Online marketplaces are the main engines of legal and illegal e-commerce, yet their empirical properties are poorly understood due to the absence of large-scale data. We analyze two comprehensive datasets containing 245M transactions (16B USD) that took place on online marketplaces between 2010 and 2021, covering 28 dark web marketplaces, i.e., unregulated markets whose main currency is Bitcoin, and 144 product markets of one popular regulated e-commerce platform. We show that transactions in online marketplaces exhibit strikingly similar patterns despite significant differences in language, lifetimes, products, regulation, and technology. Specifically, we find remarkable regularities in the distributions of transaction amounts, number of transactions, inter-event times and time between first and last transactions. We show that buyer behavior is affected by the memory of past interactions and use this insight to propose a model of network formation reproducing our main empirical observations. Our findings have implications for understanding market power on online marketplaces as well as inter-marketplace competition, and provide empirical foundation for theoretical economic models of online marketplaces.
Jianhong Lin, Emiliano Marchese, Claudio J. Tessone, Tiziano Squartini
The Bitcoin Lightning Network (BLN) was launched in 2018 to scale up the number of transactions between Bitcoin owners. Although several contributions concerning the analysis of the BLN binary structure have recently appeared in the literature, the properties of its weighted counterpart are still largely unknown. The present contribution aims at filling this gap, by considering the Bitcoin Lightning Network over a period of 18 months, ranging from 12th January 2018 to 17th July 2019, and focusing on its weighted, undirected, daily snapshot representation - each weight representing the total capacity of the channels the two involved nodes have established on a given temporal snapshot. As the study of the BLN weighted structural properties reveals, it is becoming increasingly ‘centralized’ at different levels, just as its binary counterpart: (1) the Nakamoto coefficient shows that the percentage of nodes whose degrees/strengths ‘enclose’ the 51% of the total number of links/total weight is rapidly decreasing; (2) the Gini coefficient confirms that several weighted centrality measures are becoming increasingly unevenly distributed; (3) the weighted BLN topology is becoming increasingly compatible with a core–periphery structure, with the largest nodes ‘by strength’ constituting the core of such a network, whose size keeps shrinking as the BLN evolves. Further inspection of the resilience of the weighted BLN shows that removing such hubs leads to the network fragmentation into many components, an evidence indicating potential security threats — as the ones represented by the so called ‘split attacks’.
Edoardo Fadda, Junda He, Claudio Tessone, Paolo Barucca
Reaching consensus -- a macroscopic state where the system constituents display the same microscopic state -- is a necessity in multiple complex socio-technical and techno-economic systems: their correct functioning ultimately depends on it. In many distributed systems -- of which blockchain-based applications are a paradigmatic example -- the process of consensus formation is crucial not only for the emergence of a leading majority but for the very functioning of the system. We build a minimalistic network model of consensus formation on blockchain systems for quantifying how central nodes -- with respect to their average distance to others -- can leverage on their position to obtain competitive advantage in the consensus process. We show that in a wide range of network topologies, the probability of forming a majority can significantly increase depending on the centrality of nodes that initiate the spreading. Further, we study the role that network topology plays on the consensus process: we show that central nodes in scale-free networks can win consensus in the network even if they broadcast states significantly later than peripheral ones.
Matthieu Nadini, Alberto Bracci, Abeer ElBahrawy, Philip Gradwell · 6 authors
Dark web marketplaces (DWMs) are online platforms that facilitate illicit trade among millions of users generating billions of dollars in annual revenue. Recently, two interview-based studies have suggested that DWMs may also promote the emergence of direct user-to-user (U2U) trading relationships. Here, we quantify the scale of, and thoroughly investigate, U2U trading around DWMs by analysing 31 million Bitcoin transactions among users of 40 DWMs between June 2011 and Jan 2021. We find that half of the DWM users trade through U2U pairs generating a total trading volume greater than DWMs themselves. We then show that hundreds of thousands of DWM users form stable trading pairs that are persistent over time. Users in stable pairs are typically the ones with the largest trading volume on DWMs. Then, we show that new U2U pairs often form while both users are active on the same DWM, suggesting the marketplace may serve as a catalyst for new direct trading relationships. Finally, we reveal that stable U2U pairs tend to survive DWM closures and that they were not affected by COVID-19, indicating that their trading activity is resilient to external shocks. Our work unveils sophisticated patterns of trade emerging in the dark web and highlights the importance of investigating user behaviour beyond the immediate buyer-seller network on a single marketplace.
In this piece, we overview Isaac Asimov's most iconic work, the Foundation series, with two primary goals: to provide quantitative insights about the novels and bridge data science with digital art. First, we rely on data science and text processing tools to describe certain properties of Asimov's career and the novels, focusing on the different worlds in Asimov's universe. Then we transform the books' texts into a network centered around Asimov's planets and their semantic context. Finally, we introduce the world of crypto art and non-fungible tokens (NFTs) by transforming the visualized network into a high-end digital piece of art minted as an NFT. Additionally, to pay tribute to Asimov's devotion to robotics and artificial intelligence, we use OpenAI's Generative Pre-trained Transformer 3 (GPT-3) to draft several paragraphs of this paper.
Blockchains are still perceived chiefly as a new technology. But each blockchain is also a community and a social experiment, built around social consensus. Here I discuss three examples showing how collective intelligence can help, threat or capitalize on blockchain-based ecosystems. They concern the immutability of smart contracts, code transparency and new forms of property. The examples show that more research, new norms and, eventually, laws are needed to manage the interaction between collective behaviour and the blockchain technology. Insights from researchers in collective intelligence can help society rise up to the challenge.
This discussion applies quantitative finance methods and economic arguments to cryptocurrencies in general and bitcoin in particular -- as there are about $10,000$ cryptocurrencies, we focus (unless otherwise specified) on the most discussed crypto of those that claim to hew to the original protocol (Nakamoto 2009) and the one with, by far, the largest market capitalization. In its current version, in spite of the hype, bitcoin failed to satisfy the notion of "currency without government" (it proved to not even be a currency at all), can be neither a short nor long term store of value (its expected value is no higher than $0$), cannot operate as a reliable inflation hedge, and, worst of all, does not constitute, not even remotely, a safe haven for one's investments, a shield against government tyranny, or a tail protection vehicle for catastrophic episodes. Furthermore, bitcoin promoters appear to conflate the success of a payment mechanism (as a decentralized mode of exchange), which so far has failed, with the speculative variations in the price of a zero-sum maximally fragile asset with massive negative externalities. Going through monetary history, we show how a true numeraire must be one of minimum variance with respect to an arbitrary basket of goods and services, how gold and silver lost their inflation hedge status during the Hunt brothers squeeze in the late 1970s and what would be required from a true inflation hedged store of value.
Matthieu Nadini, Laura Alessandretti, Flavio Di Giacinto, Mauro Martino · 6 authors
Non Fungible Tokens (NFTs) are digital assets that represent objects like art, collectible, and in-game items. They are traded online, often with cryptocurrency, and are generally encoded within smart contracts on a blockchain. Public attention towards NFTs has exploded in 2021, when their market has experienced record sales, but little is known about the overall structure and evolution of its market. Here, we analyse data concerning 6.1 million trades of 4.7 million NFTs between June 23, 2017 and April 27, 2021, obtained primarily from Ethereum and WAX blockchains. First, we characterize statistical properties of the market. Second, we build the network of interactions, show that traders typically specialize on NFTs associated with similar objects and form tight clusters with other traders that exchange the same kind of objects. Third, we cluster objects associated to NFTs according to their visual features and show that collections contain visually homogeneous objects. Finally, we investigate the predictability of NFT sales using simple machine learning algorithms and find that sale history and, secondarily, visual features are good predictors for price. We anticipate that these findings will stimulate further research on NFT production, adoption, and trading in different contexts.
Jan A. Fischer, Andres Palechor, Daniele Dell’Aglio, Abraham Bernstein · 5 authors
Bitcoin is built on a blockchain, an immutable decentralised ledger that allows entities (users) to exchange Bitcoins in a pseudonymous manner. Bitcoins are associated with alpha-numeric addresses and are transferred via transactions. Each transaction is composed of a set of input addresses (associated with unspent outputs received from previous transactions) and a set of output addresses (to which Bitcoins are transferred). Despite Bitcoin was designed with anonymity in mind, different heuristic approaches exist to detect which addresses in a specific transaction belong to the same entity. By applying these heuristics, we build an Address Correspondence Network: in this representation, addresses are nodes are connected with edges if at least one heuristic detects them as belonging to the same entity. %addresses are nodes and edges are drawn between addresses detected as belonging to the same entity by at least one heuristic. %nodes represent addresses and edges model the likelihood that two nodes belong to the same entity %In this network, connected components represent sets of addresses controlled by the same entity. In this paper, we analyse for the first time the Address Correspondence Network and show it is characterised by a complex topology, signalled by a broad, skewed degree distribution and a power-law component size distribution. Using a large-scale dataset of addresses for which the controlling entities are known, we show that a combination of external data coupled with standard community detection algorithms can reliably identify entities. The complex nature of the Address Correspondence Network reveals that usage patterns of individual entities create statistical regularities; and that these regularities can be leveraged to more accurately identify entities and gain a deeper understanding of the Bitcoin economy as a whole.
Dániel Kondor, Nikola Bulatovic, József Stéger, István Csabai · 5 authors
Bitcoin and Ethereum transactions present some of the largest real-world complex networks that are publicly available for study, including a detailed picture of their time evolution. As such, they have received a considerable amount of attention from the network science community along with analyses from economic and cryptographic perspectives. Among these studies, in an analysis on the early instance of the Bitcoin network, we have shown the clear presence of the preferential attachment, or the “rich-get-richer” phenomenon. Now, we revisit this question, using a recent version of the Bitcoin network that has grown almost 100-fold since our original analysis. Furthermore, we additionally carry out a comparison with Ethereum, the second most important cryptocurrency. Our results show that preferential attachment continues to be a key factor in the evolution of both the Bitcoin and Ethereum transactoin networks. To facilitate further analysis, we publish a recent version of both transaction networks, and an efficient software implementation that is able to evaluate linking statistics necessary for learn about preferential attachment on networks with several hundred million edges.
Konstantinos Stylianou, Leonhard Spiegelberg, Maurice Herlihy, Nic Carter
When network products and services become more valuable as their userbase grows (network effects), this tendency can become a major determinant of how they compete with each other in the market and how the market is structured. Network effects are traditionally linked to high market concentration, early-mover advantages, and entry barriers, and in the cryptoasset market they have been used as a valuation tool too. The recent resurgence of Bitcoin has been partly attributed to network effects too. We study the existence of network effects in six cryptoassets from their inception to obtain a high-level overview of the application of network effects in the cryptoasset market. We show that contrary to the usual implications of network effects, they do not serve to concentrate the cryptoasset market, nor do they accord any one cryptoasset a definitive competitive advantage, nor are they consistent enough to be reliable valuation tools. Therefore, while network effects do occur in cryptoasset networks, they are not a defining feature of the cryptoasset market as a whole.
Blockchain and general purpose distributed ledgers are foundational technologies which bring significant innovation in the infrastructures and other underpinnings of our socio-economic systems. These P2P technologies are able to securely diffuse information within and across networks, without need for trustees or central authorities to enforce consensus. In this contribution, we propose a minimalistic stochastic model to understand the dynamics of blockchain-based consensus. By leveraging on random-walk theory, we model block propagation delay on different network topologies and provide a classification of blockchain systems in terms of two emergent properties. Firstly, we identify two performing regimes: a functional regime corresponding to an optimal system function; and a non-functional regime characterised by a congested or branched state of sub-optimal blockchains. Secondly, we discover a phase transition during the emergence of consensus and numerically investigate the corresponding critical point. Our results provide important insights into the consensus mechanism and sub-optimal states in decentralised systems.
In seeking to explain aspects of real-world economies that defy easy understanding when analysed via conventional means, Nobel Laureate Robert Shiller has since 2017 introduced and developed the idea of Narrative Economics, where observable economic factors such as the dynamics of prices in asset markets are explained largely as a consequence of the narratives (i.e., the stories) heard, told, and believed by participants in those markets. Shiller argues that otherwise irrational and difficult-to-explain behaviors, such as investors participating in highly volatile cryptocurrency markets, are best explained and understood in narrative terms: people invest because they believe, because they have a heartfelt opinions, about the future prospects of the asset, and they tell to themselves and others stories (narratives) about those beliefs and opinions. In this paper we describe what is, to the best of our knowledge, the first ever agent-based modelling platform that allows for the study of issues in narrative economics. We have created this by integrating and synthesizing research in two previously separate fields: opinion dynamics (OD), and agent-based computational economics (ACE) in the form of minimally-intelligent trader-agents operating in accurately modelled financial markets. We show here for the first time how long-established models in OD and in ACE can be brought together to enable the experimental study of issues in narrative economics, and we present initial results from our system. The program-code for our simulation platform has been released as freely-available open-source software on GitHub, to enable other researchers to replicate and extend our work
The statistical concept of Gambler's Ruin suggests that gambling has a large amount of risk. Nevertheless, gambling at casinos and gambling on the Internet are both hugely popular activities. In recent years, both prospect theory and lab-controlled experiments have been used to improve our understanding of risk attitudes associated with gambling. Despite theoretical progress, collecting real-life gambling data, which is essential to validate predictions and experimental findings, remains a challenge. To address this issue, we collect publicly available betting data from a \emph{DApp} (decentralized application) on the Ethereum Blockchain, which instantly publishes the outcome of every single bet (consisting of each bet's timestamp, wager, probability of winning, userID, and profit). This online casino is a simple dice game that allows gamblers to tune their own winning probabilities. Thus the dataset is well suited for studying gambling strategies and the complex dynamic of risk attitudes involved in betting decisions. We analyze the dataset through the lens of current probability-theoretic models and discover empirical examples of gambling systems. Our results shed light on understanding the role of risk preferences in human financial behavior and decision-makings beyond gambling.
We consider the privacy of interactions between individuals in a network. For many networks, while nodes are anonymous to outside observers, the existence of a link between individuals implies the possibility of one node revealing identifying information about its neighbor. Moreover, while the identities of the accounts are likely hidden to an observer, the network of interaction between two anonymous accounts is often available. For example, in blockchain cryptocurrencies, transactions between two anonymous accounts are published openly. Here we consider what happens if one (or more) parties in such a network are deanonymized by an outside identity. These compromised individuals could leak information about others with whom they interacted, which could then cascade to more and more nodes' information being revealed. We use a percolation framework to analyze the scenario outlined above and show for different likelihoods of individuals possessing information on their counter-parties, the fraction of accounts that can be identified and the idealized minimum number of steps from a deanonymized node to an anonymous node (a measure of the effort required to deanonymize that individual). We further develop a greedy algorithm to estimate the \emph{actual} number of steps that will be needed to identify a particular node based on the noisy information available to the attacker. We apply our framework to three real-world networks: (1) a blockchain transaction network, (2) a network of interactions on the dark web, and (3) a political conspiracy network. We find that in all three networks, beginning from one compromised individual, it is possible to deanonymize a significant fraction of the network ($>50$%) within less than 5 steps. Overall these results provide guidelines for investigators seeking to identify actors in anonymous networks, as well as for users seeking to maintain their privacy.
Samin Aref, Ly Dinh, Rezvaneh Rezapour, Jana Diesner
Balance theory explains the forces behind the structure of social systems, which are commonly modeled as static undirected signed networks. We expand this modeling approach to incorporate directionality of edges, and consider three levels of analysis: triads, subgroups, and the whole network. For triad-level balance, we operationalize a new measure by utilizing semicycles that satisfy the condition of transitivity. For subgroup-level balance, we propose measures of cohesiveness (intra-group solidarity) and divisiveness (inter-group antagonism) to capture balance within and among subgroups of the network using the most fitting partition of nodes into two groups. For network-level balance, we re-purpose the normalized line index to incorporate directionality, and provide the proportion of edges whose position suits balance. Through extensive computational analysis, we quantify and analyze patterns of social structure in triads, subgroups, and the whole network across a range of social settings from college students and Wikipedia editors to philosophers and Bitcoin traders. We then apply our multilevel framework of analysis to examine balance in temporal and multilayer networks, which demonstrates the generalizability of our approach to evaluating balance, and leads to new observations on balance with respect to time and layer dimensions. Our complementary findings on a variety of social networks highlight the need to evaluate balance at different levels. We propose a comprehensive yet parsimonious approach to address this need.
Nicolò Vallarano, Claudio J. Tessone, Tiziano Squartini
Cryptocurrencies are distributed systems that allow exchanges of native (and non-) tokens between participants. The availability of the complete historical bookkeeping opens up an unprecedented possibility: that of understanding the evolution of a cryptocurrency's network structure while gaining useful insights into the relationships between users' behavior and cryptocurrency pricing in exchange markets. In this article we review some recent results concerning the structural properties of the Bitcoin Transaction Networks , a generic name referring to a set of three different constructs: the Bitcoin Address Network , the Bitcoin User Network , and the Bitcoin Lightning Network . The picture that emerges is of a system growing over time, which becomes increasingly sparse and whose mesoscopic structural organization is characterized by the presence of an increasingly significant core-periphery structure. Such a peculiar topology is accompanied by a highly uneven distribution of bitcoins, a result suggesting that Bitcoin is becoming an increasingly centralized system at different levels.
Shahar Somin, Goren Gordon, Alex Pentland, Erez Shmueli · 5 authors
Following the birth of Bitcoin and the introduction of the Ethereum ERC20 protocol a decade ago, recent years have witnessed a growing number of cryptographic tokens that are being introduced by researchers, private sector companies and NGOs. The ubiquitous of such Blockchain based cryptocurrencies give birth to a new kind of rising economy, which presents great difficulties to modeling its dynamics using conventional semantic properties. Our work presents the analysis of the dynamical properties of the ERC20 protocol compliant crypto-coins' trading data using a network theory prism. We examine the dynamics of ERC20 based networks over time by analyzing a meta-parameter of the network, the power of its degree distribution. Our analysis demonstrates that this parameter can be modeled as an under-damped harmonic oscillator over time, enabling a year forward of network parameters predictions.
Lorenzo Lucchini, Laura Alessandretti, Bruno Lepri, Angela Gallo · 5 authors
"Code is law" is the funding principle of cryptocurrencies. The security, transferability, availability and other properties of a crypto-asset are determined by the code through which it is created. If code is open source, as it happens for most cryptocurrencies, this principle would prevent manipulations and grant transparency to users and traders. However, this approach considers cryptocurrencies as isolated entities thus neglecting possible connections between them. Here, we show that 4% of developers contribute to the code of more than one cryptocurrency and that the market reflects these cross-asset dependencies. In particular, we reveal that the first coding event linking two cryptocurrencies through a common developer leads to the synchronisation of their returns in the following months. Our results identify a clear link between the collaborative development of cryptocurrencies and their market behaviour. More broadly, our work reveals a so-far overlooked systemic dimension for the transparency of code-based ecosystems and we anticipate it will be of interest to researchers, investors and regulators.
Ivan Garibay, Toktam A. Oghaz, Niloofar Yousefi, Ece C. Mutlu · 26 authors
This paper explains the design of a social network analysis framework, developed under DARPA's SocialSim program, with novel architecture that models human emotional, cognitive and social factors. Our framework is both theory and data-driven, and utilizes domain expertise. Our simulation effort helps in understanding how information flows and evolves in social media platforms. We focused on modeling three information domains: cryptocurrencies, cyber threats, and software vulnerabilities for the three interrelated social environments: GitHub, Reddit, and Twitter. We participated in the SocialSim DARPA Challenge in December 2018, in which our models were subjected to extensive performance evaluation for accuracy, generalizability, explainability, and experimental power. This paper reports the main concepts and models, utilized in our social media modeling effort in developing a multi-resolution simulation at the user, community, population, and content levels.
This work focuses on the electric power market, comparing the status quo with the recent trend towards the increase in distributed self-generation capabilities by prosumers. Starting from the existing tension between the intrinsically hierarchical current structure of the electricity distribution network and the substantially distributed and self-organising nature of the self-generation, we explore the limitations imposed by the current conditions. Initially, we introduce a potential multi-layered architecture for a Peer-to-Peer (P2P) energy market, discussing the fundamental aspects of local production and local consumption as part of a microgrid. Secondly, we analyse the consequent changes for the different users' roles, also in connection with some incentive models connected with the decentralisation of the power production. To give a full picture to the reader, we also scrutinise relevant elements of energy trading, such as Smart Contract and grid stability. Thirdly, we present an example of a typical P2P settlement, showcasing the role of all the previously analysed aspects. To conclude, we performed a review of relevant activities in this domain, to showcase where existing projects are going and what are the most important themes covered. Being this a work in progress, many open questions are still on the table and will be addressed in the next stages of the research. Eventually, by providing a reference model as base for further discussions and improvements, we would like to engage ourselves in a dialog with the different users and the broad community, oriented towards a more fair and ecological-friendly solution for the electricity market of the future.
Jianhong Lin, Kevin Primicerio, Tiziano Squartini, Christian Decker · 5 authors
Abstract The Bitcoin lightning network (BLN), a so-called ‘second layer’ payment protocol, was launched in 2018 to scale up the number of transactions between Bitcoin owners. In this paper, we analyse the structure of the BLN over a period of 18 months, ranging from 12th January 2018 to 17th July 2019, at the end of which the network has reached 8.216 users, 122.517 active channels and 2.732,5 transacted Bitcoins. Here, we consider three representations of the BLN: the daily snapshot one, the weekly snapshot one and the daily-block snapshot one. By studying the topological properties of the binary and weighted versions of the three representations above, we find that the total volume of transacted Bitcoins approximately grows as the square of the network size; however, despite the huge activity characterising the BLN, the Bitcoins distribution is very unequal: the average Gini coefficient of the node strengths (computed across the entire history of the Bitcoin lightning network) is, in fact, ≃0.88 causing the 10% (50%) of the nodes to hold the 80% (99%) of the Bitcoins at stake in the BLN (on average, across the entire period). This concentration brings up the question of which minimalist network model allows us to explain the network topological structure. Like for other economic systems, we hypothesise that local properties of nodes, like the degree, ultimately determine part of its characteristics. Therefore, we have tested the goodness of the undirected binary configuration model (UBCM) in reproducing the structural features of the BLN: the UBCM recovers the disassortative and the hierarchical character of the BLN but underestimates the centrality of nodes; this suggests that the BLN is becoming an increasingly centralised network, more and more compatible with a core-periphery structure. Further inspection of the resilience of the BLN shows that removing hubs leads to the collapse of the network into many components, an evidence suggesting that this network may be a target for the so-called split attacks .
Diogo Pacheco, Pik-Mai Hui, Christopher Torres-Lugo, Bao Tran Truong · 6 authors
Coordinated campaigns are used to influence and manipulate social media platforms and their users, a critical challenge to the free exchange of information online. Here we introduce a general, unsupervised network-based methodology to uncover groups of accounts that are likely coordinated. The proposed method constructs coordination networks based on arbitrary behavioral traces shared among accounts. We present five case studies of influence campaigns, four of which in the diverse contexts of U.S. elections, Hong Kong protests, the Syrian civil war, and cryptocurrency manipulation. In each of these cases, we detect networks of coordinated Twitter accounts by examining their identities, images, hashtag sequences, retweets, or temporal patterns. The proposed approach proves to be broadly applicable to uncover different kinds of coordination across information warfare scenarios.
Abeer ElBahrawy, Laura Alessandretti, Leonid Rusnac, Daniel Goldsmith · 6 authors
Dark markets are commercial websites that use Bitcoin to sell or broker transactions involving\ndrugs, weapons, and other illicit goods. Being illegal, they do not offer any user protection, and\nseveral police raids and scams have caused large losses to both customers and vendors over the past\nyears. However, this uncertainty has not prevented a steady growth of the dark market phenomenon\nand a proliferation of new markets. The origin of this resilience have remained unclear so far, also due\nto the difficulty of identifying relevant Bitcoin transaction data. Here, we investigate how the dark\nmarket ecosystem re-organises following the disappearance of a market, due to factors including raids\nand scams. To do so, we analyse 24 episodes of unexpected market closure through a novel datasets\nof 133 million Bitcoin transactions involving 31 dark markets and their users, totalling 4 billion USD.\nWe show that coordinated user migration from the closed market to coexisting markets guarantees\noverall systemic resilience beyond the intrinsic fragility of individual markets. The migration is\nswift, efficient and common to all market closures. We find that migrants are on average more active\nusers in comparison to non-migrants and move preferentially towards the coexisting market with\nthe highest trading volume. Our findings shed light on the resilience of the dark market ecosystem\nand we anticipate that they may inform future research on the self-organisation of emerging online\nmarkets.