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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]