This study analyzes the interevent time distributions of diverse human activities in the virtual world of the MMORPG Pardus, highlighting the complexity of human action dynamics across multiple types of interactions. It finds that these distributions exhibit bursty dynamics, periodic patterns, and varying decay constants related to different actions, with notable increases in activity during historical events. The research contributes to understanding the intricacies of human behavior in digital environments.

1. Interevent time distributions
of human multi-level activity
in a virtual world
Yurij Holovatch
Lviv, Ukraine

2. In collaboration with:
Olesya Mryglod
Stefan Thurner
Benedikt Fuchs
Michael Szell
Supported by:
IRSES N612707 (Dyonicos)

3. MOTIVATION
² Distribution functions characterising sequences of human actions over time are
highly non-trivial, and their origins remain largely unclear: writing letters (Oliveira’05,
Malmgren’09), checking out books, performing financial transactions (V´azquez’05),
writing e-mails (Kleinberg’03, Bar´abasi’07), web browsing, editing Wikipedia (Jo’12,
Yasseri’12) etc.
² The common feature of the above mentioned observations is that they are based
on the analysis of human actions of a single type: either writing e-mails, or letters,
or making phone calls, etc.
² What is the action dynamics of multi-level human activity (writing both e-mails,
and letters, and making phone calls, etc).
² A testing ground: virtual world.

4. MMOG PARDUS
² Online since 2004
² Open-ended game
² Self-organized social
environment
² More than 400,000 registered
players (>14,000 active)
² economic life (mining, trade,
production and consumption of
commodities, etc)
² social life (chat, forum, private
messages, establishing friendships
or hostile relations, status demon-stration)

5. 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 ...
² Communication (C)
² Trade (T)
² Marking friends in the list (F)
² Removing enemies from the list
(X)
² Attack (A)
² Marking enemies in the list (E)
² Removing friends from the list
(D)

6. INTEREVENT TIME DISTRIBUTION
100
10−2
10−4
10−6
104 105 106 107 108 10−8
t [sec]
Binned P(t)
−2.09
(a)
bin size: 6h
106
10−4
102 103 104 105
100
10−2
10−4
t [sec]
Binned P(t)
−1.12
(b)
bin size: 1min
a. b.
Distribution of the interevent time ¿ for all players who performed at least 50
actions. (a) entire observation period (1,238 days), bin size is 6 hours=21; 600
sec. (b) first 24 hours, bin size is 1 min. Inset: same as (a) for for six days.
Circadian rhythms are clearly visible.

7. BURSTINESS
B = ¾¡m
¾+m
(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 of
burstiness 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.

8. ACTION-SPECIFIC DYNAMICS
Inverse cumulative distribution of interevent
times ¿ for different kinds of actions. Inset:
same plot in log-linear scale, for ¿ > 2 ¢ 107
sec (> 8 months).
² Immediate reaction (¿ · 360 sec)
² Early day (6 min < ¿ < 8 hours):
P¸(¿) » ¿¡®
² Late day (8 h. < ¿ < 24 h.):
P¸(¿) » exp (¡¿=¿0)
² Long times (¿ > 2 ¢ 107 sec)

9. GLOBAL DYNAMICS AND ACTIVITY PATTERNS:
WAR AND PEACE
16000
14000
12000
10000
8000
6000
4000
0 500 1000
Time [days]
Number of actions
war I war II war III
Number of actions per day on the time-line.
The three coloured vertical stripes
indicate war periods, the vertical line in-dicates
the introduction of a major new
game feature.
Faction #1
Faction #2
Faction #3
Neutral
200 400 600 800 1000 1200
3
2.5
2
1.5
1
0.5
x 104
Time [days]
Number of communication events
(a)
war I war II war III
Number of weekly actions for different
factions of players. Activity of players in-volved
in wars is increased. (a) commu-nication
C.

10. CONCLUSIONS
² Interevent time distributions in the Pardus universe are highly non-trivial.
² Presence of periodic patterns on different scales.
² Bursty dynamics.
² Different kinds of actions are characterized by different decay constants.
² Periods of increased activity in the Pardus due to history specific events.
² Physica A 419, 681-690 (2014) [arXiv:1407.2006]