Interevent time distributionsof human multi-level activityin a virtual world

Yurij Holovatch

Lviv, Ukraine

In collaboration with:

Olesya Mryglod

Stefan Thurner

Benedikt Fuchs

Michael Szell

Supported by:

IRSES N612707 (Dyonicos)

MOTIVATION

• Distribution functions characterising sequences of human actions over time arehighly non-trivial, and their origins remain largely unclear: writing letters (Oliveira’05,Malmgren’09), checking out books, performing financial transactions (Vazquez’05),writing e-mails (Kleinberg’03, Barabasi’07), web browsing, editing Wikipedia (Jo’12,Yasseri’12) etc.

• The common feature of the above mentioned observations is that they are basedon the analysis of human actions of a single type: either writing e-mails, or letters,or making phone calls, etc.

• What is the action dynamics of multi-level human activity (writing both e-mails,and letters, and making phone calls, etc).

• A testing ground: virtual world.

MMOG PARDUS

• Online since 2004

• Open-ended game

• Self-organized socialenvironment

• More than 400,000 registeredplayers (>14,000 active)

• economic life (mining, trade,production and consumption ofcommodities, etc)

• social life (chat, forum, privatemessages, establishing friendshipsor hostile relations, status demon-stration)

MULTILEVEL HUMAN ACTIVITY

Player 146 ... AAAAAACTT EEX FTTTTTX CCCTTTTT AC ...

Player 199 ... CCA BBCAAAAATTA AACCCCCBX CFFFF ...

Player 701 ... CCCCTTTT TCTCT FF CXXTT CCCCC TTT ...

Player 171 ... AAAACC CCC C CCC AA TTT FCC EED ...

• Communication (C)

• Trade (T)

• Marking friends in the list (F)

• Removing enemies from the list(X)

• Attack (A)

• Marking enemies in the list (E)

• Removing friends from the list(D)

INTEREVENT TIME DISTRIBUTION

104

105

106

107

108

10−8

10−6

10−4

10−2

100

τ [sec]

Bin

ned

P(τ

)

−2.09

(a)

bin size: 6h

106

10−4

102

103

104

105

10−4

10−2

100

τ [sec]

Bin

ned

P(τ

)

−1.12

(b)

bin size: 1min

a. b.

Distribution of the interevent time τ for all players who performed at least 50actions. (a) entire observation period (1,238 days), bin size is 6 hours=21,600sec. (b) first 24 hours, bin size is 1 min. Inset: same as (a) for for six days.Circadian rhythms are clearly visible.

BURSTINESS

B = σ−mσ+m

(a)

(b)

(c)

(a)

(b)

(c)

(d)

(e)

(f)

B=0.94

B=-0.38

B=0.006

B=0.53

B=0.53

B=0.53

Action streams of players with different values ofburstiness B. Lines mark times of executed actions,the distance between lines is the interevent time.

Pardus (all action types): B ' 0.53.Mobile phone communication (Jo et al., 2012): B ' 0.2.Wikipedia editing (Yasseri et al., 2012): B ' 0.6.

ACTION-SPECIFIC DYNAMICS

Inverse cumulative distribution of intereventtimes τ for different kinds of actions. Inset:same plot in log-linear scale, for τ > 2 · 107

sec (> 8 months).

• Immediate reaction (τ ≤ 360 sec)

• Early day (6 min < τ < 8 hours):P≥(τ) ∼ τ−α

• Late day (8 h. < τ < 24 h.):P≥(τ) ∼ exp (−τ/τ0)

• Long times (τ > 2 · 107 sec)

GLOBAL DYNAMICS AND ACTIVITY PATTERNS:

WAR AND PEACE

0 500 1000

4000

6000

8000

10000

12000

14000

16000

Time [days]

Num

ber

of a

ctio

ns

war I war II war III

Number of actions per day on the time-line. The three coloured vertical stripesindicate war periods, the vertical line in-dicates the introduction of a major newgame feature.

200 400 600 800 1000 1200

0.5

1

1.5

2

2.5

3x 10

4

Time [days]

Num

ber

of c

omm

unic

atio

n ev

ents

(a)

war I war II war III

Faction #1Faction #2Faction #3Neutral

Number of weekly actions for differentfactions of players. Activity of players in-volved in wars is increased. (a) commu-nication C.

CONCLUSIONS

• Interevent time distributions in the Pardus universe are highly non-trivial.

• Presence of periodic patterns on different scales.

• Bursty dynamics.

• Different kinds of actions are characterized by different decay constants.

• Periods of increased activity in the Pardus due to history specific events.

• Physica A 419, 681-690 (2014) [arXiv:1407.2006]