Human Mobility in the Metaverse

TL;DR

This paper investigates how human mobility patterns manifest in the metaverse, where traditional geographic costs do not constrain movement. By analyzing two data streams—a 2D virtual land mobility network in Decentraland and a contract mobility network inferred from NFT purchases across Ethereum and Polygon—the authors uncover persistent, nonuniform mobility: exploration is sublinear, a small set of locations garner most visits, and the mobility network is highly centralized with heavy-tailed degree and flow distributions. To explain these features, they extend the Exploration and Preferential Return (EPR) framework to a meta-mobility model (m-EPR) that introduces a popularity-driven bias, leading to accurate reproduction of both individual-level visitation statistics and aggregate network structure. The results imply that popularity-based dynamics, rather than spatial distance or conventional commuting costs, drive metaverse mobility, offering a principled basis for predicting the structure of emergent digital mobility networks and their economic implications. The work thus links fundamental human mobility patterns to meta-space economics, with potential implications for virtual urban planning and digital asset markets.

Abstract

The metaverse promises a shift in the way humans interact with each other, and with their digital and physical environments. The lack of geographical boundaries and travel costs in the metaverse prompts us to ask if the fundamental laws that govern human mobility in the physical world apply. We collected data on avatar movements, along with their network mobility extracted from NFT purchases. We find that despite the absence of commuting costs, an individuals inclination to explore new locations diminishes over time, limiting movement to a small fraction of the metaverse. We also find a lack of correlation between land prices and visitation, a deviation from the patterns characterizing the physical world. Finally, we identify the scaling laws that characterize meta mobility and show that we need to add preferential selection to the existing models to explain quantitative patterns of metaverse mobility. Our ability to predict the characteristics of the emerging meta mobility network implies that the laws governing human mobility are rooted in fundamental patterns of human dynamics, rather than the nature of space and cost of movement.

Figures (26)

• Figure 1: Measuring meta-mobility.(A) To quantify mobility in the metaverse, we explore two separate datasets: Mobility in a 2-dimensional virtual world (left) and in the network space (right). In the virtual world, an individual, posing as an avatar, can move through a 2D virtual environment via local movements or teleportation. Using the trajectories of all individuals in the virtual world, we created a mobility network, whose nodes are lands and a link captures the movement between two locations. We track the mobility of the same individuals in the network space, capturing virtual marketplaces through their NFT purchases, allowing us to build a time-resolved contract network. For example, a user with screen name pikelpyramid, purchased an NFT from the Decentraland contract and the subsequently purchased a new NFT from Sandbox, creating a link between Decentraland and Sandbox. (B) Visualization of the Decentraland virtual world. Each land in the virtual world is identified by its (x, y) coordinates, organized in a 2D symmetrical layout. The lands are colored based on the number of visitors. We mark the parcels that were sold during our observation period, with points sized based on the selling price of land. (C) The Ethereum contract network traveled by our users. The nodes (contracts) are sized based on the number of users that visit the contract, and the top 10 network communities are colored for clarity.
• Figure 2: Individual mobility patterns.(A) Distribution of number of visitors in the virtual world. We find that the proportion of visitors to different locations (lands) can be well-approximated by $P(S) \propto S^{-\alpha}$, where $\alpha_{D1} = 1.98$ and $\alpha_{D2} = 1.92$. (B) Distribution of number of users per node of the network. We find a fat-tailed distribution in number of visitors by contract, well-approximated by the power law exponent $\alpha_{Ethereum} = 2.02$ and $\alpha_{Polygon} = 2.07$. (C) Distance travelled in each displacement. We measure the jump distance, $\delta_r$, as the Manhattan distance between two parcels. We find that individuals rarely move past a distance of 10. (D) Contract jump distance. We calculate jump distance, $\delta_r$, as the shortest path length between two contracts in the network. A distance of $\delta_r = 0$ indicates purchase of a new NFT from the same contract. We find that the majority of the jumps occur in short distances, irrespective of the blockchain. Time allocation at different (E) lands and (F) contracts. We compare the mean visitation frequency $f_{i} = n/S$, where $n$ is the total time spent and $S$ is the number of locations, to the dispersion in visitation counts across all locations, $\sigma_f$. We find that $\sigma_f \propto f^{\beta}$, following $\beta_{vw}= 1.01$ in the virtual world, and $\beta_{ethereum} = 1.01$; $\beta_{polygon} = 0.98$ in the network space. As $\beta \sim 1$ it suggests that as individuals explore more, they tend to unevenly distribute their time across all locations. Number of unique locations visited over time. We measure the number of unique locations visited ($S(n)$) as a function of number of steps taken ($n$). We find that $S(n)\propto n^{\mu}$ scales as (G)$\mu_{vw} = 0.52$ in the virtual world and (H)$\mu_{ethereum} = 0.61$, $\mu_{polygon} = 0.52$ in the network space. These insights reveal a sub-linear scaling in the exploration new locations, suggesting that an individuals' inclination to visit more land decreases over time. (I) Location preference and time spent. We rank the locations visited based on the total number of visits to those locations, and display the proportion of time spent at each ranked location in the virtual world. This relationship is well-approximated using a power law with exponent $\alpha_{vw} = 1.35$. Inset shows the same plot in the linear scale. (J) Proportion of NFTs purchased from different contracts. Main panel shows the ranked frequency of locations based on the Ethereum blockchain, and the inset shows the results based on the Polygon blockchain. In both systems, the distribution of preference is well-approximated using a power law ($\alpha_{ethereum} = 1.05$, $\alpha_{polygon} = 1.39$).
• Figure 3: Foundation of the mobility model. We first organize the possible visiting locations $a$ to $g$, into whether the location has been previously visited (green) or unvisited (gray). At each movement, an individual decides to explore a new location (gray) with probability $p_{new} \propto S^{-\gamma}$, where $S$ represents the number of previously visited locations. With its complementary probability, $1-p_{new}$, an individual decides to revisit a previously visited location (green). In the EPR formulation, when visiting a new location, the individual randomly selects a new location drawn at some distance $\delta_r$. In the proposed m-EPR model, the individual is biased towards the more popular locations, sampled according to the probability $\pi = m_a/\sum_{j} m_j$, where $m_a$ is the popularity of the location $a$. When deciding to revisit a previously visited location, in the EPR model the individual selects based on their individual past visitation history, $\pi_i = m^{i}_g/\sum_{j} m^{i}_j$, where $m^{i}_g$ represents the number of visits to the location $g$ by individual $i$. In contrast, in the m-EPR model, an individual revisits a location according to the probability $\pi = m_g/\sum_{j} m_j$, where $m_g$ represents the total number of visits to the location $i$ by all individuals. In contrast to the EPR model, where an individual randomly selects a new location and preferentially re-visits location based on only their individual visitation history ($\pi_i$), the m-EPR model allows individuals to select new locations and revisit old locations based on their global popularity ($\pi$).
• Figure 4: Capturing models of meta-mobility.(A) Degree distribution of lands in the mobility network. We observe a fat tailed distribution in degrees, well-approximated by a power law, $P(k) \propto k^{-\alpha}$ as $\alpha_{vw} = 1.98$. (B) Degree distribution of contracts in the contract network. We observe a heavy tailed distribution where few contracts receive most of the connections, well-approximated by a power law, $P(k) \propto k^{-\alpha}$, where $\alpha_{ethereum} = 2.9$ and $\alpha_{polygon} = 2.4$. (C) Degree distribution from the model simulations. We show the results from the EPR model and the m-EPR model, finding that the m-EPR model recreates the heterogeneous degree distribution as $\alpha^{M} = 2.1 \pm 0.06$. We show the link weight, $w_{ij}$, distribution of the network for (D) virtual world mobility and (E) contract mobility. The link weight distribution follows a power law decay as $P(w_{j}) \propto w_{ij}^{-\alpha}$, where $\alpha_{vw}= 2.18$ in the virtual world and $\alpha_{ethereum} = 2.85$; $\alpha_{polygon} = 2.5$ in the contract network. We display link weight distributions between nodes at different physical distances ($\delta_r$). (F) Link weight distribution from model simulations. We find that the m-EPR model is able to uncover the concentrated flows between locations with $\alpha^{M} =2.19 \pm 0.03$ in the network. (G) Relationship between degree of land in the virtual world mobility network and its number of visitors. We find that the two variables scales as $N_{S} \propto k^{\beta}$, where $\beta_{vw} = 1.05$. (H) Relationship between degree of contract in the contract mobility network and its number of visitors. We find that $N \propto k^{\beta}$, where $\beta_{ethereum} = 1.05$ and $\beta_{polygon} = 1.13$. (I) Relationship between degree and visitors from model simulations. We find that them-EPR model obtains a positive scaling between the two variables ($\beta^{M} = 0.96 \pm 0.03$).
• Figure S1: Individual mobility in the virtual space. We show examples of mobility in the virtual space by 20 random individuals in the metaverse. These trajectories highlight the use of large jump distances followed by small movements in nearby locations.