Auctions – Timothy P. Hubbard and Harry J. Paarsch
Trigger warning: – allocazione delle risorse – tassonomia: pubblica/primo prezzo (inglese: ascendente; olandese: discendente), pubblica/secondo prezzo, privata/primo prezzo, privata/secondo prezzo – bluff minimizzato – 4 funzioni – efficienza allocativa ed efficienza per il cliente –
Auction Formats and Pricing Rules
What’s an Auction?
After the reigning emperor had been overthrown in AD 193, the entire Roman Empire was sold at auction.
When computer programmer Pierre Omidyar sold a broken laser pointer for more than $14 using his online company AuctionWeb, he surely had no idea his website, now eBay, would become a Fortune 500 company.
Babylonians used auctions to sell wives.
Note:MOGLI ALL’ ASTA
slaves were frequently sold at auction.
Suppliers of milk to public schools in several US states were found guilty of bid-rigging,
Note:SCANDALO DEL LATTE
With use dating back to at least 500 BC, the auction is among the oldest market institutions.
music has been traditionally sold as a good intended to be enjoyed by the consumer who purchased the album. …many listeners of a band’s album likely have not purchased the music. Perhaps this is why the American hip-hop group Wu-Tang Clan announced in the summer of 2014 plans to sell at auction the only copy of their album Once Upon A Time In Shaolin.
an auction is a way of allocating an object or acquiring a service.
Famous authors have used auctions to sell the right to publish books from manuscripts;
at some universities, opportunities for students to enroll in courses are allocated using auctions.
Filene’s Basement was a discount retailer in Boston that automatically marked down all items by increasingly higher percentages over a thirty-day period before giving unsold items to charity.
Despite their durability and flexibility, auctions appear underappreciated, not just by the typical person, but also by many economists. …In fact the word “auction” is scarcely even heard within the walls of economics classrooms around the world. …
when policy makers around the world decided to sell off the rights to use the electromagnetic spectrum for such devices as cell phones, they turned to auction researchers to design markets
Note:LO SPAZIO ELETTROMAGNETICO
William S. Vickrey specifically, but Eric S. Maskin and Roger B. Myerson for their work in mechanism design, and Vernon L. Smith and Alvin E. Roth for their work concerning alternative market mechanisms too.
Note:I NOBEL “ASTISTI”
Types of Auctions
The two auction formats are the open (sometimes referred to as the oral or the open outcry format) and the sealed-bid, perhaps best thought of as the closed
Note:APERTA E CHIUSA
Under the first, the winner must pay what was bid; this is referred to as the first-price rule, at least by economists.
Under the second, the winner must pay what the highest opponent bid (the second-highest bid), so this is referred to as the second-price
These two partitions yield four combinations of auction formats… Perhaps the best-known type of auction is the oral, ascending-price auction, which is sometimes referred to as the English auction.
Latin word auctus—the past participle of the verb augere, which means to augment or to raise. …The English auction is used by the world’s two largest auction houses Christie’s and Sotheby’s to sell high-quality antiques, art, jewelry, and wine among other things. …
In contrast to the oral, ascending price of the English auction is the oral, descending-price auction, often referred to as the Dutch auction, perhaps because this type of auction is used to sell flowers in the town of Aalsmeer in the Netherlands. …calls out successively lower prices, but often a clock is used to automate the task. Specifically, the clock is set at a very high price …The first buyer to stop the clock, either by shouting “Stop!” or by using some other device, wins the auction and must pay the current price on the clock. …
note that at English auctions many bids can be (and are often) made, so the bidding process can take some time, whereas at Dutch auctions only one bid is observed—that
Note:TANTE OFFERTE/UNA OFFERTA
This distinction is important for the Dutch flower auctions at which more than twenty million flowers are sold on a typical day. when Google went public in the summer of 2004, it was reported to have sold its shares using the Dutch auction.
Note:GOOGLE E FIORI
Dutch and English auctions are dynamic in the sense that price changes are visible to bidders as the auction progresses, hence the term “open.”
Today, however, many auctions are held electronically, with bidders accessing a computer server on which the auction is conducted virtually. For example, the Portland Fish Exchange (PFEX) in Maine, the oldest all-display, fresh seafood auction in the United States, is an electronic auction. …the PFEX is actually a hybrid Dutch–English auction: the price starts at a set opening price determined by the auctioneer and initially drops; when one bidder expresses interest in a certain type (size and species) of fish, the price then rises in one-cent increments until no one is willing to increase the price further. …
At sealed-bid auctions, buyers indicate how much they are willing to pay for the object on sale by submitting a bid in secret to the auctioneer, traditionally in a sealed envelope,
Note:ASTE IN BUSTA CHIUSA
two different pricing rules can be used
Note:DUE PREZZI POSSIBILI
At first-price… this format is also referred to as a pay-your-bid auction…. In contrast, at a second-price, sealed-bid auction, the winning bidder pays the second-highest bid tendered. This small difference in the pricing rules generates important differences in behavior
PRIMO E SECONDO PREZZO
first-price, sealed-bid auctions are employed extensively and play central roles in the decisions made by policy makers in most countries.
In short, if a government agency seeks to purchase a good or service, then it often must solicit bids from several suppliers… the public procurement process is exactly like a first-price, sealed-bid auction, except that the winning bidder is paid to provide a good or service… these procurement auctions are often referred to as low-price, sealed-bid auctions or reverse auctions.
White House reports that more than one of every six dollars spent by the federal government is paid to such contractors.
Note:UN SESTO DELLA SPESA PUBBLICA
The second-price, sealed-bid auction is commonly referred to as the Vickrey
stamp collectors had used second-price, sealed-bid auctions during the late nineteenth century, Consider a philatelist living in a remote location during the 1800s and seeking to sell some stamps. An English auction held locally would likely not have attracted a large group …In contrast, if stamp sales could be publicized and bids submitted through the mail …
Note:RIUNIRE OFFERENTI DISTANTI
when awarding a procurement contract using an auction, some government agencies choose the bidder whose tender is closest to the average bid. In Italy, between 2000 and 2006, procurement contracts were awarded using an average-bid pricing rule whenever five or more bidders submitted tenders.
Note:ITALIA: VINCE L’ OFFERTA MEDIA
When to Use Auctions, and Why
Simply put, auctions are a way of equating demand and supply…. opportunity cost represents the value of a resource in its next-best alternative…. First, a reasonable price was discovered and the allocation problem solved. Second, the ticket was awarded to the friend who was willing to pay the most to see the game; such an allocation is referred to as efficient because the object went to the bidder who valued the ticket the most. Third, the price discovered through the auction represents the opportunity cost of the ticket, the value of the ticket in its next-best use. Fourth, the auction generated attractive outcomes for both the buyer and the seller—in
Note:I 4 SERVIZI FORNITI DA UN’ ASTA
Missing from the example above is the element of time. Not only do auctions have the attractive allocational properties discussed but the rules can be structured so that such allocations are achieved in a timely manner.
Note:RISPARMIO DI TEMPO
It’s likely that you and your friends or siblings left abandoned games of Monopoly for hours,
Note:AGGIRARE I MONOPOLI
Central to the study of auctions… is the notion of asymmetric information: the seller of an object does not know any bidder’s valuation for that object.
transparent way of allocating the ticket. None of your friends will be offended because each agreed to respect the rules and outcome of the auction.
Note:NESSUNO SI OFFENDE
With the collapse of the Soviet Union, how did the former republics transition from planned economies to market-based economies? In part, by privatizing state-owned assets, which were often sold at auction.
Note:URSS… PROVATIZZAZIONE E ASTE
Auctions are ideal for selling objects that have no standard value. Sometimes, the object at auction may be unique, as in the case of formerly state-owned enterprises;
Note:OTTIME PER MERCI UNICHE
prices are likely to vary depending on daily circumstances. For example, the world’s largest fish market in the Tsukiji district of Tokyo uses the auction. …fish, uncertainty …fish move constantly in the ocean; weather patterns are unpredictable too. …even today many Roman Catholics still eat fish on Fridays. In addition the quality of the fish can vary depending on how the fish are caught, … Fish are also one of the most perishable of commodities. …
Note:OTTIME X PREZZI VOLATILI…ESEMPIO QUELLO DEL PESCE
Auctions are one area of economics where theoretical and empirical work is most closely linked,
TEORIA E PRASSI
The price on the clock rises continuously; as the price ascends, bidders no longer interested in the object lower their paddles. Eventually only two bidders remain active, but the price continues to ascend. When one of those bidders drops out, the clock stops.
Note:MODELLO DELL’OROLOGIO IN ASCESA
Economists also refer to this model of an English auction as the button auction model: bidders press down on a button as the prices ascends. A bidder releases the button once the price exceeds what he is willing to pay. … English auction has a simple solution because each player has a weakly dominant strategy.
Strict dominance for Alice meant that regardless of what Bob chose to do, Alice would be strictly better off if she confessed. Weak dominance is just like this, except that it allows for ties. … Weakly dominant strategies are nice to have—if you’re the bidder, it’s hard to go wrong.
Note:L’OFFERENTE NON PUO’ SBAGLIARE
What makes the bidding strategy at the English auction so simple to understand is that the increases in the asking price are observed by all bidderse
TRASPARENZA DELL’ASTA INGLESE
the winning bidder at a Vickrey auction pays the second-highest submitted bid…. in the baseline model, it is again a weakly dominant strategy for bidders to tender bids that equal their valuations.
Note:ESISTE UNA STRATEGIA DOMINANTE NELLA VICKREY? OVVERO: PENSO SOLO A RENDERE PUBBLICA LA MIA VALUTAZIONE?
To understand the bidding strategy, suppose that a bidder has a valuation of $41, and investigate the potential consequences of bidding something other than $41. First, consider bidding something less than $41, say, $35. If $35 is the highest bid submitted, then the auction is won and the second-highest submitted bid is paid. For example, suppose that the second-highest bid was $29. Then the difference between the valuation, $41, and the price paid, $29, yields a payoff of $12. Of course, this exact outcome would have obtained had a bid of $41 been tendered as well. …suppose that the highest bid is, say, $82, in which case neither a bid of $35 nor one of $41 would have won the object; no harm no foul. … In contrast, imagine the highest bid is something like $39. By submitting a bid of $35, the auction is lost, and the payoff is zero. Tendering $35 leaves our bidder regretting the decision …Next consider bidding something more than $41, say, $44. If $44 is not the highest tender submitted, then the bidder earns nothing—the … if $44 is the highest bid, two things can happen: first, if the second-highest bid is $39, then the auction is won with a bid of $44 and also would have been won with a bid of $41; in both cases, a payoff of $2 is earned. …If the second highest bid is $42, and the auction is won with a bid of $44, then the payoff involves a loss of $1. …Since neither bidding less nor bidding more ever does better, a bidder cannot gain from bidding anything but the drawn valuation. Bidding the drawn valuation is a weakly dominant strategy. …
Note:ANALISI… RISPOSTA: SI’
bidding high increases the odds that you win but decreases the payoff if you win; bidding low decreases the odds that you win but increases the payoff if you win. Clearly, a trade-off exists. At second-price auctions, however, your payoff should you win is unaffected by what you bid, so no such trade-off exists. …Finally, an interdependence exists among the bidders—your chances of winning depend not only on your bid, but also on how your bid compares to all the other bids. …
Note::PRIMO PREZZO. NO STRATEGIA DOMINANTE… DIFFERENZA COL SECONDO PREZZO… PUOI BLUFFARE…
all bidders are using the same rule to convert a drawn valuation into a bid, submitted bids will differ. Second, players with high valuations bid more than those with low valuations. Third, the bids are lower than drawn valuations: bidders shade their bids below their true valuations. In other words, they lie about what the object is worth to them.
Note:NASH: SI OFFRE MENO ANCHE SE LE PRIORITÀ SONO RISPETTATE
An important difference exists between what someone would like to do before the auction is held when information is incomplete, and what the same person would do after the auction concludes and the bids have been revealed.
Note:PRIMA E DOPO
it is important that the rules of the auction be respected. Obviously, after discovering that he has lost the auction, Bob would like to approach the seller, to try to negotiate an agreement
Sellers are bound by the policies they announce before bids are received; they cannot change the rules after having seen all of the bids.
In the absence of a legal system, however, commitment can still play a powerful role, especially when reputation is important.
Although the Dutch auction has an open format, the information revealed during the auction is not at all informative to bidders. The only time bidders learn anything from their rivals is when the auction is over: the only action a bidder can take is to stop the clock,
Note:OLANDESI: POCHE INFO
the bidder is breathless with excitement because the longer the clock goes unstopped, the cheaper will be the object. As the price descends, however, the odds that a rival bidder will stop the clock increase.
The problem faced by a bidder at a Dutch auction is then exactly the same problem as the one faced by a bidder deciding what tender to submit at a first-price, sealed-bid auction.
Note:BUSTE E OLANDESI
Despite the fact that these two types of auctions are quite different, the Dutch and first-price, sealed-bid auctions are actually the same strategically. Economists refer to these auctions as strategically equivalent. …Not only are the first-price, sealed-bid and Dutch auctions strategically equivalent, but within the baseline model English and Vickrey auctions are as well.
Properties of Outcomes
two basic reasons: first, to allocate an object; second, to earn revenue.
Note:ALLOCARE E INCASSARE IL MASSIMO
When it comes to allocating the object, we are interested in the notion of efficiency.
did the participant who valued the object the most end up with the object at the conclusion of the auction?… all four types of auctions are efficient.
Note:TUTTE LE ASTE SONO EFFICIENTI: CHI DESIDERA DI PIU’ OTTIENE
A second reason auctions are used is to generate revenue for the seller.
Note:E CHI VENDE?
can the seller expect any one of the four types of auctions considered thus far to yield revenues higher than the others? Initially surprising to many, the answer to this question is no.
Note:NON CE N’ È UNA MIGLIORE A PRIORI
you might think that a second-price auction should do better because, as we have shown, bidders all tender higher bids in this environment. …Of course, at a second-price auction, the seller receives the second-highest bid, not the highest bid. Revenue equivalence tells us that, once bidder behavior is internalized, these two factors balance each other out perfectly. …
Note:VICKREY NON RISOLVE
This remarkable result, which is referred to as the revenue equivalence theorem, is perhaps the most famous result in all of auction theory.
Note:TEOREMA DELLE ASTE EQUIVALENTI
the relevant comparison is one based on average revenues—in expectation.
Note:SI GUARDA ALLA MEDIA
Could the seller change the rules to garner even more revenue? In other words, are these four types of auctions optimal?
ESISTONO ASTE MIGLIORI PER IL VENDITORE? SÌ BASTA ASSUMERE ALTRE REGOLE
Other Assumptions and Rules
The neutrality of the revenue equivalence theorem induces ambivalence; the seller’s choice seems unimportant.
When one of the assumptions is relaxed, it matters which type of auction is used.
…the reserve price—the minimum acceptable bid.
the highest bid must exceed the minimum acceptable price, otherwise the object goes unsold. At many auctions, sellers impose reserve prices. Why?
Note:PERCHÈ UN PREZZO MINIMO
reserve price must be set before the auction begins and its existence must be made known to all participating at the auction.
Note:FISSATO PRIMA E PUBBLICAMENTE
For example, outside Dallas, Texas, the Vetro Glassblowing Studio & Gallery hosts its “Truth or Consequences Auction” each fall. …the artist specifies a minimum acceptable price for the glass piece on sale. …If the reserve price is not met, then a rope securing the top piece is released allowing the metal to destroy the artwork. …
Note:DISTRUGGERE IL BENE
at a second-price auction, the reserve price can be particularly effective as an insurance device, especially when the seller may receive one high, acceptable bid, but many other low bids.
Note:BUSTE SECONDO PREZZO
In 1990 the New Zealand government sold the rights to use electromagnetic spectrum for radio and television as well as mobile phones at auction, but reserve prices were not imposed. To allocate the licenses, the government opted to use the Vickrey auction. Unfortunately, for the government (the seller), unusually low revenues were garnered. …Some licenses received just one bid; in the absence of a reserve price, those bidders got the licenses for free! …
NUOVA ZELANDA E LA VENDITA DELLE FREQUENZE
Clearly, however, a trade-off exists: setting too high a reserve price increases the odds that the object goes unsold but potentially increases the revenues a seller earns when the object is sold.
Note: INCONVENIENTE DEL PREZZO MINIMO
Perhaps surprising to the reader, the optimal reserve price exceeds the seller’s own valuation for the object.
Note:AL VENDITORE CONVIENE BLUFFARE
those having valuations above $50 behave more aggressively because the valuations of rivals who participate are now known to exceed the reserve price. That is, rivals who participate are a self-selected group of bidders having higher-than-average valuations….From an economist’s perspective, the downside of using reserve prices is that the auctions are no longer efficient…the object goes unsold, which is clearly an inefficient outcome. …
With a secret reserve price, the bidders understand that a minimum acceptable bid exists, but they are not told its specific value. Christie’s and Sotheby’s are well known to use secret reserve prices…. At first-price auctions, in the baseline model, no incentive exists for the seller to keep the reserve price hidden as the seller can always do at least as well by publicizing the threshold price as opposed to keeping it hidden.
Note:QUANDO CONVIENE IL PREZZO MINIMO SEGRETO
In some sense, this is like another player is at auction. Still, such a policy does not generate the needed increase in aggressiveness from bidders to outperform an optimally set… Above, we focused on the symmetric IPV paradigm. The word symmetric implies that bidders’ valuations are drawn from the same urn, a potentially restrictive assumption. If valuations are drawn from different urns, then the model is referred to as asymmetric.
Note:IN CASO DI SEGRETO VALUTAZIONI ASIMMETRICHE
Asymmetries can arise for any number of reasons. For example, if bidders have different budget constraints,
Note:ALTRO ELEMENTO DI ASIMMETRIA: RICCHEZZA DEI BIDDER
A bidder from Vermont at an auction of an antique tractor in rural New Hampshire faces different costs for transporting the machine back to his property than a farmer from Wisconsin.
Another fundamental change would involve having losing bidders pay, too.
Note:FAR PAGARE I PERDENTI
In practice, many auctions require payment from all bidders who participate.
Note:QUOTA D’ ISCRIZIONE
The auction ends at a prespecified time or if during some period no bidders have paid the bid fee to increase the price,
Note:OFERTE A PAGAMEMTO
the all-pay auction is efficient… relative to the first-price auction in the baseline model, bidders will choose to shade their bids by even more at all-pay auctions because payment is required regardless of the outcome. Consequently, as you can see, iPads can sometimes be won online for $40.
All-pay auctions are also a valuable way of selling an object when bidders are interested in the amount of money generated at auction, which is often true for supporters of a charity.
Researchers at Middlebury College conducted auctions both in experimental settings and at real-world fundraising auctions conducted by schools in Vermont and Oregon as well as various Rotary International service clubs throughout the United States. The researchers found that all-pay auctions generate more revenues for charities than winner-pay auctions… evidence for charities to raise money by using what they refer to as a bucket auction. The bucket auction works as follows: one randomly selected bidder in the room is given the opportunity to put a nonrefundable chip (which has a fixed monetary value) into a bucket. The bucket is then passed to another bidder in the room who decides whether to place a chip into the bucket. The bucket continues circulating around …The bidder who drops the last chip in the bucket is declared the winner. …
Note:ASTA DEL SECCHIELLO
Another reason for discussing the all-pay auction is that it illustrates how other situations in the real world can be modeled as auctions, even though they obviously are not.
Note:ASTA DEI PERDENTI: TUTTO E’ TRASFORMABILE IN ASTA
Alternative Models of Valuations
Differences in bidders’ signals generate differences in the bids tendered at auction…. The linkage principle states that a seller can expect to increase revenues by providing information to bidders. The linkage principle is the second most famous result in auction theory.
Note:DARE INFORMAZIONI PAGA
That is why, for example, the English auction does better for the seller than the Vickrey auction in this setting: bidders can learn about others’ private information as the auction is conducted. … For example, government agencies often provide engineers’ estimates to firms who bid on the right to perform some task. Christie’s and Sotheby’s list professional estimates of a painting’s value in their auction catalogs….
Note:EFFETTO DEL SEGNALE.