions are used for selling stamps. eBay chose open auctions. Economic theory endorses this decision: the open auction yields, on average, a price that is closer to the item’s true value than do the other forms of auction.3 This is because bidders have more information in an open auction. If you win, the level of your winning bid reflects others’ bids as well your own prior estimate of the item’s value.

pages: 898 words: 266,274

The Irrational Bundle by Dan Ariely

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Here is the logic: if the creators realized that they were uniquely overimpressed with their own frogs and cranes, they would bid more when using the second-price auction (when only their value matters) than when using the first-price auction (when they should also take into account the values of others). In contrast, if the creators did not realize that they were the only ones who overvalued their origami and they thought that others shared their perspective, they would bid a similarly high amount in both bidding procedures. So did the origami builders understand that others didn’t see their creations as they did? We found that creators bid the same amount when they considered only their own evaluation for the product (second-price auction) as when they also considered what noncreators would bid for it (first-price auction). The lack of difference between the two bidding approaches suggested not only that we overvalue our own creations but also that we are largely unaware of this tendency; we mistakenly think that others love our work as much as we do.