We explore the burgeoning field of GameFi through a detailed network analysis of The Sandbox, a prominent decentralized application (dApp) in this domain. Utilizing the bow-tie model, we map out transaction data within The Sandbox, providing a novel perspective on its operational dynamics. Our study investigates the varying impacts of external support, uncovering a surprising absence of enduring effects on network activity. We also investigate the network's response to several notable incidents, including the Ronin Hack and the United States Securities and Exchange Commission's hearing on cryptocurrencies, revealing a generally resilient structure with limited long-term disturbances. A critical aspect of our analysis focuses on the "whales," or major stakeholders in The Sandbox, where we uncover their pivotal role in influencing network trends, noting a significant shift in their engagement over time. This research sheds light on the intricate workings of GameFi ecosystems and contributes to the broader discourse on the intersection of the Web, AI, and society, particularly in understanding the resilience and dynamics of emerging digital economies. We particularly note the parallels of the long-tail behavior we see in web-based ecosystems appearing in this niche domain of GameFi. Our findings hold significant implications for the future development of equitable and sustainable GameFi dApps, offering insights into stakeholder behavior and network resilience in the face of external challenges and opportunities.
The increasing use of cryptoassets for international remittances has proven to be faster and more cost-effective, particularly for migrants without access to traditional banking. However, the inherent volatility of cryptoasset prices, independent of blockchain-based remittance mechanisms, introduces potential risks during periods of high volatility. This study investigates the intricate dynamics between XRP price fluctuations across diverse crypto exchanges and the correlation of the largest singular values of the correlation tensor of XRP transaction networks. Particularly, we show the impact of arbitrage opportunities across different crypto exchanges on the relationship between XRP price and correlation tensor spectra of transaction networks. Distinct periods, non-bubble and bubble, showcase different characteristics in XRP price fluctuations. Establishing a connection between XRP price and transaction networks, we compute correlation tensors and singular values, emphasizing the significance of the largest singular value. Comparisons with reshuffled and Gaussian random correlation tensors validate the uniqueness of the empirical tensor. A set of simulated weekly XRP prices, resembling arbitrage opportunities across various crypto exchanges, further confirms the robustness of our findings. It reveals a pronounced anti-correlation during bubble periods and a non-significant correlation during non-bubble periods with the largest singular value, irrespective of price fluctuations across different crypto exchanges.
There have been several studies into measuring the level of decentralization in Ethereum through applying various indices to indicate the relative dominance of entities in different domains in the ecosystem. However, these indices do not capture any correlation between those different entities, that could potentially make them the subject of external coercion, or covert collusion. We propose an index that measures the relative dominance of entities based on the application of correlation factors. We posit that this approach produces a more nuanced and accurate index of decentralization.
Non-fungible tokens (NFTs), which are immutable and transferable tokens on blockchain networks, have been used to certify the ownership of digital images often grouped in collections. Depending on individual interests, wallets explore and purchase NFTs in one or more image collections. Among many potential factors of shaping purchase trajectories, this paper specifically examines how visual similarities between collections affect wallets' explorations. Our model characterizes each wallet's explorations with a Lévy flight and shows that wallets tend to favor collections having similar visual features to their previous purchases while their behaviors vary widely. The model also predicts the extent to which the next collection is close to the most recent collection of purchases with respect to visual features. These results are expected to enhance and support recommendation systems for the NFT market.
On 25 January 2022, following a beginning to the year which had been affected by major political unrest resulting in the deaths of more than 230 people 1 , Kazakhstan was hit by a major power blackout. For around twelve hours, the entire southern regions of the country were left without power, as were Uzbekistan and Kyrgyzstan, two neighboring countries with which the southern country shares the same electricity network. This event is the culmination of several months of over-consumption, power surges and localized outages on the Central Asian networks. In Kazakhstan, electricity consumption rose by 8% in 2021, according to Ministry of Energy 2 , the national electricity operator, compared with the 1-2% annual increase previously recorded. This explosion in consumption is said to have been driven by the widespread development of cryptocurrency mining, a digital activity that can be extremely energy-intensive when operated on a large scale.
Methodologies to infer financial networks from the price series of speculative assets vary, however, they generally involve bivariate or multivariate predictive modelling to reveal causal and correlational structures within the time series data. The required model complexity intimately relates to the underlying market efficiency, where one expects a highly developed and efficient market to display very few simple relationships in price data. This has spurred research into the applications of complex nonlinear models for developed markets. However, it remains unclear if simple models can provide meaningful and insightful descriptions of the dependency and interconnectedness of the rapidly developed cryptocurrency market. Here we show that multivariate linear models can create informative cryptocurrency networks that reflect economic intuition, and demonstrate the importance of high-influence nodes. The resulting network confirms that node degree, a measure of influence, is significantly correlated to the market capitalisation of each coin ($ρ=0.193$). However, there remains a proportion of nodes whose influence extends beyond what their market capitalisation would imply. We demonstrate that simple linear model structure reveals an inherent complexity associated with the interconnected nature of the data, supporting the use of multivariate modelling to prevent surrogate effects and achieve accurate causal representation. In a reductive experiment we show that most of the network structure is contained within a small portion of the network, consistent with the Pareto principle, whereby a fraction of the inputs generates a large proportion of the effects. Our results demonstrate that simple multivariate models provide nontrivial information about cryptocurrency market dynamics, and that these dynamics largely depend upon a few key high-influence coins.
Nicolò Vallarano, Tiziano Squartini, Claudio J. Tessone
The open availability of the entire history of the Bitcoin transactions opens up the possibility to study this system at an unprecedented level of detail. This contribution is devoted to the analysis of the mesoscale structural properties of the Bitcoin User Network (BUN), across its entire history (i.e. from 2009 to 2017). What emerges from our analysis is that the BUN is characterized by a core-periphery structure a deeper analysis of which reveals a certain degree of bow-tieness (i.e. the presence of a Strongly-Connected Component, an IN- and an OUT-component together with some tendrils attached to the IN-component). Interestingly, the evolution of the BUN structural organization experiences fluctuations that seem to be correlated with the presence of bubbles, i.e. periods of price surge and decline observed throughout the entire Bitcoin history: our results, thus, further confirm the interplay between structural quantities and price movements observed in previous analyses.
Elohim Fonseca dos Reis, Alexander Teytelboym, Abeer ElBahraw, Ignacio De Loizaga · 5 authors
Dark web marketplaces have been a significant outlet for illicit trade, serving millions of users worldwide for over a decade. However, not all users are the same. This paper aims to identify the key players in Bitcoin transaction networks linked to dark markets and assess their role by analysing a dataset of 40 million Bitcoin transactions involving 31 markets in the period 2011-2021. First, we propose an algorithm that categorizes users either as buyers or sellers and shows that a large fraction of the traded volume is concentrated in a small group of elite market participants. Then, we investigate both market star-graphs and user-to-user networks and highlight the importance of a new class of users, namely `multihomers' who operate on multiple marketplaces concurrently. Specifically, we show how the networks of multihomers and seller-to-seller interactions can shed light on the resilience of the dark market ecosystem against external shocks. Our findings suggest that understanding the behavior of key players in dark web marketplaces is critical to effectively disrupting illegal activities.
Gabriele Di Antonio, Gianni Valerio Vinci, Luciano Pietronero, Marco Alberto Javarone
Taking informed decisions, namely acting rationally, is an individual attitude of paramount relevance in nature and human societies. In this work, we study how rationality spreads in a community. To this end, through an agent-based model, we analyse the dynamics of a population whose individuals, endowed with a rational attitude controlled by a numerical parameter, play a simple game. The latter consists of multiple strategies, each associated with a given reward. The proposed model is then used as a benchmark for studying the behaviour of Bitcoin users, inferred by analysing transactions recorded in the Blockchain. Remarkably, a population undergoing a sharp transition from irrational to rational attitudes shows a behavioural pattern similar to that of Bitcoin users, whose rationality showed up as soon as their cryptocurrency became worth just a few cents (USD). To conclude, a behavioural analysis that relies on an entropy measure combined with a simple agent-based model allows us to detect the rise of rationality across a community. Although further investigations are essential to corroborate our results, we deem the proposed approach could also get used for studying other social phenomena and behaviours.
Samuel W. Akingbade, Marian Gidea, Matteo Manzi, Vahid Nateghi
We present a heuristic argument for the propensity of Topological Data Analysis (TDA) to detect early warning signals of critical transitions in financial time series. Our argument is based on the Log-Periodic Power Law Singularity (LPPLS) model, which characterizes financial bubbles as super-exponential growth (or decay) of an asset price superimposed with oscillations increasing in frequency and decreasing in amplitude when approaching a critical transition (tipping point). We show that whenever the LPPLS model is fitting with the data, TDA generates early warning signals. As an application, we illustrate this approach on a sample of positive and negative bubbles in the Bitcoin historical price.
A cryptocurrency is a digital asset maintained by a decentralised system using cryptography. Investors in this emerging digital market are exploring the profitability potential of portfolios in place of single coins. Portfolios are particularly useful given that price forecasting in such a volatile market is challenging. The crypto market is a self-organised complex system where the complex inter-dependencies between the cryptocurrencies may be exploited to understand the market dynamics and build efficient portfolios. In this letter, we use network methods to identify highly decorrelated cryptocurrencies to create diversified portfolios using the Markowitz Portfolio Theory agnostic to future market behaviour. The performance of our network-based portfolios is optimal with 46 coins and superior to benchmarks up to an investment horizon of 14 days, reaching up to 1,066% average expected return within 1 day, with reasonable associated risks. We also show that popular cryptocurrencies are typically not included in the optimal portfolios. Past price correlations reduce risk and may improve the performance of crypto portfolios in comparison to methodologies based exclusively on price auto-correlations. Short-term crypto investments may be competitive to traditional high-risk investments such as the stock market or commodity market but call for caution given the high variability of prices.
The fervor for Non-Fungible Tokens (NFTs) attracted countless creators, leading to a Big Bang of digital assets driven by latent or explicit forms of inspiration, as in many creative processes. This work exploits Vision Transformers and graph-based modeling to delve into visual inspiration phenomena between NFTs over the years, i.e., the visual influence that can be detected whenever an NFT appears to be visually close to another that was published earlier in the market. Our goals include unveiling the main structural traits that shape visual inspiration networks, exploring the interrelation between visual inspiration and asset performances, investigating crypto influence on inspiration processes, and explaining the inspiration relationships among NFTs. Our findings unveil how the pervasiveness of inspiration led to a temporary saturation of the visual feature space, the impact of the dichotomy between inspiring and inspired NFTs on their financial performance, and an intrinsic self-regulatory mechanism between markets and inspiration waves. Our work can serve as a starting point for gaining a broader view of the evolution of Web3.
Arthur A. B. Pessa, Matjaž Perc, Haroldo V. Ribeiro
Cryptocurrencies are considered the latest innovation in finance with considerable impact across social, technological, and economic dimensions. This new class of financial assets has also motivated a myriad of scientific investigations focused on understanding their statistical properties, such as the distribution of price returns. However, research so far has only considered Bitcoin or at most a few cryptocurrencies, whilst ignoring that price returns might depend on cryptocurrency age or be influenced by market capitalization. Here, we therefore present a comprehensive investigation of large price variations for more than seven thousand digital currencies and explore whether price returns change with the coming-of-age and growth of the cryptocurrency market. We find that tail distributions of price returns follow power-law functions over the entire history of the considered cryptocurrency portfolio, with typical exponents implying the absence of characteristic scales for price variations in about half of them. Moreover, these tail distributions are asymmetric as positive returns more often display smaller exponents, indicating that large positive price variations are more likely than negative ones. Our results further reveal that changes in the tail exponents are very often simultaneously related to cryptocurrency age and market capitalization or only to age, with only a minority of cryptoassets being affected just by market capitalization or neither of the two quantities. Lastly, we find that the trends in power-law exponents usually point to mixed directions, and that large price variations are likely to become less frequent only in about 28\% of the cryptocurrencies as they age and grow in market capitalization.
Luca Mungo, Silvia Bartolucci, Laura Alessandretti
Abstract Since the introduction of Bitcoin in 2009, the dramatic and unsteady evolution of the cryptocurrency market has also been driven by large investments by traditional and cryptocurrency-focused hedge funds. Notwithstanding their critical role, our understanding of the relationship between institutional investments and the evolution of the cryptocurrency market has remained limited, also due to the lack of comprehensive data describing investments over time. In this study, we present a quantitative study of cryptocurrency institutional investments based on a dataset collected for 1324 currencies in the period between 2014 and 2022 from Crunchbase, one of the largest platforms gathering business information. We show that the evolution of the cryptocurrency market capitalization is highly correlated with the size of institutional investments, thus confirming their important role. Further, we find that the market is dominated by the presence of a group of prominent investors who tend to specialise by focusing on particular technologies. Finally, studying the co-investment network of currencies that share common investors, we show that assets with shared investors tend to be characterized by similar market behaviour. Our work sheds light on the role played by institutional investors and provides a basis for further research on their influence in the cryptocurrency ecosystem.
Pedro D. Manrique, Frank Huo, Sara El Oud, Minzhang Zheng · 6 authors
Online communities featuring 'anti-X' hate and extremism, somehow thrive online despite moderator pressure. We present a first-principles theory of their dynamics, which accounts for the fact that the online population comprises diverse individuals and evolves in time. The resulting equation represents a novel generalization of nonlinear fluid physics and explains the observed behavior across scales. Its shockwave-like solutions explain how, why and when such activity rises from 'out-of-nowhere', and show how it can be delayed, re-shaped and even prevented by adjusting the online collective chemistry. This theory and findings should also be applicable to anti-X activity in next-generation ecosystems featuring blockchain platforms and Metaverses.
Cryptocurrency markets have attracted many interest for global investors because of their novelty, wide on-line availability, increasing capitalization, and potential profits. In the econophysics tradition, we show that many of the most available cryptocurrencies have return statistics that do not follow Gaussian distributions, instead following heavy-tailed distributions. Entropy measures are applied, showing that portfolio diversification is a reasonable practice for decreasing return uncertainty.
Marco Alberto Javarone, Gabriele Di Antonio, Gianni Valerio Vinci, L. Pietronero · 5 authors
The energy sustainability of blockchains, whose consensus protocol rests on the Proof-of-Work, nourishes a heated debate. The underlying issue lies in a highly energy-consuming process, defined as mining, required to validate crypto-asset transactions. Mining is the process of solving a cryptographic puzzle, incentivised by the possibility of gaining a reward. The higher the number of users performing mining, i.e. miners, the higher the overall electricity consumption of a blockchain. For that reason, mining constitutes a negative environmental externality. Here, we study whether miners' interests can meet the collective need to curb energy consumption. To this end, we introduce the Crypto-Asset Game, namely a model based on the framework of Evolutionary Game Theory devised for studying the dynamics of a population whose agents can play as crypto-asset users or as miners. The energy consumption of mining impacts the payoff of both strategies, representing a direct cost for miners and an environmental factor for crypto-asset users. The proposed model, studied via numerical simulations, shows that, in some conditions, the agent population can reach a strategy profile that optimises global energy consumption, i.e. composed of a low density of miners. To conclude, can a Proof-of-Work-based blockchain become energetically sustainable? Our results suggest that blockchain protocol parameters could have a relevant role in the global energy consumption of this technology.
Marco Alberto Javarone, Gabriele Di Antonio, Gianni Valerio Vinci, Raffaele Cristodaro · 6 authors
Abstract The behaviour of Bitcoin owners is reflected in the structure and the number of bitcoin transactions encoded in the Blockchain. Likewise, the behaviour of Bitcoin traders is reflected in the formation of bullish and bearish trends in the crypto market. In light of these observations, we wonder if human behaviour underlies some relationship between the Blockchain and the crypto market. To address this question, we map the Blockchain to a spin-lattice problem, whose configurations form ordered and disordered patterns, representing the behaviour of Bitcoin owners. This novel approach allows us to obtain time series suitable to detect a causal relationship between the dynamics of the Blockchain and market trends of the Bitcoin and to find that disordered patterns in the Blockchain precede Bitcoin panic selling. Our results suggest that human behaviour underlying Blockchain evolution and the crypto market brings out a fascinating connection between disorder and panic in Bitcoin dynamics.
Gabriele Di Bona, Alberto Bracci, Nicola Perra, Vito Latora · 5 authors
Decentralization is a pervasive concept found across disciplines, including Economics, Political Science, and Computer Science, where it is used in distinct yet interrelated ways. Here, we develop and publicly release a general pipeline to investigate the scholarly history of the term, analysing 425,144 academic publications that refer to (de)centralization. We find that the fraction of papers on the topic has been exponentially increasing since the 1950s. In 2021, 1 author in 154 mentioned (de)centralization in the title or abstract of an article. Using both semantic information and citation patterns, we cluster papers in fields and characterize the knowledge flows between them. Our analysis reveals that the topic has independently emerged in the different fields, with small cross-disciplinary contamination. Moreover, we show how Blockchain has become the most influential field about 10 years ago, while Governance dominated before the 1990s. In summary, our findings provide a quantitative assessment of the evolution of a key yet elusive concept, which has undergone cycles of rise and fall within different fields. Our pipeline offers a powerful tool to analyze the evolution of any scholarly term in the academic literature, providing insights into the interplay between collective and independent discoveries in science.
Carolina E S Mattsson, Teodoro Criscione, Frank W Takes
Circulation is the characteristic feature of successful currency systems, from community currencies to cryptocurrencies to national currencies. In this paper, we propose a network analysis approach especially suited for studying circulation given a system's digital transaction records. Sarafu is a digital community currency that was active in Kenya over a period that saw considerable economic disruption due to the COVID-19 pandemic. We represent its circulation as a network of monetary flow among the 40,000 Sarafu users. Network flow analysis reveals that circulation was highly modular, geographically localized, and occurring among users with diverse livelihoods. Across localized sub-populations, network cycle analysis supports the intuitive notion that circulation requires cycles. Moreover, the sub-networks underlying circulation are consistently degree disassortative and we find evidence of preferential attachment. Community-based institutions often take on the role of local hubs, and network centrality measures confirm the importance of early adopters and of women's participation. This work demonstrates that networks of monetary flow enable the study of circulation within currency systems at a striking level of detail, and our findings can be used to inform the development of community currencies in marginalized areas.
Carlo Campajola, Raffaele Cristodaro, Francesco Maria De Collibus, Tao Yan · 6 authors
More than ten years ago the blockchain was acclaimed as the solution to overcome centralised trusted third parties for online payments. Through the years the crypto-movement changed and evolved, although decentralisation remained the core ideology and the necessary feature every new crypto-project should provide. In this paper we study the concept of centralisation in cryptocurrencies using a wide array of methodologies from the complex systems literature, on a comparative collection of blockchains, in order to define the many different levels a blockchain system may display (de-)centralisation and to question whether the present state of cryptocurrencies is, in a technological and economical sense, actually decentralised.
Alyssa Blackburn, Christoph Huber, Yossi Eliaz, Muhammad Shahzads Shamim · 9 authors
Bitcoin is a digital currency designed to rely on a decentralized, trustless network of anonymous agents. Using a pseudonymous-address-linking procedure that achieves >99% sensitivity and >99% specificity, we reveal that between launch (January 3rd, 2009), and when the price reached $1 (February 9th, 2011), most bitcoin was mined by only sixty-four agents. This was due to the rapid emergence of Pareto distributions in bitcoin income, producing such extensive resource centralization that almost all contemporary bitcoin addresses can be connected to these top agents by a chain of six transactions. Centralization created a social dilemma. Attackers could routinely exploit bitcoin via a "51% attack", making it possible for them to repeatedly spend the same bitcoins. Yet doing so would harm the community. Strikingly, we find that potential attackers always chose to cooperate instead. We model this dilemma using an N-player Centipede game in which anonymous players can choose to exploit, and thereby undermine, an appreciating good. Combining theory and economic experiments, we show that, even when individual payoffs are unchanged, cooperation is more frequent when the game is played by an anonymous group. Although bitcoin was designed to rely on a decentralized, trustless network of anonymous agents, its early success rested instead on cooperation among a small group of altruistic founders.
We quantify Non Fungible Token (NFT) rarity and investigate how it impacts market behaviour by analysing a dataset of 3.7M transactions collected between January 2018 and June 2022, involving 1.4M NFTs distributed across 410 collections. First, we consider the rarity of an NFT based on the set of human-readable attributes it possesses and show that most collections present heterogeneous rarity patterns, with few rare NFTs and a large number of more common ones. Then, we analyze market performance and show that, on average, rarer NFTs: (i) sell for higher prices, (ii) are traded less frequently, (iii) guarantee higher returns on investment (ROIs), and (iv) are less risky, i.e., less prone to yield negative returns. We anticipate that these findings will be of interest to researchers as well as NFT creators, collectors, and traders.
Carlo Campajola, Marco D'Errico, Claudio J. Tessone
We propose a novel framework to analyse the velocity of money in terms of the contribution (MicroVelocity) of each individual agent, and to uncover the distributional determinants of aggregate velocity. Leveraging on complete publicly available transactions data stored in blockchains from four cryptocurrencies, we empirically find that MicroVelocity i) is very heterogeneously distributed and ii) strongly correlates with agents' wealth. We further document the emergence of high-velocity intermediaries, thereby challenging the idea that these systems are fully decentralised. Further, our framework and results provide policy insights for the development and analysis of digital currencies.