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Measuring social dynamics in a massive multiplayer online game

Michael Szell, Stefan Thurner

arXiv:0911.1084v1physics.soc-ph

TL;DR

The paper addresses the lack of empirical, falsifiable approaches for quantifying collective human behavior, especially under difficult social-data conditions. It analyzes practically all recorded actions in the Pardus MMOG to test social-network and sociological hypotheses, finding distinct positive- and negative-tie structures, network densification, quantitative communication laws, and support for social balance theory. These findings position MMOG communities as potential models for studying real-world collective behavior, within acknowledged scope limitations.

  • Problem

    Quantifying collective human behavior empirically is difficult because social systems are complex and high-quality, large-scale data are scarce.

  • Method

    The study analyzes practically all player actions recorded over three years in Pardus, focusing on friend, enemy, and communication networks and testing social-dynamics hypotheses.

  • Results

    The study finds different topological structures for positive and negative ties, densification across networks, communication laws involving overlap, and triad patterns consistent with social balance theory.

  • Takeaways & Limitations

    MMOG communities may serve as models for real-world communities and enable quantitative study of collective social behavior at large scale.

  • Takeaways & Limitations

    Pardus universes are continually evolving and far from equilibrium, making transient and steady-state phases difficult to distinguish for some network properties.

Abstract

from arXiv · show

Quantification of human group-behavior has so far defied an empirical, falsifiable approach. This is due to tremendous difficulties in data acquisition of social systems. Massive multiplayer online games (MMOG) provide a fascinating new way of observing hundreds of thousands of simultaneously socially interacting individuals engaged in virtual economic activities. We have compiled a data set consisting of practically all actions of all players over a period of three years from a MMOG played by 300,000 people. This large-scale data set of a socio-economic unit contains all social and economic data from a single and coherent source. Players have to generate a virtual income through economic activities to `survive' and are typically engaged in a multitude of social activities offered within the game. Our analysis of high-frequency log files focuses on three types of social networks, and tests a series of social-dynamics hypotheses. In particular we study the structure and dynamics of friend-, enemy- and communication networks. We find striking differences in topological structure between positive (friend) and negative (enemy) tie networks. All networks confirm the recently observed phenomenon of network densification. We propose two approximate social laws in communication networks, the first expressing betweenness centrality as the inverse square of the overlap, the second relating communication strength to the cube of the overlap. These empirical laws provide strong quantitative evidence for the Weak ties hypothesis of Granovetter. Further, the analysis of triad significance profiles validates well-established assertions from social balance theory. We find overrepresentation (underrepresentation) of complete (incomplete) triads in networks of positive ties, and vice versa for networks of negative ties...

1. Introduction

The paper frames MMOGs as a way to address longstanding data and measurement problems in empirical research on collective human behavior. Using Pardus logs, it studies social-network structure and dynamics while testing sociological hypotheses.

  • Social group dynamics remain difficult to study experimentally because societies are complex and social data are often limited in availability and quality.
  • MMOGs enable large-scale, low-cost recording of player actions together with the surrounding circumstances, without substantially perturbing observed behavior.
  • Pardus provides a persistent virtual setting in which hundreds of thousands of players self-organize socially and economically over periods ranging from weeks to years.
  • Network analysis: The study analyzes friend, enemy, and communication networks using high-resolution data to examine network growth, relinking, and established social-dynamics hypotheses.
  • This first study focuses on complex-network structures and dynamics and sociological hypotheses, treating online game communities as possible models for real-world communities.

2. The game

Pardus is a persistent browser-based MMOG with multiple universes, player-driven social and economic activity, and longitudinal database records. The analyzed data primarily use Artemis, while character lifetimes reflect both voluntary deletion and automatic inactivity deletion.

  • The game: Pardus is a browser-based science-fiction MMOG centered on trading, socializing, role-playing, and player interaction, without an inherent winning condition.
  • Universe populations: The population increase in Orion between days ≈800 and 1,000 followed advertising campaigns, while opening Artemis and Pegasus at day 1,000 coincided with players leaving Orion characters.
  • The game: The three universes are Orion, Artemis, and Pegasus; approximately 14,000 players are active, while more than 300,000 have registered.
  • The data analyzed: The study uses daily database backups from 2005-09-09 to 2008-09-01 and focuses on Artemis because complete data were available there apart from three days.
  • Lifetimes of characters: Characters inactive for 120 days are automatically deleted, whereas shorter lifetimes can only reflect self-induced deletion; longer lifetimes combine both deletion mechanisms.
  • Lifetimes of characters: The self-induced-deletion regime follows a power law with exponent γ = −0.063, whereas the later regime is neither a power law nor an exponential.
  • Lifetimes of characters: 7.6% of characters had zero-day lifetimes, at least 31.4% of deletions were self-induced, and approximately 13% became inactive after their first day.

Gender of characters

Characters are chosen as male or female at signup, with the choice displayed through avatar imagery; the game combines spatial movement, economic activity, communication, and private social ties.

  • Gender of characters: Players irrevocably choose a male or female character at signup, and the corresponding avatar is displayed in certain game locations.In Artemis, approximately 90% of characters are male.
  • Spatial setting: Each universe contains 400 sectors of roughly 15×15 fields, while players view a 7×7-field navigation chart centered on their current position.Nearby-sector movement occurs through wormholes, and the typical activity range remains within one cluster for several weeks or longer.
  • Economic activity: Players spend Action Points on activities, with regeneration and a daily maximum shaping how often they typically play.Characters can hold at most 6,100 APs, and 24 APs regenerate every six minutes when below the maximum.
  • Economic activity: Players earn nonconvertible credits through economic participation, including resource extraction, processing, trade, and coordination across production chains.The game includes more than 30 commodity types, while prices at system-owned bases respond to local supply and demand.
  • Social activity: Communication channels support temporary chat, persistent forum discussions, and private messages, while players can privately mark others as friends or enemies.Friend and enemy lists are private, and a character cannot be marked as both simultaneously.
  • Social activity: Friend and enemy markings serve game-mechanic purposes and indicate cooperative or uncooperative stances, but need not exactly represent affective friendship or enmity.The analysis assumes rational and affective motives coincide to a great extent.

3. Networks

The paper represents social relations as graphs, distinguishing directed, weighted, and signed networks and classifying dyads by their link patterns.

  • 3. Networks: Networks are modeled as graphs whose nodes represent entities and whose links represent connections, with directed links encoding ordered source-to-target relations.Undirected links are unordered node pairs, whereas directed links are ordered pairs.
  • 3. Networks: Symmetrization converts a directed graph into an undirected graph by adding a link whenever either direction exists.The resulting graph preserves whether at least one directed connection joins each pair.
  • 3. Networks: Weighted graphs assign non-zero real-valued weights to links, unlike unweighted graphs in which all links are treated equally.Weights generalize binary link presence by encoding link magnitude.
  • 3. Networks: A directed dyad is null, asymmetric, or mutual depending on whether it has zero, one, or two oppositely directed links.These categories distinguish absent, one-sided, and reciprocated pairwise relations.
  • 3. Networks: Signed digraphs assign each directed link a positive or negative sign, with absent links represented by zero.In social networks, signs denote positive or negative relationships.
  • 3. Networks: Signed-network valency entries distinguish null, positive-only, negative-only, and ambivalent dyads.Ambivalent dyads contain one positive and one negative tie between the same pair.

Degree

The paper characterizes network connectivity through degree, shortest paths, clustering, and efficiency, linking these measures to neighborhood structure and information exchange.

  • Degree: A node’s degree counts its links, while directed networks separately measure incoming and outgoing degree; nearest neighbors are directly connected nodes.Average degree summarizes connectivity across the network, and neighbor-degree functions describe degree correlations by node degree.
  • Degree: The geodesic between two nodes is the smallest number of links connecting them, with disconnected pairs assigned infinite distance.For a random graph, the average geodesic is approximately ln N / ln k̄.
  • Degree: A node’s clustering coefficient is the fraction of possible links among its neighbors that actually exist.The network clustering coefficient averages node-level coefficients, while a random graph has C_r = k̄/N.
  • Degree: Global efficiency summarizes concurrent information exchange across all nodes, whereas local efficiency measures system fault tolerance through neighbors’ connectivity.Both measures lie between 0 and 1.

Reciprocity

Reciprocity measures mutuality in directed networks, and the paper uses a density-independent index to distinguish reciprocal, areciprocal, and antireciprocal structures.

  • Reciprocity: Reciprocity measures whether individuals create mutual rather than asymmetric dyads.The naive index assigns 0 to networks without mutual dyads and 1 to networks containing only mutual dyads.
  • Reciprocity: The paper replaces the naive reciprocity measure with an index that accounts for link density and the minimum possible reciprocity.The density term ā is the ratio of observed to possible directed links.
  • Reciprocity: The adjusted index classifies networks as reciprocal when ρ > 0, areciprocal when ρ = 0, and antireciprocal when ρ < 0.It permits clear ordering independent of link density, unlike the alternative naive index.
  • Reciprocity: Assortative mixing coefficients are Pearson correlations between degrees at the two ends of links, with positive values indicating assortativity and negative values disassortativity.The paper measures coefficients for undirected closures and four directed in/out-degree combinations.
  • Reciprocity: A bridge is a link whose removal increases the number of disconnected components, while a local bridge of degree i gives its endpoints geodesic i after removal.These definitions identify links that connect otherwise more separated parts of a network.

A bridge

The paper defines graph-based measures for shared neighborhoods, link traffic, and connectivity. These measures support analysis of overlap, betweenness, and the largest connected component.

  • Overlap measures how many neighbors two linked nodes share, ranging from an empty to an identical common neighborhood.
  • Link betweenness counts the fraction of geodesics between node pairs that contain a given undirected link.
  • Betweenness can represent traffic when every node pair exchanges information at the same rate.
  • The largest connected component is the finite graph component containing the most nodes, measured by its node fraction Γ.
  • Directed triads have 16 isomorphism classes, including 13 connected classes and three unconnected classes labeled a, b, and c.

Triad significance profile

The study applies triad significance profiles and network-growth analyses to characterize social structure in communication, friend, and enemy networks. It combines randomized triad comparisons with preferential-attachment tests and relation-based PM-partner partitions.

  • Triad significance profile: The triad significance profile is a vector comparing each connected triad class with degree- and mutual-dyad-preserving random networks.
  • Triad significance profile: TSP normalizes 13 triad-class Z scores, enabling comparisons across networks of arbitrary sizes.
  • The networks are directed graphs whose nodes are characters, excluding isolated players; “link” denotes a directed link.
  • PM networks use weekly weighted communication links, whereas friend and enemy networks use persistent unweighted markings.
  • Preferential attachment: Preferential-attachment tests examine whether newcomers connect to existing characters according to in-degree, interpreted as popularity or disdain.
  • Preferential attachment: Friend networks show α = 0.62 for kin < 30, while enemy markings show α = 0.90 across all markings.
  • Friend and enemy relations partition character pairs into four signed-dyad classes, linking PM-partner composition to social ties.

Growing average degrees, shrinking geodesics

Across the observed networks, average degree generally increases while geodesic distances decrease. Link growth is broadly superlinear or linear, and clustering evolves differently for positive and negative ties.

  • Average degrees grow, while geodesics decrease; only the enemy network reaches a steady state shortly before day 400.
  • The L-versus-N curves mostly have slopes between 1 and 2, but fluctuations and limited N ranges make power-law fits unreliable.
  • All networks have ḡ/ḡ_r within [0.5, 2]; enemy and friend values lie slightly above 1, while PM values are usually slightly below 1.
  • Friend clustering decreases while enemy clustering increases; C/C_r falls for friend and PM networks but grows for enemy networks.
  • Friend networks maintain C/C_r > 100, consistent with high relative clustering in positive-tie social networks.

Positive reciprocity

Positive ties are more reciprocal and strongly clustered than negative ties, while communication networks show structural changes over time. Triad-significance profiles reveal distinct temporal patterns across PM, friend, and enemy networks.

  • Positive reciprocity: At day 445, reciprocity is ρ ≈0.80 for PM networks, ρ ≈0.68 for friend networks, and around ρ ≈0.1 for enemy networks.
  • Positive reciprocity: Pardus PM reciprocity around ρ ≈0.8 exceeds reported values of R = 0.4 for a message network and ρ = 0.194 for email networks.
  • On day 422, a player war coincided with structural changes in PM links, degree, geodesics, and local and global efficiency.
  • The largest-component fraction reaches Γ ≈0.973 for friends, Γ ≈0.992 for enemies, and fluctuates around Γ ≈0.985 for PMs on day 445.
  • Triad significance profiles: Enemy TSPs eventually separate into overrepresented classes {1, 2, 3, 5, 6}, neutral classes {4, 8, 9, 11}, and underrepresented classes {7, 10, 12, 13}.
  • Triad significance profiles: Friend-network triad rankings remain relatively stable except around day 290, when syndicates caused abrupt relation changes.
  • Triad dynamics: Triad transitions are estimated with 13 × 16 day-to-day-50 transition matrices, while PM transition matrices were not calculated.

5. Discussion

The discussion finds that preferential attachment does not describe friend networks, while enemy networks may be closer to that mechanism. Communication-network relationships between overlap, betweenness, and weight support Granovetter’s Weak ties hypothesis.

  • Preferential attachment: Friend networks violate all three classical preferential-attachment expectations, including linear linking probability and power-law degree distribution.The measured linking exponent is α ≈0.62 rather than α = 1, and degree distributions do not follow a power-law.
  • Preferential attachment: Enemy networks are closer to preferential attachment, with linking exponent α ≈0.90 and cumulative in-degree exponent γ ≈1.The authors nevertheless describe the enemy-network dynamics as more intricate than the classical mechanism.
  • Weak ties hypothesis: O(w) = w^0.30 relates communication weight positively to overlap, with an approximate cube-root law in PM networks.This increasing relationship matches the expected connection between tie strength and overlap.
  • Weak ties hypothesis: The method avoids sampling issues encountered in earlier mobile-phone network analysis.The authors state that their results are free of sampling bias in this respect.
  • Weak ties hypothesis: O(b) = b^-0.54 links overlap inversely to betweenness, confirming the Weak ties prediction that weaker ties can bridge communities.Logarithmically binned averages have slope γ ≈−0.54, and the result is robust across game universes and accumulation times.

Triad significance profiles (implicit evidence)

Triad significance profiles provide implicit evidence for social-balance and triadic-closure predictions. Friend and PM networks favor the predicted complete-triad motif, while enemy networks largely reverse the pattern; profiles can take hundreds of days to stabilize.

  • Triad significance profiles: Triad significance profiles summarize the relative overrepresentation or underrepresentation of network triad classes.The study uses these profiles to compare local structures across friend, enemy, and PM networks.
  • Triad significance profiles: Complete triads are expected to be overrepresented and incomplete triads underrepresented in positive-tie networks.This profile-based evidence is implicit because it does not directly establish the evolutionary transitions between triad classes.
  • Triad significance profiles: Friend and PM networks assign the minimum Z score to triad class 6 and the maximum to class 13, matching Granovetter’s prediction.Class 13 is interpreted as the strongest three-node motif and class 6 as the strongest antimotif.
  • Triad significance profiles: Enemy-network Z scores largely have signs opposite to those in friend networks, supporting the predicted reversal for negative ties.The paper notes that complete negative triads can remain ambiguous under social balance theory.
  • Triad significance profiles: Enemy-network triad significance profiles may require several hundred days to approach a steady state.Friend-network profiles also show abrupt jumps, indicating global systemic changes during network evolution.

Triad transition rates (explicit evidence)

Direct transition counts provide explicit evidence for triadic closure in friend networks: incomplete triads transition to complete ones more often than the reverse. The broader network analysis also reveals contrasting structural and temporal properties across network types.

  • Triad transition rates: 305.5 > 22.6: friend-network transitions from triad class 6 to 13 greatly exceed transitions from 13 to 6.The asymmetry matrix K−K^T visualizes the stronger outflow from incomplete to complete triads.
  • Triad transition rates: Incomplete-to-complete transitions generally outnumber reverse transitions among connected triad classes.Exceptions occur but are comparatively mild, and the observation is robust across game universes and time spans.
  • Network evolution: Growing networks show increasing average degree and shrinking geodesics, consistent with network densification and shrinking diameters.The paper reports these trends across all network types studied.
  • Social balance: The study finds no conclusive increase or decrease in social balance over time.The authors attribute this inconclusiveness to slow information propagation, system complexity, and separated time scales.
  • Enemy networks: Enemy networks have much larger in-degrees, approximately 500 versus approximately 150 in friend and PM networks.Enemy networks also show negative assortativity and two classes in average neighbor degree.
  • Enemy networks: Enemy networks show low reciprocity, unlike the high reciprocity of friend and PM networks, and their in- and out-degree distributions differ qualitatively.The authors associate these measurements with two distinct enemy-marking mechanisms.

6. Conclusion

Using three years of actions from 300,000 players, the study empirically tests social-dynamics hypotheses across several game-derived networks. It identifies quantitative communication laws, confirms social-balance patterns and triadic closure, and argues that online game communities can model wider human societies.

  • Conclusion: Three years of actions by 300,000 players support empirical tests of long-standing social-dynamics hypotheses across three social-network types.The dataset combines practically all player actions within one coherent socio-economic source.
  • Conclusion: Communication networks exhibit betweenness centrality proportional to overlap^-2 and communication strength proportional to overlap^3.The authors describe both relations as approximate, fully falsifiable social laws supporting Granovetter’s Weak ties hypothesis.
  • Conclusion: Positive-tie networks overrepresent complete triads and underrepresent incomplete triads, whereas negative-tie networks show the reverse pattern.These findings confirm established assertions from social balance theory.
  • Conclusion: Empirical transition probabilities between triad classes provide evidence for triadic closure with unprecedented precision.The analysis uses triad significance profiles to examine how network structures evolve.
  • Conclusion: Online game communities may serve as models for a wide class of human societies and enable socio-economic laboratories with natural-science-like measurement precision.This conclusion follows comparisons with data from non-virtual human groups and the study’s high-frequency measurements.
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