This article was downloaded by: [165.123.34.86] On: 02 June 2020, At: 07:12 Publisher: Institute for Operations Research and the Management Sciences (INFORMS) INFORMS is located in Maryland, USA

Management Science

Publication details, including instructions for authors and subscription information: http://pubsonline.informs.org Channel

Eduardo M. Azevedo, David M. Pennock, Bo Waggoner, E. Glen Weyl

To cite this article: Eduardo M. Azevedo, David M. Pennock, Bo Waggoner, E. Glen Weyl (2020) Channel Auctions . Management Science 66(5):2075-2082. https://doi.org/10.1287/mnsc.2019.3487

Full terms and conditions of use: https://pubsonline.informs.org/Publications/Librarians-Portal/PubsOnLine-Terms-and- Conditions

This article may be used only for the purposes of research, teaching, and/or private study. Commercial use or systematic downloading (by robots or other automatic processes) is prohibited without explicit Publisher approval, unless otherwise noted. For more information, contact [email protected]. The Publisher does not warrant or guarantee the article’s accuracy, completeness, merchantability, fitness for a particular purpose, or non-infringement. Descriptions of, or references to, products or publications, or inclusion of an advertisement in this article, neither constitutes nor implies a guarantee, endorsement, or support of claims made of that product, publication, or service. Copyright © 2020, INFORMS

Please scroll down for article—it is on subsequent pages

With 12,500 members from nearly 90 countries, INFORMS is the largest international association of operations research (O.R.) and analytics professionals and students. INFORMS provides unique networking and learning opportunities for individual professionals, and organizations of all types and sizes, to better understand and use O.R. and analytics tools and methods to transform strategic visions and achieve better outcomes. For more information on INFORMS, its publications, membership, or meetings visit http://www.informs.org MANAGEMENT SCIENCE Vol. 66, No. 5, May 2020, pp. 2075–2082 http://pubsonline.informs.org/journal/mnsc ISSN 0025-1909 (print), ISSN 1526-5501 (online)

Channel Auctions

Eduardo M. Azevedo,a David M. Pennock,b Bo Waggoner,c E. Glen Weylb a The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104; b Microsoft Research, Redmond, Washington 98052; c University of Colorado, Boulder, Colorado 80303 Contact: [email protected], http://orcid.org/0000-0001-6048-6506 (EMA); [email protected] (DMP); [email protected], http://orcid.org/0000-0002-1366-1065 (BW); [email protected], http://orcid.org/0000-0001-8824-6977 (EGW)

Received: August 5, 2019 Abstract. Standard formats feature either an upper bound on the equilibrium price Revised: August 16, 2019 that descends over time (as in the ) or a lower bound on the equilibrium price Accepted: August 16, 2019 that ascends over time (as in the ). We show that in some settings with Published Online in Articles in Advance: costly information acquisition, auctions featuring both (viz., a narrowing channel of prices) March 4, 2020 outperform the standard formats. This Channel auction preserves some of benefits of both https://doi.org/10.1287/mnsc.2019.3487 the English (truthful revelation) and Dutch (security for necessary information acquisition) auctions. Natural applications include housing, sites like eBay, recording Copyright: © 2020 INFORMS transactions on blockchains, and spectrum rights.

History: Accepted by Joshua Gans, business strategy. Funding: E. M. Azevedo acknowledges support from the Sloan Research Fellowship [Grant FG2018- 10387].

Keywords: games group decisions • auctions • marketing • pricing • economics • game theory • bargaining theory

1. Introduction until the number of bidders remaining at the lower- When the competitive market price for an asset is not bound price is at most the number of objects remaining widely known and relevant information is held by unassigned. We refer to this design as a Channel auction many parties, auctions are a common method for because it involves a narrowing channel of prices simultaneously determining prices and allocating the honing in on the optimum and because it mixes asset in question. The central goal of auction design is features of ascending (usually called English) and 1 to facilitate the acquisition, revelation, and integra- descending (usually called Dutch) price auctions. tion of this information to facilitate this process. In In this paper, we analyze Channel auctions in a this sense, auctions are a search and information setting where informationacquisitionmaybeim- processing scheme, like those studied in computer portant but also may be unnecessary and wasteful. science, albeit one involving many agents with po- Our main result gives conditions under which an tentially conflicting incentives. optimal Channel auction generates higher welfare Despite this parallel, common dynamic auction de- than the standard auction formats. The intuition is signs are quite different from search schemes employed that Channel auctions give bidders information that in computer science. In computer science, search pro- the final price will be in some interval. This allows tocols involving bounds honing in on an answer from bidders to wait until the price is guaranteed to be close both sides (such as binary search, jump search, and to their possible valuations to incur information ac- interpolation search) are more efficient in many cir- quisition costs. In contrast, standard auction formats fi cumstances than are linear search protocols that start at only give information that the nal price will be ei- one end and approach an answer. Yet, nearly all auc- ther below some value (in the Dutch auction) or tions involve a linear procedure. The goal of this paper above some value (in the English auction). We discuss is to suggest that this may be improved in cases by some potential applications, including the sale of narrowing in on equilibrium prices rather than starting houses and online auctions, where we argue it is al- on one side and moving toward them. ready informally in use, though not widely discussed We propose an auction in which an upper-bound as such. price descends as a lower-bound price rises. Bidders all begin in the auction at the lower-bound price; this 2. Background represents a commitment to buy at this price. As this Most auctions fall into one of two camps. Since the lower-bound price rises, bidders may at any time pioneering work of Vickrey (1961), economists have drop out. Any bidder who is still in the auction may tended to endorse or extend English auctions.These buy at the upper-bound price at any time she wishes involve a price or prices that gradually move upward and be awarded an object. This process continues from zero or a low number toward the levels that clear

2075 Azevedo et al.: Channel Auctions 2076 Management Science, 2020, vol. 66, no. 5, pp. 2075–2082, © 2020 INFORMS the market. Participants stay in the auction until they while most sales will occur through the English phase are no longer willing to pay the price offered, and even- expiring. In this design, a channel of prices between tually the number of remaining participants matches the Dutch and the English gradually narrows in the supply. on the equilibrium price, similar to the honing of a Economists have been attracted to this format be- binary search. cause the points at which bidders drop out will Another important potential advantage of the typically reflect their values, given there is no cost of Channel auction, on which we focus in the next staying in until one’s best estimate of value is reached. section, relates to the possibility that information This tends to suggest goods will be allocated to their acquisition may turn out to be wasteful. Consider a highest value (Vickrey 1961) and that much infor- bidder who does not know how much the object is mation will be revealed in the process by observing worth to her and has an opportunity to pay a price for bidders drop out (Milgrom and Weber 1982). This information about its value. The analysis of Kleinberg information helps to ensure that a good allocation is et al. (2018) indicates that she will not be willing to pay made if it informs bidders about how much the objects this price (or may end up regretting paying it) unless may be worth to them (Dasgupta and Maskin 2000). she has confidence that the price is below some level. The other common auction format operates on the Effectively, if the price is above some level, it is out of opposite principle. In Dutch auctions, prices start at a her price range, and she would like to know that high level and gradually descend. At any point, a before she investigates it. participant may claim an object at the quoted price Conversely, if the price turns out to be low, she may and the process proceeds until no objects remain. regret having acquired information because she Since Vickrey, Dutch auctions have been seen mostly would have been willing to take the object without as a foil to highlight the benefits of English auctions, knowing its exact value to her, and thus acquiring as bidders typically will wait until the price has fallen information turns out to have been a waste. Effec- below the amount they would be willing to pay before tively, if the price is low enough, she would buy the claiming the object. Because this incentive to delay object regardless of how good she finds it to be. purchase may differ across bidders and because the A Channel auction can avoid both the risk of too high Dutch process reveals little about bidders’ informa- a price and the risk of too low a price. tion until it is too late for other bidders to act, Dutch Before the formal analysis, we illustrate these main auctions have been seen as inferior. points in a simple example.2 A seller is auctioning off However, Kleinberg et al. (2018) show that Dutch an object to three buyers. Two of the buyers, whom we auctions have an important advantage: they provide refer to as the competitors, are identical. The com- bidders with a useful price guarantee as the auction petitors’ valuation is $1, $50.10, or $100 with equal proceeds. Because it is often necessary for bidders to probability. The competitors know their common research a purchase, they will often be unwilling to valuation, so that they always compete away their seriously engage with the auction if the price may rise rents in the auction. The third buyer, whom we refer arbitrarily high. Most people, for example, would not to as the collector, has a valuation v uniformly dis- spend hours looking at a house if they had no clear tributed between $0 and $100, independently of the sense of at least an upper bound on what its price might valuation of the competitors. The collector has to pay be. English auctions provide no such upper bound: a $10 to learn her valuation. bidder may fear that after looking at the house, the price Consider what happens in a standard ascending will head far beyond what she would ever consider auction. The collector should stay in the auction at a paying. During a Dutch auction, on the other hand, price up to $1 without acquiring information. She will upper bounds always exist and thus bidders can feel win at a price of $1 whenever the competitors have a safe investing in acquiring information, at least as value of $1, which happens with probability 1/3. In necessary for a purchase. Thus in cases where infor- that case, profits equal the expected valuation of $50 mation acquisition is important, the Dutch format may minus $1, for a total of $49. But, if prices go up to $1.01, greatly outperform the English format. what should the collector do? In that case, she knows This suggests an improvement on both schemes. If that the price will be at least $50.10. Therefore, she the role of the upper-bounding Dutch prices is pri- cannot make profits without acquiring information. marily to give bidders security, while the role of the But information is costly, so she has to gauge whether lower bounding English price is to promote infor- it is better to acquire information or to drop out. mation revelation, it may be possible to have a bit of The expected profits of acquiring information are each of these advantages. A Dutch price can descend the product of the probability that the final price is as an English price rises. The Dutch price provides $50.10, the probability that v is greater than $50.10, security and occasionally may be used for allocation, and the conditional expectation of v minus $50.10. Azevedo et al.: Channel Auctions Management Science, 2020, vol. 66, no. 5, pp. 2075–2082, © 2020 INFORMS 2077

This equals Note that the English and Dutch auctions are special ()cases of the Channel auction. The English auction 1 100 − 50.10 50.10 + 100 ¯ ¯ · · − 50.10 ≈ $6.22. corresponds to the case of p(t)v · t and P(t)v, 2 100 2 where v¯ is greater than any bidder’svaluation.The Therefore, the collector does not acquire information Dutch auction corresponds to the case of p(t)0and and instead drops out of the auction as soon as the P(t)v¯ ·(1 − t). price hits $1.01. The key point is that the gain from acquiring in- formationiszerowhenthecompetitors’ value is $100, 4. Theory but the gain is about $12.45 when the competitors’ 4.1. Model value is $50.10. Therefore, investing in information is We consider an auction game with information ac- fruitless half of the time. It would be advantageous for quisition. Three risk-neutral bidders with quasi-linear the collector to know whether getting information preferences want to acquire an object. One of the bid- ’ is fruitless before incurring the information acquisi- ders is the collector. The collector s valuation v for the tion cost. object has a distribution F with density f . The collector This is where a Channel auction can increase effi- is uncertain about her valuation. She needs to pay an ciency. Namely, the seller can first run a descending inspection cost c to learn her valuation. If she receives price phase where a Dutch price descends to $99. The the object without inspection, she eventually learns ev- E[ ] object will be sold in this phase only when the com- erything at no cost, receiving an average payoff v , ¯ petitors’ value is $100.3 After the Dutch phase, the which we denote v. seller runs the standard ascending English phase. Even The collector faces two other competitors.Thecom- though the ascending phase works exactly like the petitors have the same value w for the object, which traditional ascending auction, the outcome is different. they both know. The competitors also know each ’ When the price reaches $1.01, the collector knows that others value. Their value w has a distribution G with the competitors’ valuation is $50.10. So her value of density g with bounded support and is independent ’ acquiring information is about $12.45, and she will from the collector svalue. acquire information. The remainder of this paper The object is initially owned by a risk-averse seller defines Channel auctions and formalizes this main with quasi-linear preferences and zero value for the fi insight in a simple model. object. Social welfare is de ned as the sum of indi- vidual utilities.5 3. Definition of the Single-Item Channel Auction 4.2. First-Best The simplest, single-item Channel auction works as We start with the first-best with no asymmetric in- follows. There is a single object to be auctioned to one formation, that is, how to maximize social welfare of N bidders. Time t starts at 0 and proceeds until one given the information available to the bidders. Ini- of three conditions listed below is met. The auction tially, the bidders only know w.Sowehavetodecide ( ) has a weakly decreasing upper price P t at time t, whether to inspect given w,thendecidehowtoal- “ ” called the Dutch price, at which any bidder still in locate the object. We call the optimal inspection de- the auction can clinch the object. The auction also has cision conditional on w the first-best inspection strategy. ( )≤ ( ) aweaklyincreasinglowerpricep t P t , called the We call the set of values of w for which inspection is “ ” English price, at which every bidder remaining in optimal the first-best inspection range.Wecallthe the auction commits to be willing to purchase the optimal welfare first-best welfare. 4 object. At any time, bidders in the auction can buy The following proposition summarizes the optimal ( ) theobjectatapriceofP t or drop out of the auction. inspection strategy. The three conditions for termination of the auction are as follows: Proposition 1 (First-Best Inspection Strategy). Consider fi 1. Only a single bidder remains in the auction. In the rst-best inspection strategy. Given F and c, there are this case, that bidder pays the English price and re- values of w for which it is optimal to inspect if and only if ceives the object. + 2. A bidder claims the object. In this case, that E[(v − v¯) ]≥c. (1) bidder pays the Dutch price and receives the object. σ ≤ ≤ σ,¯ 3. The Dutch and English prices converge. In this If this holds, inspection is optimal if and only if w case, the object is uniformly randomly allocated among where – + the remaining bidders at the common Dutch English E[(v − σ¯) ]c, (2) price. E[(σ − )+] . ( ) We illustrate this basic process in Figure 1. v c 3 Azevedo et al.: Channel Auctions 2078 Management Science, 2020, vol. 66, no. 5, pp. 2075–2082, © 2020 INFORMS

Figure 1. (Color online) Illustration of a Single-Item Channel Auction with Continuous Price Changes

Notes. As the ascending price rises (ascending line), bidders drop out of the auction (bars). The auction may end when a bidder claims the item at the Dutch price (End 1) or at the English price when only one bidder remains (End 2).

+ Proof. There are three options: E[(w − v) ] < c, or strictly above σ¯, in which case + 1. Do not inspect and allocate to the collector, E[(v − w) ] < c. obtaining v¯. We next observe that v¯ is the unique value of w such 2. Do not inspect and allocate to a competitor, + + that E[(w − v) ]E[(v − w) ]. This implies that M(w) obtaining w. is maximized at w  v¯, because one term is strictly 3. Inspect and allocate to the larger value (v or w), decreasing in w and the other is strictly increasing. So obtaining E[max{w, v}] − c. there exists w with M(w)≥c if and only if M(v¯)≥c. □ First, we consider the condition that option 3 is better than option 1: The proposition makes two points. First, the first- best inspection range is a (possibly empty) interval. E[max{w, v}] − c ≥ v¯ This is intuitive. If the competitors’ value is very low, ⇐⇒ E[max{w, v}] − E[v]≥c then it is better to just give the object to the collector ⇐⇒ E[max{w, v}−v]≥c without incurring the inspection cost. Likewise, if the competitors’ value is very high, it is better to just give ⇐⇒ E[( − )+]≥ . w v c theobjecttooneofthecompetitors.Soinspectionis fi worthwhile only for w between σ and σ¯. The left side is strictly increasing in w,sowe nd this fi holds if and only if w ≥ σ. Similar calculations show Second, the rst-best inspection strategy is related that option 3 is better than option 2 if and only if w ≤ σ¯. to option pricing. As mentioned in Kleinberg et al. (2018), Equation (2)defining σ¯ is a standard formula This proves that inspection is optimal if and only if σ¯ σ ≤ w ≤ σ¯. in option pricing. Namely, value is the strike price of This also shows that there exist cases where in- a call option for an underlying asset with value v and spection is optimal if and only if σ ≤ σ¯. It only remains actuarially fair price c (cf. Dixit and Pindyck 1994). to prove that this is the case if and only if Equation (1) Given that it is always possible to allocate to a holds. Let competitor for w,inspectingcanbeinterpretedas paying c for the option to allocate to the collector + + ≥ M(w) : min{E[(w − v) ] , E[(v − w) ]}. instead. If v w, we exercise the option, gaining the asset for value v but giving up or “paying a price” of w. We first claim that σ ≤ σ¯ if and only if there exists w Therefore, it is worthwhile to purchase the option such that M(w)≥c.Ifσ ≤ σ¯,thenM(w)≥c for every (inspect the item) only if w is less than the strike price. w in between, by the above calculations. If σ>σ¯, Similarly, σ is the strike price of a put option for an then every w is either strictly below σ, in which case asset with value v and fair price c. Given that it is Azevedo et al.: Channel Auctions Management Science, 2020, vol. 66, no. 5, pp. 2075–2082, © 2020 INFORMS 2079 always possible to allocate to the collector without Proposition 2. If there is positive prior probability on all inspecting, for a welfare of v,inspectioncanbe three possibilities w < σ, w > σ¯, and σ

P(t)(1 − t)·max{w|w ∈ support(G)} + t · σ,¯ Proof. The case where inspection is never optimal, σ>σ¯ • ≤ ≤ , is trivial. We now consider the interesting case for 1 t 2, where σ ≤ σ¯. ( )( − )·σ¯ +( − )· We show that the collector inspects precisely when p t t 1 2 t 0 socially optimal, and the item is awarded in a socially and P(t)σ¯. optimal way. First, imagine the collector knew w, which could only improve her utility. Given a fixed We consider perfect Bayesian equilibrium. The exact value of w, the collector’s utility for choosing to inspect games can be specified in standard ways as in Milgrom at any time before the end of the auction would be and Weber (1982) but are cumbersome. So we follow + the literature in stating the results and analyzing the U(w) : E[(v − w) ]−c. key points in the proof without defining all of the moves in each game. We assume elimination of This follows because she pays c to inspect and wins weakly dominated strategies. This implies that in only in the event v ≥ w,payingw. equilibrium of a Dutch, an English, or a Channel auc- Now by definition, if and only if w ≥ σ¯,thenU(w)≤0. tion, a competitor obtains the item whenever a price If and only if w ≤ σ, direct calculation shows U(w)≤ reaches w. In a Dutch portion of an auction, a com- v¯ − w, which is the expected utility for obtaining the petitor has negative utility for claiming the item if the item without inspection. Therefore, if the collector price is still above w, while either competitor will knew w exactly, she would conclude that a best re- attempttooutbidtheotherifhewaitsforthepriceto sponse is to not win the item if w ≥ σ¯; win the item go strictly below w, so this cannot occur in equilib- without inspecting if w ≤ σ,payingw;andinspect rium. In the English portion, we have assumed no otherwise, winning if v ≥ w and paying w.Notethis weakly dominated strategies, so competitors do not matches the socially optimal inspection and alloca- drop out either strictly before or strictly after the tion decision. price reaches w. Now, we argue the collector can achieve this opti- We establish two results. The firstresultshowsthat mal utility without knowing w as follows: do not claim the Dutch and English auctions cannot achieve first- the item during the Dutch portion; wait to inspect best welfare. until the English price rises to σ; then inspect and drop Azevedo et al.: Channel Auctions 2080 Management Science, 2020, vol. 66, no. 5, pp. 2075–2082, © 2020 INFORMS out when the English price exceeds v.Thisisabest by the findings of Cao and Zhang (2018), who find response by all players, hence an equilibrium. □ that, in a closely related context, information acqui- sition costs are typically a large fraction (approxi- 4.4. The Channel Auction Captures the Benefits of mately 40%) of the value of objects purchased. But Traditional Formats that information acquisition is “optional” in the sense Channel auctions have two other notable properties. that the amount of information individuals acquire Both properties hold by definition and capture key before purchasing varies widely across individuals, advantages of the English and Dutch auctions. The contexts, and price levels. These conditions suggest that first advantage is that the Dutch and Channel auctions explicitly incorporating a descending Buy It Now price solveanexposureproblem.Atanypointintheauc- and thus effectively converting to a Channel auction tion, a bidder who invests in collecting some in- could add clarity to the process and could help over- formation is guaranteed to be able to buy the object at come the primary cost of delay that Einav et al. (2018) the price P(t).6 So the bidder does not run the risk of find is the cause of the increasing switching away investing in evaluating the item and then finding out from auctions toward sales at fixed prices. Two im- that she is outbid. In fact, the only points in time when portant differences are that the Buy It Now price is not it makes sense for a bidder to incur the inspection cost determined in a formal auction and that it may go is when the inspection can influence her decision. away once bidding starts. Naturally, a bidder may inspect and decide to wait for Many individual sales that used to be conducted at prices to go down further, but she is always guar- garage sales and later on eBay are now conducted on anteed to be able to buy at P(t).Ofcourse,thisbenefit Facebook. Facebook garage sale groups exist for applies only to the extent that the Dutch price actu- millions of locations around the world. In a garage ally falls to levels sufficient to provide appropriate sale group, the convention is as follows. The seller guarantees to participants. posts a picture and short description of the item and a The second advantage is that with private values, price to the group’s news feed. The first buyer willing the Channel and English auctions make it a domi- to pay the price gets the item. Some people may post a nant strategy for a bidder to stay in the auction as long comment that they are willing to buy for less than the as the English price p(t) is below her expected valu- seller’s price. Thus the convention is a Dutch auction ation.7 This has some of the traditional advantages where the price never descends and an informal of strategy-proofness, such as outcomes being less English auction. In practice, if the item does not sell, sensitive to higher-order beliefs, lowering the costs of the seller will repost with a lower price, implementing strategizing, producing preference data, and not dis- an informal and manual Dutch auction. So in an in- advantaging bidders who are less sophisticated. We formal way, these communities are implementing caution that the Channel auction has a muted version of Channel auctions. With a small amount of logic, these these advantages because the optimal clinching does garage sale posts could be mechanized, adding a depend on other players’ strategies. clock to descend the seller’sprice(say,by$1perday), and allowing more formal bids below the seller value. 5. Applications and Discussion Such formalization may be particularly useful in We discuss three areas where it may be possible to use contexts where communication is harder and trust Channel auctions. lower, such as more decentralized versions of this procedure facilitated by blockchain technologies. 5.1. Online Consumer Goods eBay auctions are not Channel auctions. But, because 5.2. Real Estate of the way the auctions are run, there are some simi- Home buyers are often legally required, by govern- larities to an informal Channel auction. The Dutch price ments and/or lenders, to conduct detailed inspec- is the eBay Buy It Now price, which rarely decreases. tions and appraisals. Still, these processes do not However, if an object fails to sell after a long period of resolve all potential uncertainties about the value of a time, we suspect sellers will lower this price, thereby home. If a foreclosed home is cheap enough, a buyer effectively decreasing the Dutch price. Simultaneously, may need little due diligence to be confident in a good eBay runs an English ascending auction. Einav et al. return on investment. But if the price of a foreclosed (2018) show that more commoditized objects tend to home goes up, the buyer may need to spend con- be purchased using Buy It Now, and some items, with siderable time and effort to evaluate whether the less certain value, tend to be purchased in the English opportunity is worthwhile. In a way, real estate works auction (see also Ding 2015 and references therein). like an informal Channel auction, analogous to the This suggests that allowing both a descending and consumer goods example given earlier. A buyer can an ascending price may be useful. This is reinforced usually buy a house at the seller’s price. The seller will Azevedo et al.: Channel Auctions Management Science, 2020, vol. 66, no. 5, pp. 2075–2082, © 2020 INFORMS 2081 lower the price over time if the house is not selling. to uncertainty about latency in transaction inclu- Otherwise, buyers compete in an informal English- sion, potentially creating security cost and some style auction.8 degree of chaos. A potential alternative is a batched Channel auction that takes place in the run-up to 5.3. Cryptocurrencies theepochassociatedwiththeblockinquestionand Many assets within cryptocurrency and blockchain that closes just before the block does, so that prices can communities are sold via auction and involve sub- be increasingly well forecast as the block closing stantial information acquisition. Two examples are approaches. Given the rapid growth of this space and auctions for including transactions in blocks and the strong openness to experimentation, this may be auctions for wallet addresses. We brieflydescribe the nearest-term application for Channel auctions. each and discuss how Channel auctions could im- Another interesting application in this burgeoning prove outcomes in each case. space is domain names (such as addresses for wal- In popular cryptocurrencies such as bitcoin and lets where tokens are held). Many within the block- ether, the demand to include transactions in the chain space refer to the movement as Web 3.0, and blocks that constitute the only reliable record of domain names and other addresses are important real changes in the state of the system has outstripped the estate in blockchain communities. Within Ethereum, space available to record these transactions. Trans- Maurelian (2016) describes the auction currently being action fees are used to clear the market, most com- used to sell names. At any time, anyone can show in- monlybyeverytransactionproposer(viz.,currency terest in a name and start an English auction that lasts user) submitting a bid price for including their trans- three days for this name. action in a block, block makers and validators taking the Adifficulty this system creates, however, is that top set of offers. Assuming that the value of inclusion trolls may sit and watch for auctions and if an in- continues to rise and limits on availability remain tight, teresting name arises may enter the auction and ex- the quality of price discovery and allocation via these tract surplus from someone attempting to register a competitive processes will play a significant role in the name. This problem is particularly acute in block- success of cryptocurrency communities. chain environments because everything is, by design, Transactions waiting to be included are held in a public in a way that invites such front-running be- queue called a mempool. Transactions are pulled havior. This may undermine investments that are from this pool in a priority order given by the trans- complementary with obtaining this name, harm ac- action fee they bid. Thus, in practice, the transaction fee quisition of information, create exposure problems, chosen determines the rate at which the transaction is and so forth. A natural solution is to add a Dutch included on a block, and most transactions are even- element to the system. Since it began operation in tually processed in a low-demand period. As demand 2017, the current system has had a deadline of four grows, latency in posting transactions is thus expected years until it stops accepting new registrations. A to rise. global declining price could be introduced that is a A number of projects have recently been devel- cap on the price of currently unregistered domains. oped to increase the value and reduce the volume of This cap could gradually fall until that final date, transactions posted to the fully public, decentralized guaranteeing a buy-it-now price for domain names. chains. Some prominent examples within the Ether- English auctions could still be triggered, but any eum community are State Channels and Plasma. Both participant could buy a name immediately at the global of these solutions aim to create lower-cost means of Dutch price. This approach would bring the benefits recordingtransactionsbyconductingmanytrans- of the Channel auction while preserving the general actions off the main chain and reporting only sum- structure of the present system. maries or net versions on the public chain. Eventually, the optimal versions of such protocols may be adaptive 5.4. Discussion of the Assumptions in the sense that they will post to the public chain We consider a particular and stylized setting that has less frequently if and when transaction fees are high, three bidders, a specific joint distribution of valua- though they will also post more frequently when more tions, and a specific information structure. This stylized consequential transactions have take place internally setting makes it simple to explain the potential ad- and thus the security of a summary on the public chain vantages of Channel auctions. But it also stacks the is needed. comparison in favor of Channel auctions, since it is a In such cases, price signals and a thoughtful allo- setting where the advantages appear with no costs. cation process will be critical to allow the algorithms More important, in our stylized setting we can or individuals administering these side chains and reach first-best welfare with a simple Channel auc- channels to determine when it makes sense to post to tion, with a Dutch phase followed by an English the public chain. The present queue structure leads phase. But, in general, the optimal Channel auction Azevedo et al.: Channel Auctions 2082 Management Science, 2020, vol. 66, no. 5, pp. 2075–2082, © 2020 INFORMS might be different. For example, we may want to Endnotes switch more often between the Dutch and English 1 Although the English Channel actually runs between England and phases, so that effectively the Dutch price changes France rather than England and Holland, the pun seems close enough during the English phase. Or we may want to forbid to be worth making. 2 clinching the object at the Dutch price at some points We thank an anonymous referee for this example. 3 (effectively setting P(t)∞ sometimes, so that P It can be shown that the collector does not want to clinch the object would not be weakly decreasing).9 An interesting during the Dutch phase. This will become clear from the theoretical analysis in Section 4 because the strike price σ¯ in this example is about direction for future research is to consider more $89.44. general settings and to derive prescriptions for how to 4 More precisely, the ascending phase is a Japanese auction, where design Channel auctions. prices rise according to a clock, as opposed to an English auction, We also make the stark assumption that the col- where prices rise in an open outcry. lector can instantaneously learn her valuation upon 5 We consider this particular, stylized setting rather than general joint paying the inspection cost. In practical applications, distributions of valuations and information structures. As such, our inspection takes time. Therefore, depending on the analysis is closer to an example than to a general analysis of Channel auctions. This stylized setting both stacks the comparison in favor of application, it may or may not be practical for in- Channel auctions and makes the analysis simple so that we can make spection to occur during the auction. For example, it the key points in a transparent way. may be reasonable to have a privatization auction 6 This relies on mild assumptions about the dynamic game that the with a descending Dutch phase, followed by an as- bidders play. This property will hold, for example, if prices are cending English phase that takes place a month later. updated in discrete time, but at each price update, bidders take turns And it may be reasonable to have a large spectrum deciding whether to drop out or clinch. 7 auction that takes place over the course of a month, so This property also relies on mild assumptions about the exact dy- fi namic game played by bidders. that rms can perform research on their valuations as 8 the auction proceeds. However, in other settings, Whereas this description often applies to individuals selling their homes, sales may be different. It is rare for banks to both auctions have to be conducted more quickly so that list a house and subsequently run an auction. We thank an anony- inspection during the auction is not practical. It mous referee for pointing this out. would be interesting to model this issue formally to 9 We thank an anonymous referee for making this point. better understand the situations where Channel auc- tions can perform well. References Cao X, Zhang J (2018) Prelaunch demand estimation. Accessed 6. Conclusion February 5, 2020, https://www.gsb.stanford.edu/sites/gsb/ files/mkt_02_18_cao.pdf. The most puzzling thing about Channel auctions is Dasgupta P, Maskin E (2000) Efficient auctions. Quart. J. Econom. 115(2): why they are not already more prevalent, at least as a 341–388. formal proposal by economists. If Dutch auctions Ding A (2015) Buy it now: An analysis of the effects of buy prices have some benefits and English auctions others, then in auction listings. Unpublished thesis, Stanford University, it is natural that there are circumstances in which Stanford, CA. Dixit A, Pindyck R (1994) Investment Under Uncertainty (Princeton combining lower and upper bounds on prices through a University Press, Princeton, NJ). process of honing in would be superior to either. Our Einav L, Farronato C, Levin J, Sundaresan N (2018) Auctions versus analysis formalizes this point in a simple setting. We posted prices in online markets. J. Political Econom. 126(1):178–215. hope that our results will inspire further research and Kleinberg R, Waggoner B, Weyl EG (2018) Descending price co- fi practical experimentation on this topic. ordinates ef cient search. Preprint, submitted March 25, 2016, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2753858. Maurelian (2016) Explaining the Ethereum namespace auction. Medium (November 16), https://medium.com/the-ethereum-name-service/ Acknowledgments explaining-the-ethereum-namespace-auction-241bec6ef751. Microsoft Corporation has patents pending on many of the Milgrom PR, Weber RJ (1982) A theory of auctions and competitive methods described in this document. The authors thank Eva bidding. Econometrica 50(5):1089–1122. Beylin and Vitalik Buterin for useful comments on this paper Vickrey W (1961) Counterspeculation, auctions and competitive and Charlie Thompson for research assistance. sealed tenders. J. Finance 16(1):8–37.