AA rating system for art markets on the blockchain
Massimo FranceschetDepartment of Mathematics, Computer Science, and PhysicsUniversity of Udine – Italy [email protected]
Giovanni ColavizzaDepartment of Media StudiesUniversity of Amsterdam – the Netherlands [email protected]
April 14, 2020
Abstract
Establishing the market value of art is a known challenge. A tra-ditional distinction between primary (first-sale) and secondary (re-sale)markets in fact relates to two approaches to value-estimation and pric-ing: that of the gallery and that of the auction house, respectively. Toovercome this dichotomy, we propose a novel rating system for the actorsof art markets , equally adaptable to primary and secondary markets. Weintroduce a time-aware variant of the HITS Web ranking method , whichcaptures the interlocked role of artists and collectors and rapidly adaptsto changes in the relative importance of the actors part of a market. Weapply the proposed method to crypto art , a novel form of born-digital artexchanged on blockchains, and show that the proposed method outper-forms alternatives when used to guide market investment.
Blockchain technology, while commonly associated with cryptocurrencies, hasshown potential to bring radical structural change to the arts and creative indus-tries [49]. Blockchains are already used in the arts including to record prove-nance and authenticity registries [32], to guarantee digital scarcity [36, 4, 5],to create fractional equity [51], and to allow novel forms of copyright registry[50]. Another form of blockchain-enabled innovation in the arts and creativeindustries is crypto art . Crypto art uses blockchain technology to “tokenize”unique copies of born-digital artworks, and thereby to exchange them. As asignificant by-product, crypto art is generating increasing amounts of openlyavailable structured and unstructured data.1 a r X i v : . [ c s . C Y ] A p r rt markets specialize in the exchange of cultural objects. The main distinc-tion within art markets is made between primary markets, which focus on first-time sales from living artists, and secondary markets, which focus on re-sales[45]. The primary art market is mostly served by galleries, while the secondarymarket is primarily the territory of auction houses. With respect the approachtaken to price art, the two markets differ markedly. The primary market reliespersonal connections and pricing scripts [44], also based on some notion of anartist’s prestige, while the secondary market focuses on best-offer auctions [3].Methods for price estimation and for constructing art market indexes have also,consequently, diverged. Little work exists on the primary market, primarilydue to the scarcity of available data, while estimations for the secondary mar-ket are done either using the re-sale history of individual artworks, or some oftheir measurable characteristics [23]. Both approaches possess limitations. Are-sale history is not available for first-time sales, while selecting and measuringartwork features for price estimation is complex and sometimes not possible.In this work, we propose a novel rating system for the actors of art markets ,which works equally well for primary and secondary markets. We borrow fromthe Web page ranking literature, specifically from the seminal HITS method[28], and propose a time-aware variant which better captures the interlockedrole of artists and collectors. We test the proposed method on crypto art data,and suggest possible applications. The origins of the blockchain go back to the crypto-anarchism and cypherpunk movements of the late 1980s. These activists advocated the widespread useof strong cryptography to guarantee confidentiality and security while sendingand receiving information over computer networks, in an effort to protect theirprivacy, their political and economic freedom [31]:
Combined with emerging information markets, crypto anarchy willcreate a liquid market for any and all material which can be put intowords and pictures .The following excerpt from the
Cypherpunk Manifesto by Eric Hughes isparticularly telling since it contains, some 30 years in advance, all the ingredientsthat inspire modern blockchain technology [26]:
We the Cypherpunks are dedicated to building anonymous systems.We are defending our privacy with cryptography, with anonymousmail forwarding systems, with digital signatures, and with electronicmoney. [...] Cypherpunks write code. We know that software can’tbe destroyed and that a widely dispersed system can’t be shut down .Blockchains are hard to grasp at first. The basic scientific research fromwhich the technology emerged – a journal paper and a US patent of Stuart2aber, a cryptographer, and Scott Stornetta, a physicist [24, 25] – is distinctfrom the financial systems it later generated – the rise (and fall) of bitcoin andother cryptocurrencies [35, 15].Haber and Stornetta were trying to deal with epistemological problems ofhow we trust what we believe to be true in a digital age [49, 24]:
The prospect of a world in which all text, audio, picture and videodocuments are in digital form on easily modifiable media raises theissue of how to certify when a document was created or last changed.The problem is to time-stamp the data, not the medium.
In particular, they started from two questions [49]:1.
If it is so easy to manipulate a digital file on a personal com-puter, how will we know what was true about the past? How can we trust what we know of the past without having totrust a central authority to keep the record?
These questions configure an extremely challenging problem. The prob-lem was solved by Haber and Stornetta [24] and, 17 years later, by SatoshiNakamoto [35] as well, using a combination of tools borrowed from mathemat-ics, computer science, economics and political science. This makes blockchaintechnology a truly interdisciplinary and fascinating topic.A blockchain is a distributed ledger, using cryptography to secure an evolv-ing consensus about a token with economic value. The atomic elements of ablockchain are the blocks . A block is a container of data. In its simplest form, itcontains an identification number, a timestamp of the block creation, and data(usually, transactions moving some digital asset from a sender to a receiver).Each block has a fingerprint called hash that is used to certify the informa-tion content of the block. Block hashes are created using cryptographic hashfunctions: functions that map data of an arbitrary size to a fixed-size string ofbits. A popular family of hash algorithms is the Secure Hash Algorithm (SHA),designed by the United States National Security Agency (NSA) [1]. Blocks arechronologically concatenated into a chain by adding to each block a field withthe hash of the previous block in the chain. It follows that the hash of eachblock is computed including the hash of the previous block, meaning that toalter one block and for the chain to remain valid, one would need to modify notonly the hash of that particular block, but also the hash of all following blocksof the chain. However, hashes alone are not enough to prevent tampering, sincehash values can be rapidly computed by computers. A proof of work methodis needed to control the difficulty of creating new blocks, and to maintain theblock creation process at a steady pace. To mine (create) a new block one hasto solve a computational problem that is hard to solve and easy to verify. This Satoshi Nakamoto is the pseudonymous used by the person or persons who developedbitcoin, authored the bitcoin white paper, and created and deployed bitcoin’s original referenceimplementation.
3s a cryptographic puzzle that can be attacked only with a brute-force approach(i.e., by trying all possibilities), so that only the sheer computational power ofminers counts.A block transaction represents an interaction between parties, typically atransfer from sender to receiver of cryptocurrencies or of any other digital assetwith economic value recorded on the blockchain ( token ). Each transaction hasa fee that must be payed by the sender and each potential miner includes inits block a subset of pending transactions. The miner of the block gets the feesof all blocked transactions plus a fixed, newly minted amount of crypto coins(this is how new coins are introduced in the cryptocurrency economy). Fur-thermore, blockchains use asymmetric cryptography (also known as public-keycryptography) to implement digital signatures of transactions. Each transactionis signed with the sender’s private key and anyone can verify the authenticity ofthe transaction using the sender’s public key. Asymmetric cryptography thusenables a trusted exchange between users who do not trust one another. Fi-nally, the blockchain ledger is distributed over a peer-to-peer network , so thateach node of the network has a copy of the entire blockchain. This furtherhampers the tampering of information on blockchains [53].
In their original proposal, Haber and Stornetta envisaged the adoption of blockchainsbeyond texts [24]:
Of course digital time-stamping is not limited to text. Any stringof bits can be time-stamped, including digital audio recordings, pho-tographs, and full-motion videos. [...] time-stamping can help todistinguish an original photograph from a retouched one.
Today, the adoption of blockchain technologies are rapidly expanding in thearts sector. The potential to impact traditional entrepreneurial organizationswithin the arts and creative industries, including art markets, involves on allactors – artists, collectors, galleries, auction houses, in the first place [49].
Provenance and authenticity are two major and related issues in both tra-ditional and digital art. Where provenance describes a chain of ownership,authentication proves the correct authorship. Blockchains combine provenanceand authentication features, providing a chained record of ownership that isdependent on the validity of the starting point of the blockchain record. For ex-ample, the company Verisart launched in 2015 to provide a trusted database ofauthentic artworks. Verisart relies on blockchain technology to combine trans-parency, anonymity and security to protect records of creation and ownershipof artworks.Another company in this space is Artory, which provides a secure, publicregistry for artworks and objects. Utilizing blockchain technology and end-to-end encrypted messaging, collectors confidentially register their artworks fordigital signature by trusted art institutions – for instance, an auction house or4allery. Once artwork data and provenance are verified, Artory issues a digitallysigned, blockchain-secured certificate of registration accessible in the private,encrypted collector’s vault. Collectors are never publicly listed as the owner ofthe artwork, and they remain completely anonymous, however, they are able touse their certificates of registration as anonymous evidence of ownership duringtransactions. In fall 2018, Artory became the first company to list a majorauction sale on a blockchain when it became the registrar of the EbsworthCollection, sold at Christie’s New York for $318 million on November 13, 2018[27].Codex Protocol also partners with auction houses to vet the entry point ofrecords onto the blockchain. Codex records are an online lockboxes that allow tosafely store and share information about an item, for instance provenance docu-mentation like attestations from appraisers or sale bills from auction houses. InMay 2018, the Ethereal Summit hosted the first auction issuing Codex-securedtitles for all pieces sold. During the auction, a specially commissioned Cryp-toKitty digital collectible was sold for a record-breaking $140,000.Blockchains also allow the fractional or shared ownership of (tokens of) indi-vidual artworks. From a collector’s point of view, the possibility of “tokenizing”single artworks allows investors to diversify their portfolios, to reduce theirinvestment exposure and to ease buying or selling tokens. For example, thecompany Maecenas bought Andy Warhol’s
14 Electric Chairs , and divided itup into shares sold as so-called ART tokens. The company raised $1.7m for31.5% of the artwork at a valuation of $5.6m.Finally, blockchains have been used to deal with a central challenge to sell-ing digital art: how to create a limited edition of a file that can be easilyreproduced.
Crypto art is a rising art movement in the ‘cypher space’ [21]. Itassociates digital artworks with unique and provably rare tokens that exist on ablockchain; these codes are the equivalent of the artist’s signature. The conceptis based on the idea of digital scarcity, which allows one to buy, sell, and tradedigital art as if it were physical [4, 5, 6]. The real potential of the emergingcrypto art is that it leverages blockchain technologies to equip a born-digitalartwork with the main characteristics of any traditional collectible: uniqueness.Early examples of crypto art include CryptoKitties, CryptoPunks, Autoglyphs,and Rare Pepe. The most popular crypto art galleries today are SuperRare,KnownOrigin, MakersPlace as well as the more recent Async Art.
SuperRare is among the most important crypto art galleries, by popularityand volume of exchanged artworks. An overview of market activity by salefrequency and amount is given in Figure 2. The typical workflow of crypto arton SuperRare is as follows:1. an artist creates a digital artwork (an image or animation) and uploadsit to the gallery. The author specifies the title, description, a list of tagwords and possibly a price; 5. the smart contract of the gallery creates a non-fungible token on theEthereum blockchain associated with the artwork, and transfers the tokento the artist’s digital wallet ;3. the gallery distributes the artwork file over the IPFS peer-to-peer net-work ; hence neither the token nor the artwork are on any central server;4. collectors can place bids on the artwork by transferring the bid amount tothe smart contract of the gallery (the collector can withdraw bids at anytime) or they can buy directly at the price set by the artist;5. eventually, the artist accepts a bid; the smart contract of the gallerythen transfers the artwork’s token to the collector’s wallet and the agreedamount of ETH to the artist’s wallet;6. the artwork remains on the market. Each re-sale in the secondary marketof the SuperRare gallery rewards also the original artist [51]. The most distinctive facet of crypto art, one that sets it apart from thetraditional art system, is its velocity . In crypto art something can happenat every instant: an artist forges a new piece or accepts a bid made from acollector, a collector makes a bid for an artwork or directly buys it, two artistsor collectors exchange artworks. The workflow of crypto art is also potentiallyvery fast: where the working time granularity in traditional art might be ofmonths or even years, the time granularity in crypto art is often of hours or evenminutes, and could go down to any granularity supported by Ethereum. Thisconfigures the crypto art system as an almost real-time stream of events, moreakin to financial trading than traditional art. The variety of data is anotherfacet of the crypto art system. SuperRare data includes structured data liketoken metadata and event transactions, as well as unstructured data such as thetext that describes the artworks and the static and animated multimedia thatform the artworks themselves. Finally, if we see the collection of all marketplaces Ethereum is a public blockchain featuring a smart-contract (scripting) functionality. Asmart contract is a computerized transaction protocol that executes the terms of a contract.Ether (ETH for short) is the cryptocurrency generated by the Ethereum platform as a rewardto mining nodes. Non-fungible tokens represent something unique (for instance, a one-of-a-kind collectible). They are not interchangeable and cannot be divided, as opposed to fungibletokens (cryptocurrencies), which are interchangeable and can be split in smaller pieces whosesum is equivalent to the whole. A digital wallet is a software that allows blockchain users tomanage and securely store their own private keys instead of recording them manually. The InterPlanetary File System (IPFS) is a protocol and peer-to-peer network for storingand sharing hypermedia in a distributed file system. IPFS uses content-addressing storageto uniquely identify each file, a way to store information so it can be retrieved based on itscontent, not its location. Each file is identified by the hash of its content. IPFS lets youaddress large amounts of data and place permanent links into blockchain transactions. The art market is split up into the primary and secondary market. If an artwork comesstraight out of an artists studio, by way of a gallery or a contemporary art fair, it is mostlikely being offered for sale for the first time. This is the primary art market when the pricefor the piece is also established for the first time. The secondary market usually trades inestablished and sought-after artists. Once a piece has been acquired on the primary marketand is being re-sold, it is now part of the secondary market or second-hand market. volume of data becomes significant. All in all, the crypto art system therefore showsthe three Vs (volume, variety and velocity) that are typically associated with big data applications [18].The SuperRare dataset reflects these properties. To date (4th March, 2020),the gallery displays 8,311 artworks, 55% of which have been sold at least onceon the primary market. The secondary market is still limited, with only 7% ofsold artworks that were sold more than once. Overall, artists earned 3,374 ETH(or $571,075 using the exchange rate at the transaction time). The artist thatsold the most on both the primary and secondary market made $41,817, whilethe collector who bought the most spent $103,595 for 339 artworks. The meanprice for an artwork is 0.69 ETH (or $117). There are 1804 users registered inthe gallery, however, most of them are by-standers: 192 users created at leastone piece (hence, they are accredited artists) and 174 of them sold at least onecreated artwork, while 290 users bought at least one artwork. As a curiosity, byanalysing the frequency of events over week days, we found that on Mondaysand Tuesdays artworks are typically created, on Tuesdays bids are commonlymade, on Fridays sales usually happen, and during weekends the activity is quitefaint.The SuperRare dataset was partly acquired from the gallery’s API, andpartly directly from the gallery. All analyses were conducted in R, taking ad-vantage of the tidyverse packages [52].
Art markets allow the exchange of cultural objects. These objects are eithersupplied directly by the artist, via their studio or through a gallery, or by pre-vious owners who want to sell them, usually via dealers or auction houses. Thisdifference in supply, matched by specialized intermediaries, is used to establisha distinction between primary and secondary markets . Primary markets focuson first-time sales from living artists, while secondary markets focus on re-sales[45]. Art markets are rather peculiar markets when assessed using classical mar-ket theory, for a variety of reasons, including [11, 37, 12, 43, 44, 8, 42, 20, 13]:diverse buying motivations and complex, qualitative value judgements, hetero-geneous and inelastic supply (of artworks), high transaction costs and lack ofliquidity, non-divisibility (an artwork needs to be bought and sold in full), lackof transparency leading to information asymmetries, mostly dealing with “cre-dence goods” whose value is determined by symbolic capital and the art culturalapparatus which is inextricably connected to the market.Traditionally, the primary and secondary market have been separated. Theprimary market, galleries in particular, work with a selection of artists thatthey promote over time. The main pricing system that galleries use is based on OpenSea is the main secondary marketplace for digital goods, including collectibles, gam-ing items, digital art, and other digital assets that are backed by a blockchain like Ethereum.It presently contains over 4 million digital assets.
We can consider this multiplier as a gallery-specific artist rating.
The logicof a gallery is that of curating the price of an artist over time through socialand interpersonal relations. In the secondary market, instead, the pricing ofartworks happens primarily via auctions, in view of maximizing profits accordingto supply and demand [3, 34]. In both markets, direct deals are also frequent. Inrecent decades, the distinction between the primary and the secondary marketshas started to blur, especially for highly famous and costly artists [45]. Adefining event in this respect was the Scull sale in 1973, where for the first timehigh prices for contemporary artists were paid at an auction [41]. More recently,in 2008, Sotheby’s devoted an entire auction to Damien Hirst’s works, an eventwhich so far remains exceptional [46].Methods for art price estimation have mostly been developed for the purposeof constructing price indexes for investment [7, 2, 17, 9, 14, 33, 16, 39, 30, 10, 22].Two families of methods have emerged from economics: repeat-sales regression(RSR) and hedonic regression (HR) [23]. Repeat-sales regression uses the pricesof the same object traded at two or more points in time. Hedonic regression,instead, regresses prices on characteristics of artworks (e.g., size, artist, style,and more) and uses the regression residuals to compute price indexes. WhileRSR allows to bypass the issue of measuring the heterogeneous characteristicsof artworks entirely, HR allows to estimate the price of artworks in the absenceof a previous trading history. While pricing on the secondary market has beenamply studied in previous literature, little work exists on the primary market“since data on the primary market barely exist” [45]. Consequently, previousliterature has almost exclusively relied on auction data to apply these methods.Nevertheless, using auction data remains particularly problematic as it focuseson just one side of the art market, the secondary market, and is biased towardspopular artists or Old (i.e., dead) Masters.We concern ourselves with the pricing of art on any market, either primaryor secondary. In particular, we propose a method to establish a rating forartists coupled with a rating for collectors, calculated independently from thecharacteristics of artworks, which can be hard to measure, and from re-salehistory, which is often absent. Our rating system can therefore be used asthe artist multiplier when applying pricing scripts in a gallery setting, and as amodel variable for hedonic regression when considering price indexes or auctions.How is crypto art similar or different to the traditional art market system?First of all, crypto art uses auctions for both primary and secondary sales, withinthe same (online) gallery. Secondly, crypto art still does not possess a culturalapparatus comparable to traditional art, with recognized experts, museums andleading galleries or collectors, yet all these developments are rapidly takingplace. Thirdly, crypto art is fully transparent with respect to previous sale his-tory and ownership (all transactions and the provenance chain are stored on apublic blockchain). Lastly, crypto art is highly social and fast paced, showcas-ing dynamics akin to social networks. Crypto art also shares several traits with8raditional art markets, for example the diverse buying motivations, the inelas-tic supply, and the non-divisibility of artworks (although even these are rapidlychanging, as some galleries already fractionalize artwork ownership). Whilein several respects crypto art differs from the traditional art market, its mainobjective remains the exchange of artworks. Furthermore, crypto art is antici-pating developments which are rapidly taking place in traditional art markets,such as the digitization, commercialization and financialization of transactions[48, 47, 29].
Presently, there exists no standard nor any shared proposal for defining ratingsfor crypto artists and artworks. This despite the public availability of all dataflow of crypto art, including artwork images and metadata and event trans-actions (bid placing, withdrawing and accepting, direct sales, price setting).All these data are accessible either trough gallery APIs or block explorers likeEtherscan for Ethereum. In this section, we propose a rating method for artistsand collectors applicable to any art market.A characteristic of the art market, one that allows to draw a parallelismwith the scientific publication system or with the Web, is the mechanism ofendorsement of artists and collectors. Both works of art and science can beendorsed by the respective communities, thus gaining in popularity and, forartworks, in commercial value. A scientific paper (author) is endorsed when apeer references it in another article. An artwork (artist) is endorsed when acollector makes a bid or a direct buy. The number of bids made for the artwork,or the number of times the artwork is traded among collectors, might indicatethe popularity of the piece of art in the artistic setting, as much as the number ofcitations from other scholars accrued by a paper is an indicator of its popularitywithin a scientific community. Furthermore, besides popularity, one can alsoinvestigate the prestige of the works of art and of scholarly publications and,indirectly, of artists and authors. We might argue that a bid to an artwork madeby a prestigious collector, or a citation to an article given by an authoritativescientist, are more important than endorsements given by unknown individuals.Fraiberger et al. [20] draw an interesting parallel between the conceptsof performance and success in different contexts. For example in sports, theperformance of an athlete is easily measurable and comparable with that ofother athletes. In this case, performance and success are strongly correlated.In other scenarios, such as art, wine tasting or cooking, the intrinsic qualityof a work is difficult to assess. In these cases, performance is only one of theingredients of success. The position of the actor within the often invisible socialnetwork that tangles their work is often what determines their success. In art,this network involves artists, collectors, galleries, curators, agents, art historians,auction houses.We focus here on the relationship between artists and collectors. We startfrom the intuition that important collectors buy from important artists and im-portant artists sell to important collectors, and borrow the Hyperlink-Induced9opic Search (HITS) method [28], originally developed to detect hubs and au-thorities on the Web. Artists create and sell artworks, they are the sources ofart. Collectors buy and pull together artworks, they have some sense of wheregood art is, they are the art hubs . In practice, the market is considerably morecomplex. The figure of the art investor, that is someone trading in art by buy-ing in view of re-selling artworks, is also a crucial one. A sizable amount oftrades in the art market are mediated by galleries or dealers, offering dedicatedmarketplaces. Lastly, reputation (and thus higher quotes) is not only acquiredthrough sales but also via exhibitions in prestigious venues and, for example,media coverage [19, 20].In the SuperRare dataset, the complementary actors of the artist and thecollector are usually well-defined, as shown in Figure 1. Note that most usersare either sellers, buyers or by-standers. There are few traders, that is usersthat buy art to resell it. The Kendall’s correlation between sales and purchasesis in fact negative (-0.19). As a consequence, we conclude that a secondarymarket has not yet fully developed on SuperRare and similar galleries [21], asalso noticed above. Despite using the selling mechanism of the auction, typicalof the secondary market in traditional art, crypto art galleries primarily operateon the primary market. They therefore offer a valuable test case for the HITSmethod we propose, which focuses on the interconnected roles of artist andcollector.
HITS’s assumes that in certain networks there can be found two types of im-portant nodes [28]: authorities , that contain reliable information on the topic ofinterest, and hubs , that tell us where to find authoritative information. A nodemay be an authority, a hub, both or neither. For instance, on the Web hubs arepages that compile lists of resources relevant to a given topic of interest, whileauthorities are pages that contain explicit information on the topic. In an arti-cle citation network, hubs are for example review papers that mainly referenceother papers containing relevant information on a given topic, while authoritiesare articles that contain the explicit information. This calls for two distinctyet interrelated notions of centrality: authority and hub centrality. There is amutual recursion underlying the definition of the roles of authorities and hubsthat can be concisely expressed as follows:A node is an authority if it is linked to by hubs (nodes with highhub centrality); a node is a hub if it links to authorities (nodes withhigh authority centrality).Formally, let A be the adjacency matrix of a directed network. The authoritycentrality x i of node i is proportional to the hub centrality of the nodes thatlink to it, that is: 10 i = α (cid:88) k A k,i y k On the other hand, the hub centrality y i of node i is proportional to theauthority centrality of the nodes linked by it, that is: y i = β (cid:88) k A i,k x k where α and β are constants. If the network is weighted, then A i,j is a posi-tive number that represents the strength of the relationship between nodes i and j : the higher the weight, the stronger the link. Notice how the above equationsuse these weights: stronger links give more (authority and hub) centralities. Inmatrix form the above equations write: x = αyAy = βxA T In this formulation the mutual reinforcement between hubs and authorities isevident: authorities ( x ) depend on hubs ( y ) and hubs ( y ) depend on authorities( x ), with the mediation of the network structure encoded in matrix A .We can rephrase Kleinberg’s thesis in the art setting as follows:A leading artist sells to leading collectors and a leading collectorbuys from leading artists.Our first proposal is therefore the following. We start by building two net-works. The first network, called buyer/creator network , links buyers to creatorsof art. More precisely, the nodes of the network are active users in a market-place, that is those that made at least one sale, or at least one buy, or thatcreated at least one piece of art. The links are drawn as follows. Suppose thereis a sale transaction in which user A sells to user B an artwork T for a price P,where C is the artist that originally created T. We add to the network a linkfrom B (the buyer) to C (the creator of the art) weighted by the price P. In fact,P is expressed in fiat money (dollars) using the Ether to dollar exchange rate ofthe day of the transaction. This link represents an endorsement of artist C bybuyer B, independently of the current owner A of the token T (yet notice thatif the token is sold on the primary market, then A and C coincide).The second network, called buyer/seller network , links buyers to sellers ofart. The network nodes are defined as for the first network above. Given a saletransaction in which user A sells to user B an artwork T for a price P, we addto the network a link from B (the buyer) to A (the seller of the art) weightedwith price P expressed in fiat money (dollars), independently of the creator ofthe artwork.On the buyer/creator network we compute the following node centralitymeasures:1. For creators (artists): 11 n sell : the unweighted in-degree, which corresponds to the numberof artworks created by the artist that were sold on either the primaryor secondary market of the gallery; • a sell : the weighted in-degree, which corresponds to the overall amountmade by sales of artworks created by the artist on either the primaryor secondary market of the gallery; • authority : the Kleinberg’s HITS authority rating.2. For buyers (collectors): • n buy : the unweighted out-degree, which corresponds to the numberof artworks purchased by the collector; • a buy : the weighted out-degree, which corresponds to the overallamount spent by the collector for purchases of artworks; • hub : the Kleinberg’s HITS hub rating.Furthermore, on the buyer/seller network we compute the node betweennesscentrality ( btw ), which measures the extent to which users are brokers or tradersin the art gallery, that is if they buy art in view of selling it. One potential issue with the original HITS method is that it is static. For ex-ample, suppose that a collector buys, for the same price, two artworks A andB from the same artist but at different times: artwork A is bought when theartist was unknown and artwork B after the artist became popular. Reason-ably, the collector expects a larger increase in their centrality from the secondpurchase, since in that case they acquired a piece from a more renowned artist.Unfortunately, HITS does not distinguish between the two purchases. A time-aware metric, on the other hand, would distinguish between the two scenarios,assigning to the collector different centrality gains, proportional to the artist’scentrality at the time of each sale.To overcome this issue, we propose an extension to HITS named time-awareHITS . At each time instant t , each user i has two ratings: an artist rating x i ( t )and a collector rating y i ( t ). Initially, at time 0, all users of the gallery havenull rating. Subsequently and at each sale, we modify the artist rating of theartist and the collector rating of the collector as follows. Suppose that collector j buys an artwork made by artist i spending an amount p at time t >
0. Weupdate the artist rating x i ( t ) of artist i at time t as well as the collector rating y j ( t ) of collector j at time t using the following interrelated formulas: x i ( t ) = x i ( t −
1) + P ( p, t − · P ( y j ( t − , t − y j ( t ) = y j ( t −
1) + P ( p, t − · P ( x i ( t − , t −
1) (1) Alternatively, one might decide to set the newcomer rating in a different way. For example,it could be set to a given percentile of the ratings of the gallery, or, if available, the artist’srating from another gallery where the artist has already been active.
12n the above equations, P ( p, t −
1) is the percentile of price p with respect tothe distribution of gallery prices up to time t −
1. Hence, it is a factor from 0 to1 that ponders the sale price within the price history of the gallery. Moreover, P ( x i ( t − , t −
1) is the percentile of the rating of artist i at time t − t −
1. Similarly, P ( y j ( t − , t −
1) is the percentile of the rating of collector j at time t − t −
1. These factors, also lying between 0 and1, weight the artist/collector rating relative to similar ratings accrued so far. Itis worth mentioning that we opted for a percentile approach since we noticedthat both gallery prices and ratings display a strong right-skewed distribution,therefore the mean would not provide for a good indicator of the average case.The correlation among all measures defined above is given in Figure 3 ( t authority and t hub are the time-aware authority and hub measures respectively). Noticethat the metrics cluster in three well-defined groups: • a sale group , including metrics that characterize the selling propensity ofthe actor; • a buy group , including metrics that characterize the buying propensity ofthe actor; • a betweenness group , only including the betweenness metric, which iden-tifies the trading propensity of the actor.The correlation plot highlights three roles among actors in the marketplace:art sellers (artists), art buyers (collectors), as well as art traders (re-sellers ofart). The proposed metrics can be assessed in practice to purchase art as an invest-ment, i.e., to make a profit. We propose the following approach to comparerating methods with respect to their capacity to inform investments. We takethe perspective of a collector or art gallery, interested in investing into profitableartists. We devise the following method to assess the sale prediction accuracyof a given rating method. For a given time window from t to t + 1 and a givennumber k of artists we want to invest on, the method is as follows:1. compute the rating for all artists at time t ;2. select the top- k rated artists at time t ; this is our investment ;3. get the sale increase for the selected artists moving from time t to time t + 1; We publish and maintain the proposed rankings of all SuperRare users at the followingaddress: http://users.dimi.uniud.it/~massimo.franceschet/SR/cryptorank/cryptorank.html .
13. compute the investment gain as the mean sale increase over the selectedartists, weighted by their relative ratings.We illustrate the method using a toy example with three selected artists A,B and C rated 50, 30 and 20, respectively. The relative ratings are hence 0.5,0.3 and 0.2 respectively. Suppose that, at the end of the period, artist A soldfor 2 ETH, B sold for 1.5 ETH, and C sold for 0.5 ETH. The investment gainis 0 . · . · . . · . .
55 ETH.By following the same procedure for different ratings and different contiguoustime windows, we can compare their gains at every time step and in total. Wereport results using k = 10 artists and time windows of 30 days: reasonablydifferent values do not substantially alter results. We compared the time-awareauthority metric (t authority) with alternative artist metrics (authority, n sell,a sell), over 12 monthly time windows, starting from August 1, 2018 in orderto allow for some transactions to accumulate beforehand. The average gainper period using t authority is $336, that of authority is $246, that of n sellis $285, and that of a sell is $277. Hence, the proposed time-aware authorityoutperforms the original HITS authority by a 37% margin, the number of salesby 18%, and the amount of sales by 21%. To test the robustness of our results,we run the same experiment over 1000 bootstrap runs and average the results,with a resulting gain of $310 for t authority, and of $211 for the original HITSauthority.Finally, we extend the window under consideration to 18 months, startingfrom August 1, 2018 and ending with January 2020 included. As it can beseen from Figure 2, the Winter months of 2019 and 2020 have witnessed asurge in activity on SuperRare, mainly driven by a handful of leading artistsand collectors. This surge from leading artists and collectors had a stabilizingeffect on their ratings. As it can be seen from Figure 4, the gains of both originalHITS and time-aware HITS eventually converge. Nevertheless, we highlight thisproperty of our proposed method: when the market is still unstable, with newactors coming and going, t authority dominates the original HITS, eventuallyconverging to similar results when dominant actors emerge and stabilize. Theresulting gain over 18 months and averaged over 1000 bootstrap runs is of $717for t authority, and of $608 for the original HITS authority. In this work, we brought together the worlds of Web ranking and art markets.We started by the consideration that art markets witness a separation betweenprimary and secondary markets, that is between first-time sales and re-sales,which has determined markedly different approaches to price estimation. Inorder to overcome such division, we proposed here to focus on the actors of artmarkets, starting from artists (or sellers) and collectors (or buyers). Inspired bythe original HITS method for Web page ranking, we have proposed a time-awareversion of HITS which is able to capture the interrelated roles of artists (author-ities) and collectors (hubs). Furthermore, we have proposed a complementary14etwork construction which allows to detect leading traders (actors who buyto sell) using betweenneess centrality. We have applied our method on a casestudy based on data from the SuperRare gallery, which is a leading crypto artmarketplace. The proposed time-aware HITS outperforms alternatives whenused as an investment strategy, and can be used for price estimation in galleriesas well as to construct price indexes.Crypto art is born-digital art exchanged on the Ethereum blockchain, a no-table example of the innovations which novel digital technologies are bringingto the art world. Blockchain technology, in particular, is calling for a radicalre-thinking of traditional art systems, including art markets. The open avail-ability of granular data on crypto art transactions has been instrumental inthe development of the proposed rating systems. Newly-available data promiseto further our understanding of the economics of art. At the time of writingin early 2020, with the COVID-19 epidemic crisis unfolding, art markets areforced to go digital. Crypto art, born-digital, immaterial, fast-paced and easyto exchange, heralds a future which is all too present.
Acknowledgements
We would like to thank the administrators of SuperRare for sharing the gallerydata with us. We also thank the artist duo Hackatao for inspiring discussionson early drafts of this work.
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Figure 1: Each point in the plot is a user with the number of sales on the x-axisand the number of buys on the y-axis, while 90% percentiles are plotted as lines. date nu m be r o f e v en t s (a) Number of daily accepted bids andsales. Fiat amount F r equen cy (b) Histogram of sale amounts in US dol-lars (exchange rate calculate at the timeof the sale; we cut to sales of 500 dollarsor less). Figure 2: The SuperRare art market activity over time.20 au t ho r i t y n_ s e ll t _au t ho r i t y a_ s e ll b t w hub n_bu y t _hub a_bu y authorityn_sellt_authoritya_sellbtwhubn_buyt_huba_buy Figure 3: Correlation plot for the proposed art metrics.21 time ga i n rating authorityt_authorityauthorityt_authority