Human group formation in online guilds and offline gangs driven by a common team dynamic

Quantifying human group dynamics represents a unique challenge. Unlike animals and other biological systems, humans form groups in both real (offline) and virtual (online) spaces—from potentially dangerous street gangs populated mostly by disaffected male youths to the massive global guilds in online role-playing games for which membership currently exceeds tens of millions of people from all possible backgrounds, age groups, and genders. We have compiled and analyzed data for these two seemingly unrelated offline and online human activities and have uncovered an unexpected quantitative link between them. Although their overall dynamics differ visibly, we find that a common team-based model can accurately reproduce the quantitative features of each simply by adjusting the average tolerance level and attribute range for each population. By contrast, we find no evidence to support a version of the model based on like-seeking-like (i.e., kinship or “homophily”).

Figure 1

(Color online) Internet guilds and street gangs. (a) Empirical data from World of Warcraft on all servers. (b) Cumulative distribution differs significantly from a power law. The inset shows the averaged churn $C$ of the guilds. (c) Cumulative distribution for Long Beach (i.e., “LA”) gangs. The inset shows the underlying discrete distribution.

Figure 2

(Color online) (a) WoW guild-size distributions $N\left(s\right)$ for the months June, August, October, and December 2005. The total numbers of players in these months are 80 183, 93 127, 76 686, and 93 322, respectively. (b) The cumulative guild-size distributions $N\left(s^{\prime }>s\right)$ for each of the four months.

Figure 3

(Color online) The average churn $C$ (as defined in text) as a function of guild size in the WoW data set on a log-log plot treating the data in all three servers collectively. Data are shown for the months June, August, October, and December 2005. Note that the inset of Fig. 1b shows the same data but on a linear scale and for October only.

Figure 4

(Color online) The cumulative gang-size distribution $N\left(s^{\prime }>s\right)$ for LA gangs of three main ethnic groups. (a) Cumulative gang-size distribution for gangs with ethnicity E1. The total membership is $N=608$. (b) Ethnicity E2 with total membership $N=1504$. (c) Ethnicity E3 with total membership $N=2552$.

Figure 5

(Color online) Our generic model of group dynamics. (a) The basic model setup, without yet specifying the criterion that an agent uses when seeking to join or leave a group. Two possible extremes are the team-formation model shown in Fig. 5b, where an agent seeks a group with a suitable niche in $p$ space, and the kinship model (not shown) where an agent seeks a group having members with a similar $p$ value. Details of the implementation and specific rule sets are discussed in Sec. 3.

Figure 6

(Color online) Empirical data and model comparison for (a)–(d) World of Warcraft and (e) LA gangs. Empirical data are darker (dark blue online) and the team-formation model from Fig. 5b lighter (red online). The kinship model (dashed curve) produces a poor fit in both cases.

Figure 7

(Color online) The WoW guild-size distribution $N\left(s\right)$ in October 2005. (a) Guild-size distribution treating all servers collectively. The parameters used for team formation are $N=76686$, $⟨\Delta p_i⟩=0.160$, ${\sigma }_{\Delta p}=0.022$, and $\tau =0.69$. (b) Guild-size distribution of server S1. The parameters used for team-formation simulation are $N=24033$, $⟨\Delta p_i⟩=0.160$, ${\sigma }_{\Delta p}=0.020$, and $\tau =0.67$. (c) Guild-size distribution of server S2. The parameters used for team-formation simulation are $N=24477$, $⟨\Delta p_i⟩=0.160$, ${\sigma }_{\Delta p}=0.025$, and $\tau =0.75$. (d) Guild-size distribution of server S3. The parameters used for team-formation simulation are $N=28176$, $⟨\Delta p_i⟩=0.161$, ${\sigma }_{\Delta p}=0.020$, and $\tau =0.70$. Each simulation result is obtained from one particular run of the team-formation model. Note that the parameters for different servers are very similar.

Figure 8

(Color online) The cumulative gang-size distribution $N\left(s^{\prime }>s\right)$ for LA gangs of different ethnicity. (a) $N\left(s^{\prime }>s\right)$ of membership of LA gangs of ethnicity E1. The parameters used for the team-formation model are $N=608$, $⟨\Delta p_i⟩=0.150$, ${\sigma }_{\Delta p}=0.016$, and $\tau =0.73$. (b) $N\left(s^{\prime }>s\right)$ of membership of LA gangs of ethnicity E2. The parameters used for the team-formation model are $N=1504$, $⟨\Delta p_i⟩=0.142$, ${\sigma }_{\Delta p}=0.014$, and $\tau =0.72$. (c) $N\left(s^{\prime }>s\right)$ of membership of LA gangs of ethnicity E3. The parameters used for the team-formation model are $N=2552$, $⟨\Delta p_i⟩=0.141$, ${\sigma }_{\Delta p}=0.016$, and $\tau =0.72$. Each model result corresponds to one run of the team-formation model simulation. Note that the parameters for different ethnic groups are very similar, as was the case for different servers in WoW.