Interevent time distributions of human multi-level activity in a virtual world
Olesya Mryglod, Benedikt Fuchs, Michael Szell, Yurij Holovatch, Stefan Thurner
aa r X i v : . [ phy s i c s . s o c - ph ] J u l Interevent time distributions of humanmulti-level activity in a virtual world
Olesya Mryglod a , Benedikt Fuchs b , Michael Szell e ,Yurij Holovatch a , Stefan Thurner b , c , d , ∗ a Institute for Condensed Matter Physics, National Acad. Sci. of Ukraine, 79011Lviv, Ukraine b Section for Science of Complex Systems, Medical University of Vienna, Vienna,Austria c Santa Fe Institute, Santa Fe, NM 87501, USA d IIASA, Schlossplatz 1, A-2361 Laxenburg, Austria e Senseable City Laboratory, Massachusetts Institute of Technology, Cambridge,Massachusetts, USA
Abstract
Studying human behaviour in virtual environments provides extraordinary oppor-tunities for a quantitative analysis of social phenomena with levels of accuracy thatapproach those of the natural sciences. In this paper we use records of player activi-ties in the massive multiplayer online game
Pardus over 1,238 consecutive days, andanalyze dynamical features of sequences of actions of players. We build on previouswork were temporal structures of human actions of the same type were quantified,and extend provide an empirical understanding of human actions of different types.This study of multi-level human activity can be seen as a dynamic counterpart ofstatic multiplex network analysis. We show that the interevent time distributions ofactions in the
Pardus universe follow highly non-trivial distribution functions, fromwhich we extract action-type specific characteristic “decay constants”. We discusscharacteristic features of interevent time distributions, including periodic patternson different time scales, bursty dynamics, and various functional forms on differ-ent time scales. We comment on gender differences of players in emotional actions,and find that while male and female act similarly when performing some positiveactions, females are slightly faster for negative actions. We also observe effects onthe age of players: more experienced players are generally faster in making decisionsabout engaging and terminating in enmity and friendship, respectively.
Key words: quantitative sociology, human action dynamics, time series analysis,online games
PACS:
Preprint submitted to Elsevier Science November 6, 2018
Introduction
The life of humans can be viewed as a sequence of different actions that arecarried out from birth to death. Some of these actions are carried out with highregularity on various timescales (circadian, yearly, etc.), others have significantstochastic components. By now it is well established that distribution functionscharacterising sequences of human actions over time are highly non-trivial[1–12], and their origins remain largely unclear.The very fact that distributions of human actions over time, such as distribu-tions of phone calls, follow statistical laws was known since the beginning ofthe last century [13], and triggered the origin of queueing theory [14]. Early at-tempts to understand human action sequences were based on the assumptionthat actions are carried out homogeneously in time with constant rates, whichthen lead to Poisson processes [15]. This lead to the conclusion that timesbetween consecutive actions of the same individual should be distributed ex-ponentially. Models to describe human dynamics that are based on Poissonprocesses are still widely used [16, 17]. However, the careful analysis of vari-ous patterns of human activity provides growing evidence for highly inhomo-geneous bursty distributions of human actions in time. Further there is evi-dence for non-trivial inter-dependencies of actions that influence their (usuallypower-law dominated) temporal statistics [1–12]. The latter were found bothfor traditional human actions such as writing letters [3, 7], checking out booksin libraries, performing financial transactions [4], or writing e-mails [1, 2, 6],web browsing [4], sending text messages [9], editing Wikipedia pages [10, 12],and many more. Different reasons have been suggested to explain their appear-ance. In particular, the priority queueing model [2] is a possibility to explainthe bursty mechanism of human behavior by a decision-based queueing pro-cess where individuals perform tasks according to some priority. This mayexplain the observed correspondence patterns of Darwin and Einstein [3]. Al-ternatively it has been hypothesized that human correspondence is driven notby responses to others but by the variation in an individual’s communicationneeds over the course of their lifetime [7].The common feature of the above mentioned observations is that they arebased on the analysis of human actions of a single type: either writing e-mails, or letters, or making phone calls, etc. The next step beyond thesestudies is to consider the much more involved situation where tasks of differenttypes are performed. What is the action dynamics of an individual (or of agroup of individuals) that writes both e-mails, and letters, and makes phonecalls? Carrying out actions of different types we call multi-level human activity . ∗ Corresponding author.
Email address: [email protected] (Stefan Thurner).
Pardus [21] is briefly outlined below.
Pardus is a massive multiplayer online game (MMOG) which is online since2004. It is an open-ended game with a worldwide player base of more than400,000 registered players [21, 22]. The game has a science fiction setting andfeatures three different universes. All universes have a fixed start date but noscheduled end date. Every player controls one avatar, called the player’s char-acter. The characters act within a virtual world making up their own goalsand interacting with the self-organized social environment. There is a varietyof different activities the characters can participate in, including communica-tion, trade, attack, and other forms of social actions such as establishing orbreaking friendships or enmities, see Fig. 1. Since it has been launched, the
Pardus game served as a unique testing ground to measure different observ-ables that characterize inhabitants of the virtual world and in this way tolearn about complex social processes taking place in the real world – “Whenthe same six soldiers take out a dragon in a synthetic world, the dragon is notreal but the teamwork is” [23]. Indeed, with a complete record of completeinformation about millions of actions of different kinds performed by thou-sands of people during several years from a single source, this setting providesthe unique position to achieve a detailed non-intrusive quantitative analy-sis of complex social behavior [22, 24–32]. In particular, the complex networkstructure of the Pardus society has been exposed and evidence was collectedfor several social-dynamics hypothesis, including the Granovetter weak tieshypothesis and triadic closure [28]. In this way further evidence has been pro-vided about validity of a model of online communities for human societies,allowing to operate with a precision resembling that of natural sciences [22].Further analysis of the Pardus society has revealed the network topology ofsocial interactions [24, 28], mobility of characters [25], behavioral action se-quences [26], gender differences in networking [27], and the functioning of thevirtual economy [30].The main idea of this paper is to analyze the evolution of actions within the
Pardus universe over time: what are the temporal characteristics of actionstaken by players? Is there an action-specific dynamics, and are there someglobal processes that dominate the dynamics of players in the online world?It is well established by now that a number of features of the virtual societyresemble those in the offline society, giving hope to expect that the analysis ofthe virtual world action dynamics will provide insights into human dynamicsthat is valid also for real societies. Social systems can be quantified com-prehensively by studying the superposition of its constituting socio-economicnetworks (multiplex networks, see [33–35]) [24]. The same information is con-3 layer 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 ...
Figure 1. Short segment of action sequences, performed by four
Pardus players. Dif-ferent actions are shown by different letters as explained in Section 2. The detailedanalysis of time sequences of these multi-level action streams is the main goal ofthis paper. tained in the dynamical behavioural sequences (Fig. 1) of the individuals,however with a focus on temporal aspects of the multi-level activity.The paper is organized as follows. In Section 2 we describe the database andconcentrate on the main observable of interest, the interevent time τ andits statistics. We comment on the bursty dynamics of individual characters.Action-specific dynamics is studied in Section 3. There we analyze inherentfeatures of actions of different types and compare actions performed by dif-ferent types of players such as male and female. The dynamics of the entirecommunity of players in the Pardus game is analyzed in Section 4. In par-ticular, we discuss an increase of activity during periods of war in the game.Conclusions and outlook are presented in Section 5.
The
Pardus world consists of three different game universes: Orion, Artemis,and Pegasus. In this study we concentrate on the Artemis universe becausein this Universe complete data is available for all actions of all players [22].The Artemis universe is also the most densely populated universe over time,inhabited by more than 7,000 active characters (see Table 1 for more details).Artemis was opened on June 10, 2007. Our analysis is based on the informationabout player activities during 1,238 consecutive days since the universe wasopened. Every character in the game is a pilot who owns a spacecraft, travelsin the universe and is able to perform a number of activities of different type.There is no specified goal in the game, the players make up their own goalsand interact with their self-organized social environment. Every player picks4 male or female avatar, the age of the player is measured as a the number ofdays since the first registration. We concentrate on the following actions thatcan be acted out within the game • sending private messages from one player to another (communication, C); • attacking other players or their belongings (attack, A); • trading or giving gifts (trade, T); • marking friends by adding their names to a friend list (F); • marking enemies by adding their names to an enemy list (E); • removing friends from the friend list (D); • removing enemies from the enemy list (X).More information is found in [22]. It is important to note that actions per-formed by a character (such as trade, travel, adding/removing friends) cost acertain amount of so-called action points (APs). The number of APs availableper character at once cannot exceed 6,100. For each character which owns lessAPs than their maximum, every 6 minutes 24 APs are automatically gener-ated. Once a character is out of APs, they have to wait for new APs to beregenerated. Social interactions, e.g. sending private messages, planning, co-ordination, etc., do not cost APs. This feature adds one additional differencebetween the action types and causes peculiarities in the behavior of characters,as we will see below.The above actions can be labeled as “positive” or “negative” depending ontheir nature: A, E and D are considered as negative, while C, T, F, X areconsidered positive [22,26]. In some cases this classification may be questioned.For example, thorough categorization of the private messages would have totake into account their content. However, we will classify C as a positive actionbecause only a negligible part of communication in Pardus takes place betweenenemies [22]. Since private messages are the most frequently performed actions( ≈ interevent time , i.e. the time interval between two consecutiveactions of the same person, and the waiting time , defined as the time intervalbetween the action (of one person) and reaction (of another person). Thelast quantity is sometimes understood as the “time to reciprocate”. In thecorrespondence pattern analysis the reaction on a received letter is anotherletter that is sent in reply. However, there might also be mixed reciprocity,where the type of reaction differs from an action itself – say, an email sentas a reaction on a phone call received. Because of this, we first simply focuson the interevent time, ignoring the type of action. We denote this by τ . InTab. 1 we collect the main features of the data set. The overall number ofcharacters that have performed at least one action in the Artemis universe is5 able 1Characteristics of the data set. N is the number of characters that performed actionsof a given type; N a , overall number of actions performed by these characters duringthe observation period within 1 ,
238 consecutive days. N τ is the number of intereventtime ( τ ) values. τ min , τ max are minimal and maximal values of interevent times givenin seconds.Action type N N a N τ τ max τ min All 7,818 8,373,209 8,365,391 63,882,774 0Positive 7,806 7,492,460 7,484,648 63,882,774 0Negative 6,918 880,749 873,831 91,715,678 0A 5,412 742,798 737,386 100,686,258 0T 6,883 561,327 554,444 86,705,400 0C 7,799 6,775,950 6,768,151 72,931,246 0E 5,638 105,958 100,320 100,232,580 2F 7,067 125,984 118,917 100,736,362 1X 3,653 29,199 25,546 87,400,240 1D 3,188 31,993 28,805 95,379,313 1 N = 7 , ,
238 consecutive days is N a = 8 , , N a is action type specific and ranges from N a = 6 , , N a = 29 ,
199 for X. The number of players N that are involved in anyspecific type of action is distributed rather homogeneously: several thousandsof players for each action.The histogram of the number of actions is shown in Fig. 2. The majority ofplayers performed just a few actions during the entire period, while a fewvery active players provided huge activity statistics. We find an approximatepower law scaling with an exponent of ∼ − .
18. Players with a small numberof actions typically quit the game just after registration. These players arenot representative so that we exclude all players that performed less than 50actions. Since all actions are time stamped with an accuracy of one second, wecan calculate interevent times, τ . The distribution of τ follows a power law asseen in Figs. 3a and 3b. The exponent dependents on the chosen time scale (binsize). The periodic pattern (inset) corresponds to circadian cycles [10, 11, 17].To focus on the dynamics within the first 24 hours (most frequent values for τ ) we take a bin size of 1 min, Fig. 3b. The local minimum, which appearson this scale for τ = 7 hours = 25 ,
200 sec can be explained by the “active6 Number of actions, k N u m be r o f p l a y e r s w i t h k a c t i on s −1.18 Figure 2. Number of players who performed k actions during the observation time.The majority of players performed few actions during the entire period, while a fewvery active players provided huge activity statistics. The line shows scaling with anexponent of ∼ − . −8 −6 −4 −2 τ [sec] B i nned P ( τ ) −2.09 (a)bin size: 6h −4 −4 −2 τ [sec] B i nned P ( τ ) −1.12 (b)bin size: 1min Figure 3. Distribution of the interevent time τ for all players who performed at least50 actions. (a) entire observation period (1,238 days), bin size is 6 hours=21; 600sec. The inset shows a six day period. Circadian rhythms are clearly visible. (b)First 24 hours, bin size is 1 min. working day”. Since it is more convenient to play in the morning (beforework) or in the evening (after work), interevent intervals of 7 hours are lessprobable than those for 8, 9, or 10 hours. One observes a further regime atsmall values of τ , corresponding to immediate or slightly delayed repetition.This can be observed within the first 3 minutes after the performed action.This is due to the peculiarities of different actions. For example, attacks couldbe naturally grouped into sequences due to repeatedly pressing an attackbutton to attack the same opponent, while a separate decision is needed toadd each new enemy. Further, player synchronization might play a substantialrole, where two players can react promptly when they are both online, but only7 a) (b) (c) (a) (b) (c) (d)(e) (f) B=0.94B=-0.38B=0.006 B=0.53B=0.53B=0.53
Figure 4. Action streams of players with different values of burstiness B . Lines marktimes of executed actions, the distance between lines is the interevent time. with a (significant) delay if one is offline. It is possible that the shape of theinterevent times distribution after these first “immediate” values is influencedby the login behavior of players.The power-law-like distribution of interevent times between the actions indi-cates the bursty nature of human dynamics [2, 3, 5]: periods of high activityare separated by long periods of inactivity. Although the origins of such anon-uniform distribution of actions are highly diverse, it is recognized to bean inherent feature of human dynamics. A measure for burstiness B was in-troduced in [8], its simplified version (see [10, 12]) is defined as follows: B ≡ σ − mσ + m , (1)where m is the average of the interevent time τ , and σ its standard deviation.For a regular pattern we have B ∼ −
1, for a random Poissonian process witha fixed event rate, B ∼
0, and for fat-tailed distributions of time intervals, B ∼ B . Each line marks the time of an executed action. The patterns on the left-hand side correspond to the activity with (a) maximal, (b) minimal, and (c)close to zero values of B . A random distribution of actions over the time lineis characterized by B ∼
0. It is observed that seemingly very different activitypatterns can be characterized by similar values of burstiness, Fig. 4d–f. Thehistogram of B for all players is shown in Fig. 5a. The most frequent value(maximum) ( ˆ B ≃ .
53) as well as the average (mean) ( B ≃ .
53) values are8 B =0 . (a) All actions B =0 . (b) C F r equen cy −1 −0.5 0 0.5 10200 B =0 . (c) A Burstiness
Figure 5. Histogram of burstiness calculated for (a) all action types, (b) communi-cation C, and (c) attacks A. The most frequent (maximum) ( ˆ B ) and the mean ( B ,red lines) values are ˆ B ≃ . B ≃ .
53 (a); ˆ B ≃ . B ≃ .
49 (b); ˆ B ≃ . B ≃ .
48 (c), respectively. both larger than 0.5. The average burstiness values for the process of real-worldmobile communication is more than two times smaller, B ≃ . ∼ . B , for attacks,Fig. 5b, has larger values than for communication, Fig. 5c. This illustrates theintuitive understanding of the nature of these actions: attacks appear highlyclustered within short time intervals, while communication is more uniformlydistributed over time. In this section, we ask if it is possible to discriminate between actions typesgiven only information about their interevent time distributions. We can showthat the “decay” of the interevent time distribution serves as a distinguishingfeature of action types. To quantify this decay we introduce “decay constants”and “decay exponents” that are specific for different actions. We calculate theinverse cumulative distributions of interevent times P ≥ ( τ ) for each of the sevenaction types. They are shown in Fig. 6 for communication (C), attacks (A),trade (T) and for the friendship-enmity marking actions F, D, E, and X. Dueto the massive contribution of C actions, the curve for all actions is dominatedby the C distribution. 9 igure 6. Inverse cumulative distribution of interevent times τ for all players(no binning) and for different kinds of actions. The actions are: communication(C); attack(A); giving gifts / trade (T); making friends/enemies (F/E); removingfriends/enemies (D/X). Inset: same plot in log-linear scale, for τ > · sec ( > Based on our previous observations (see Section 2), we are particularly inter-ested in the behavior on three different time scales: immediate reaction where τ does not exceed a couple of minutes; early day , τ is less than 8 hours; andthe late day , τ is between 8 and 24 hours. Our main observations are • Immediate reaction ( τ ≤
360 sec). P ≥ ( τ ) is shown in Fig. 7a. All curveshave a tendency to decay fast at small values of τ . The decay is espe-cially pronounced for A, D, F, X, and E actions. This means that shortinterevent times are typical for most of the actions. Large numbers of at-tacks or emotional addings-removings are performed one-by-one in a veryfast way (grouped into sequences), while the probabilities of τ values greaterthan 1 min start to decrease very slowly. The decay for short intereventtimes for T and C is less steep, whereas its further evolution remains morehomogeneous. • Early day (6 min < τ < P ≥ ( τ ) is best approximatedby a power law P ≥ ( τ ) ∼ τ − α , (2)with small exponents in the range of α ∼ . − . α ∼ .
24, see Fig. 7b. The exponents for each curveare collected in the second column of Tab. 2. • Late day (8 hours < τ <
24 hours). P ≥ ( τ ) in this region is shown in Fig. 7c.10
100 200 30010 −1 (a) τ [sec] P ≥ ( τ ) CAT
FDEX −1 (b) τ [sec] P ≥ ( τ ) Figure 7. Inverse cumulative distributions of τ in different time intervals. (a) τ ≤ τ ≤ sec, log-log scale (fits obtained from 6 min – 8 hoursinterval); (c) τ ≤ sec, log-linear scale (fits from 8–24 hours interval). Behavioron three different time scales is governed by different decay constants, see Tab. 2and text. We fit here the decay by the exponential function, P ≥ ( τ ) ∼ exp ( − τ /τ ) . (3)Values of τ are collected in the third column of Tab. 2. The slow exponentialdecay is described by slightly different action-specific values of τ . Thisdifference has a tendency to diminish for larger time intervals. The fastestdecay is observed for C, with τ ≃ . · − , which is twice as large as forA ( τ ≃ . · − ), and ten times larger than for the other actions. • Long times ( τ > · sec). An exponential cut-off for large τ (more thaneight months) becomes apparent in P ≥ ( τ ), see Fig. 6. The exponential decayhas similar numerical values for the different actions providing evidence fora cut off effect.The results indicate that the various types of actions are characterised bydistinct decay properies of the interevent time distributions. The values α inEq. (2) and τ in Eq. (3) may serve as “decay constants” and turn out to beaction specific. This is especially pronounced for interevent times in the timeintervals “early-day” (6 min < τ < < τ <
24 hours). The “long time” exponential decay can be safely interpreted as afinite size effect of the sample. The average values of interevent times τ alsopoint on the different speed in performing different kinds of actions. Due tothe contribution of some rare but large values of τ , as well as the periods ofnatural inactivity (circadian cycles), the values of τ are large: ∼ .
6h for C, ∼ .
8h for A, ∼ .
1h for T, ∼ .
3h for F, ∼ .
3h for D, ∼ .
3h forE, ∼ .
5h for X. τ is smallest for communication and much larger for anyother kind of activity.We conclude this section by studying players of different type. For the majorityof actions, the interevent time distributions of males and females are very sim-11 able 2Decay constants and decay exponents for various actions at different time scales.The interevent time distribution P ≥ ( τ ) for the early-day interval is governed by thepower law, Eq. (2), whereas the late-day and long-time intervals are governed by theexponential decay, Eq. (3). Values for α and τ are given in the table for differenttypes of actions. early-day α late-day τ long times τ A -0.07 -2.46e-06 -3.64e-08T -0.05 -1.81e-06 -3.71e-08C -0.24 -5.65e-06 -4.55e-08E -0.01 -0.56e-07 -3.49e-08F -0.03 -0.88e-07 -3.80e-08X -0.01 -0.29e-07 -3.41e-08D -0.01 -0.34e-07 -3.13e-08 ilar. We concentrate here on the actions where slight gender effect is present.In Fig. 8a we compare P ≥ ( τ ) (for small τ ) for the E, F, D, and X actions of fe-male (solid curves) and male (dashed curves) game characters. There is a slightgender effect in action interevent times in the process of marking friends andenemies, compatible what has been previously reported on a social networklevel in [27]. The difference for the negative actions (enemy adding and friendremoving) and the positive actions (friend adding and enemy removing) mightbe explained by underlying biological or socio-dynamic reasons. Whereas theinterevent time distributions of males and females performing positive actions(F and X) almost coincide, this is not the case for the negative actions (E andD), see Fig. 8a. The corresponding curves for females are always above thosefor males: negative actions performed by females have shorter time intervals.Whereas male and female act almost similarly when performing positive ac-tions, females are faster in negative ones. Note, however, that such differenceis not observed for the A, T, and C actions.The details of the friendship-enmity marking actions can be observed also forplayers with different experience. Fig. 8b shows P ≥ ( τ ) (for small τ ) are shownfor young (solid curves) and old (dashed curves) players: the F curves coincidefor young Pardus players. Old players are defined as those who have startedthe game at least one year before the last day of the data set. Young playersare those who are younger than one year. The other curves for old players arealways above those of the young players. The time intervals between markingsomebody as an enemy or removing the marks are shorter for experiencedplayers. The speed of marking friends is the same for all players. The majorityof friends are typically marked early on in
Pardus “life”.12 igure 8. Inverse cumulative distributions P ≥ ( τ ) (for τ ≤
360 sec) for different typeof players: (a) male (dashed) and female (solid), (b) young (solid) and old (dashed).Gender differences for actions C, T and A are minimal, we only present F, E, Dand X actions here. Whereas the interevent time distributions of males and femalesperforming positive actions (F and X) almost coincide, this is not the case for thenegative actions (E and D). The situation is different for the groups of young andold players: marking of friends is performed with about the same speed for bothages, the old players are always faster with the other actions.
We now study how actions are distributed in time. The number of all actionstypes pooled together is shown for every day in Fig. 9. The time interval startson 2007/06/12 and covers 1,238 consecutive days of players activity. Thereare four pronounced peaks in the player activity which can not be understoodwithout knowing the history of the virtual world during the observation period. • The peak of activity on March, 2008 (magenta line in figure) was caused bythe introduction of new major game features called “Syndicates” on March7, 2008 [37]. Big changes in the game usually become a hot topic to discuss,leading to the higher level of C activity. • The peak of activity in August-September, 2008 (blue stripe in figure) cor-responds to the 1 st war, that occurred in the period between 2008-08-08 and2008-09-17 (war I). • The peak of activity in January-March, 2008 (green stripe in figure) corre-sponds to the 2 nd war, 2009-01-18 – 2009-03-04 (war II). • The peak of activity in end December 2019 – February 2010 (orange stripein figure) corresponds to a 3 rd war between 2009-12-25 and 2010-02-12 (warIII).Before discussing player activity in peace and war periods we briefly explainhow a war emerges in the virtual world. According to the specifics of thegame [21] each player can belong to one of three factions (organizations) or stay13
500 100040006000800010000120001400016000 Time [days] N u m be r o f a c t i on s war I war II war III Figure 9. Number of actions (all types) per day on the timeline. There are fourpronounced peaks in the player activities that correspond to specific events thathappened in the virtual world in the observation period: the three coloured verticalstripes indicate war periods, the vertical line indicates the introduction of a majornew game feature. neutral. There are three factions in the game: 1 – “Federation”, 2 – “Empire”,3 – “Union”. Only two factions can participate in a war simultaneously. Duringthe observation period the following pairs of factions were involved in wars:Factions 1 and 2 in war I and factions 1 and 3 in the next two wars. Factions2 and 3 were never engaged in a war within the observation period.Table 3 collects basic statistics of actions during war and peace periods. Thechange in activity that leads to the overall increase of the number of actionsof players engaged in war can be analyzed in more detail by studying thedistributions for specific actions. The most distinct peaks are observed forC and A. In Fig. 10 we show the weekly number of C (a) and A (b) forthe different factions. The highest number of actions occurs in those factionsthat are involved in wars. While the general level of activity during the warsincreases, there are no distinct differences in the distributions of intereventtimes for peace and war periods, respectively.Taken that a war in a virtual world arises as a result of a complex process ofsocial interactions between the players it is tempting to seek for war precursors.To this end we decided to check whether changes in player activity (of thedifferent actions) may serve as a predictor for an upcoming war. In
Pardus war officially starts whenever a so-called “faction-relation” ratio, defined bythe game system for each pair of factions, exceeds a certain threshold value.14 able 3Statistics of behavioural time series corresponding to war and peace periods (allactions). N is the number of players that performed actions in a given period; N a isnumber of actions they performed; N τ is the number of interevent time ( τ ) values; τ max is the maximal interevent time. Also given, percentage of positive and negativeactions, percentage of actions performed by male players. The last line representsdata for the overall peace period (all war periods ignored). N N a N τ τ max [sec] % posactions % negactions % maleAll wars † ‡ † Peace periods are ignored in the calculation of t int ‡ War periods are ignored in the calculation of t int The faction-relation is evaluated daily in a specific way that takes into accountnumerous behavioural factors of all players organised in factions, for moreinformation see [21].To test if one can predict a war based on activity data only, we applied a cross-correlation analysis and scanned for potential lead effects of activity patternson the faction-relation time series. We performed a systematic scan for lead-lag relationships, involving all types of actions (some are seen in Fig. 10), allcombinations of factions, for several sizes of time-windows. While we see cleardifferences between periods of war in peace in the extend of cross-correlations,we were unable to find conclusive precursors for the onset of war. This negativefinding does not exclude the existence of other indicators that could have morepredictive power than the activity patterns alone.The cross-correlation values (colors) for all actions as a potential predictor forthe faction-relation time series are presented in Fig. 11. Lead and lag valuesare on positive and negative y-axis, respectively. War regions are marked byvertical bars.
We used records about player activities in the MMOG
Pardus to analyzeseveral dynamical features of player actions. It has been shown in previouswork that the characters in
Pardus display rich and realistic social behav-ior [22, 24–32]. This includes the complex multiplex network structure of the15
00 400 600 800 1000 12000.511.522.53 x 10 Time [days] N u m be r o f c o mm un i c a t i on e v en t s (a)war I war II war III Faction
200 400 600 800 1000 12001000200030004000500060007000 Time [days] N u m be r o f a tt a cks (b) Figure 10. Number of weekly actions for different factions of players: (a) communi-cation C; ( b) attacks A. Activity of players involved in wars increased during thewars.
Pardus society, complex multiplex network topologies of social interactions,non-ergodic behavioral action sequences, etc. In the present study we extendthese observations by a thorough analysis of the interevent time distributions P ≥ ( τ ) for the activities players can perform in the game. In particular, we haveshown that the interevent time distributions in the Pardus universe highly non-trivial in nature. One feature of these distributions is an presence of periodicpatterns on different scales, which correspond on the one hand to trivial cir-cadian cycles, on the other hand to more non-trivial periods of the workingday and to short scales of straightaway reactions. Similar to human activitiesin the real-world, non-trivial distributions go hand in hand with bursty dy-namics [2, 3, 5, 8]. The measured value of burstiness of player actions, B ≃ . P ≥ ( τ ), depending on the time scale. Theinterevent time distributions are well fitted by power law within the interval 6min < τ < < τ < < τ <
24) thedifferences between actions types become less pronounced. The average valuesof interevent times τ also indicates different speeds in performing differenttypes of actions. Even given the inactivity periods due to circadian cycles, thevalue of τ is smallest for communication and is much larger for other types.16 igure 11. Cross-correlations between the number of actions (all types pooled to-gether) and the faction relation for different factions using the sliding window ofsize 100 days. (a) factions 1 and 2. Note that they fight against each other in war I;(b) factions 1 and 3. They fight in wars II and III; (c) factions 2 and 3, who neverfight against each other. Finally, we observed periods of increased activity in the
Pardus due to historyspecific events, such as wars that were waged in the game. Our search forpotential predictive indicators that would signal the onset of war lead to thenegative conclusion that changes in player activity does not serve as reliableindicator of an upcoming massive conflict.
Acknowledgments
This work was supported in part by the 7th FP, IRSES project No. 612707Dynamics of and in Complex Systems (DIONICOS) and by Austrian ScienceFonds FWF P23378.
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