Emergence and structuring of decentralized commercial networks around dark web marketplaces

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Large number of U2U transactions

ego networks

We start our analysis by measuring the extent of the U2U network around each DWM. The percentages of users forming U2U pairs vary across DWMs, with a median value of 38% (min 23%, max 68%). The variance of the percentage of users with U2U pairs is shown in Fig. 2a. The figure shows that the number of users with U2U pairs is nearly monomial in the number of users interacting with a DWM, with an estimated exponent equal to 1.06 and (R^2 = 0.969) , see Section S1 for details on the mounting procedure. The total volume of transactions that users send to the marketplace is essentially equivalent to the volume that they receive from it (two-sided Wilcoxon test33: (L=330), (p=0.282)). It is important to note that the total volume of transactions that users send to a DWM (and therefore that they receive from it) is always less than the volume exchanged via U2U transactions, as shown in Figure 2b.

Figure 2

User-DWM and U2U transactions. (a) Total number of users interacting with a DWM versus total number of users forming U2U transactions. The dotted line is the result of a fitted power law function. (b) Dollar transaction volume sent to a DWM relative to the total transaction volume in its surrounding U2U transactions. The dotted line is the bisector and makes it easy to compare the two trading volumes. (vs) Total monthly trading volume sent to all DWMs and traded across all unique U2U pairs. We do not include trade volume received from DWMs as it is essentially equivalent to volume sent to DWMs.

Full network

Similar results hold for the full network, confirming that U2U pair formation is a ubiquitous phenomenon around DWMs. The total volume of transactions that users sent to DWMs was $3.8 billion, the volume received from DWMs was $3.7 billion, while the volume traded via U2U pairs reached $30 billion. In Figure S3, we illustrate the number of transactions, the volume of transactions and the lifetime of U2U pairs. In all cases, we observe familiar fat-tailed distributions.

We then consider the temporal evolution of transactions. We look at trade volume over time in Figure 2c, which shows that since 2011, U2U trades have always involved monthly volume greater than the volume sent to all DWMs. This highlights the economic importance of U2U transactions in the Bitcoin ecosystem compared to DWMs.

U2U network behavior

Now we will analyze users focusing on the following groups: users who do not form stable U2U pairs; users who form stable U2U pairs, of which there are users who met outside DWM and users who met inside DWM (see nomenclature in Table 2). We start by focusing our attention on identifying stable U2U pairs, that is, persistent pairs in the U2U network. For this purpose, we use the scalable activity-driven model31 to identify stable pairs in a statistically sound way (see Methods). We see that 137,667 stable U2U pairs were formed by 106,648 users and generated a trading volume of $1.5 billion. Stable pairs produce five times more trades per pair than non-stable pairs (Mann-Whitney-U two-tailed test34: MNU (=45.8 cdot 10^9), (p) corresponding to a volume of transactions 5.34 times higher (MNU (= 317 cdot 10^9), (p), see Figure S4. Stable pairs, although they represent less than 2% of the total number of U2U pairs, generate a disproportionate volume of transactions.

picture 3
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Role of users forming stable U2U pairs. (Major) PDF of the volume of transactions that users trade with any DWM. (Inset) PDF of time spent by users on any DWM. These distributions are explored for each of the 40 DWMs considered in Figures S5 and S6, respectively. The vertical lines represent the median values ​​of the respective distributions.

The high activity of users forming stable U2U pairs is not limited to the U2U network – these users are also the most active in trading with DWMs. Users of U2U stable pairs spend a median of 41 days on DWMs compared to a median of only one day for users without stable pairs. The two resulting distributions are significantly different (two-tailed Kolmogorov-Smirnov test35:KS (= 0.673), (p), see the box in Fig. 3. When we look at trading volume with DWMs, we find qualitatively similar results. Users of U2U stablecoins transact median $400 with DWMs, while other users only transact for $56. The two resulting distributions are significantly different (KS (= 0.438), (p), see Fig. 3. These results are valid not only for the complete network, but for each DWM in our data, see Figures S5 and S6.

Evolution of the U2U network

Formation of U2U stable pairs

After mapping the behavior of stable pairs, we now consider their time evolution. Specifically, we ask: how are stable pairs formed? Do DWMs stimulate their creation? A possible hypothesis is that the users meet for the first time while they are active on a DWM, i.e. after they have both traded with this DWM, see table 1 and the nomenclature of the table 2. This can be considered a plausible and conservative proxy. for users who met inside a DWM (see Methods). A total of 37,129 users encountered at least one other user in a DWM. Their transaction volume is approximately $417 million, and the percentage of users who met inside a DWM is proportional to the transaction volume sent to DWMs (Spearman36: (C=0.805), (p), see Fig. S7, which means that larger DWMs are more likely to favor user encounters than smaller DWMs. It is important to note that users who met inside a DWM make more transactions than those who met outside a DWM. In particular, users who met inside a DWM trade a median of $2212 between them, nearly double the $1379 for users who meet outside the DWM (MNU (= 1.863 cdot 10^9), (p). Additionally, users who met inside a DWM tend to transact for significantly longer (median 61 days) than users who meet outside (median 50 days) (MNU (= 2.099 cdot 10^9), (p).

Table 1 Mechanism of formation of stable U2U pairs.

Resilience of U2U Stable Pairs

So far, we have shown that users involved in stable business relationships are also very active on DWMs, where they can meet new business partners. But are DWMs and the U2U network really interdependent? In particular, do stable pairs need DWMs to survive? To answer these questions, we examine market closures, previously studied to show how active users migrate to other existing DWMs.12. Our dataset includes 33 closing events, which we study independently of each other by considering the evolution of the respective 33 market ego networks. We find that unstable U2U pairs abruptly stop interacting immediately after the DWM is closed, and thus their existence is very sensitive to the presence of the DWM. In contrast, the trading volume of stable U2U pairs is only marginally affected by the disappearance of the DWM. As a result, whereas before the DWM shutdowns, non-stable U2U pairs generate 10 times more overall trading volume than stable U2U pairs (since non-stable pairs are much more prevalent), a few weeks after the DWM, the trend is reversed: stable U2U pairs generate more trading volume than non-stable U2U pairs. Indeed, trading patterns of stable pairs are not significantly influenced by the sudden closing of DWMs, and they degrade very slowly over time, see Fig. 4.

Figure 4
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Resilience of stable U2U pairs after closing DWMs. Trading volume of U2U pairs surrounding active DWMs. (Main) U2U pairs meet that met inside a DWM. (Inset) U2U pairs meet outside of them. The plotted lines indicate the median value while the bands represent the 95% confidence interval. Day zero corresponds to the closing day of the DWM. Negative and positive numbers indicate days before and after closing, respectively. Only the 33 DWMs that closed during our period are taken into account in the analysis.

Figure 5
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Time evolution of stable pairs. (a) Monthly number of new stable U2U pairs created. (b) Monthly trading volume of stable U2U pairs.

We have shown that the U2U network is resistant to sudden external shocks, such as market closures, and does not need the centralized structure of DWMs to survive. What about long-lasting systemic stress? To answer this question, we consider the impact that the COVID-19 pandemic has had on the evolution of U2U stablecoins. Previous studies have reported that COVID-19 has a strong impact on DWMs due to delays and damage to maritime infrastructure caused by border closures.37.38. We start by studying the number of new stable U2U pairs and their trading volume during the COVID-19 period. Stablepair users encountering both inside and outside of DWMs have increased over the past two years since AlphaBay was shut down9, the largest DWM at the time. In 2020, a total of 6778 stablepair user pairs met inside a DWM, corresponding to 192% of the 2019 level and 255% of the 2018 level, see Fig. 5a. User pairs in stablecoins meeting inside a DWM traded for a total of $145 million in 2020, which is 252% of the 2019 level and 593% of the 2018 level , see Fig. 5b. We see similar trends for stable U2U pairs meeting outside of DWMs. The impact of the COVID-19 pandemic has, however, gone through different phases, punctuated by the number and level of measures put in place around the world. For users of stable pairs who have met both inside and outside of DWMs, we see that during the first lockdowns in 2020, trading volume fell compared to January of the same year, suggesting they have been negatively affected by COVID-19 restrictions. After that, the trading volume increased sharply over the whole of 2020, see Figure S8. The number of stable U2U pairs created each day, however, remained stable over time in 2020, although more U2U pairs were created compared to the same period in 2019, see Figure S9. Overall, stable U2U pairs have shown resilience in the face of systemic stress caused by COVID-19, suggesting, once again, that these trading relationships are fundamentally independent of underlying DWMs.

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