ACSEE: Antagonistic Crowd Simulation Model with Emotional Contagion and Evolutionary Game Theory
Chaochao Li, Pei Lv, Dinesh Manocha, Hua Wang, Yafei Li, Bing Zhou, Mingliang Xu
JJOURNAL OF L A TEX CLASS FILES, VOL. X, NO. X, NOVEMBER 2019 1
ACSEE: Antagonistic Crowd Simulation Modelwith Emotional Contagion and EvolutionaryGame Theory
Chaochao Li, Pei Lv, Dinesh Manocha, Hua Wang, Yafei Li, Bing Zhou, and Mingliang Xu*
Abstract —Antagonistic crowd behaviors are often observed in cases of serious conflict. Antagonistic emotions, which is the typicalpsychological state of agents in different roles (i.e. cops, activists, and civilians) in crowd violent scenes, and the way they spread throughcontagion in a crowd are important causes of crowd antagonistic behaviors. Moreover, games, which refers to the interaction betweenopposing groups adopting different strategies to obtain higher benefits and less casualties, determine the level of crowd violence. Wepresent an antagonistic crowd simulation model, ACSEE, which is integrated with antagonistic emotional contagion and evolutionarygame theories. Our approach models the antagonistic emotions between agents in different roles using two components: mental emotionand external emotion. We combine enhanced susceptible-infectious-susceptible (SIS) and game approaches to evaluate the role ofantagonistic emotional contagion in crowd violence. Our evolutionary game theoretic approach incorporates antagonistic emotionalcontagion through deterrent force, which is modelled by a mixture of emotional forces and physical forces defeating the opponents.Antagonistic emotional contagion and evolutionary game theories influence each other to determine antagonistic crowd behaviors. Weevaluate our approach on real-world scenarios consisting of different kinds of agents. We also compare the simulated crowd behaviorswith real-world crowd videos and use our approach to predict the trends of crowd movements in violence incidents. We investigate theimpact of various factors (number of agents, emotion, strategy, etc.) on the outcome of crowd violence. We present results from userstudies suggesting that our model can simulate antagonistic crowd behaviors similar to those seen in real-world scenarios.
Index Terms —Group violence, emotional contagion, evolutionary game theory (cid:70)
NTRODUCTION
Crowd simulation has received increased attention invirtual reality, games, urban modeling, and pedestrian dy-namics. One of the most important tasks in crowd sim-ulation is to generate realistic crowd behaviors. Physicalmethods [1], [2], [3], psychology principles [4], [5], [6], orapproaches from other relatively matured disciplines [7],[8], [9], [10] are leveraged into the crowd simulation toimprove the similarity between simulation results and real-world crowd movements. As pointed out in [4], emotion hasa great influence on crowd behavior and it often invokes anagent to implement either a positive or negative behavioralresponse. Thus, the emotion modeling in crowd simulationis always the main focus in latest research work. How-ever, the emotional aspect of antagonistic crowd behaviorsamong people in different roles is left unexplored [11].Analyzing the emotions of antagonistic crowd behaviors isindeed extremely important, as it can help us understandevolution process of antagonistic crowd behaviors and pre-dict trends of crowd movements.In this paper, we mainly deal with the problem of sim- • *Corresponding author. • Chaochao Li, Pei Lv, Hua Wang, Yafei Li, Bing Zhou, and MingliangXu are with Center for Interdisciplinary Information Science Research,ZhengZhou University, 450000. • Dinesh Manocha is with Department of Computer Science and Electrical & Computer Engineering, University of Maryland, College Park, MD,USA.E-mail: { ielvpei, ieyfli, iebzhou, iexumingliang } @zzu.edu.cn;[email protected]; [email protected]; [email protected] ulating antagonistic crowd behaviors. Such behaviors areassociated with acts of violation and destruction and aretypically carried out as a sign of defiance against a centralauthority or an indication of conflict between opposinggroups [12]. Our goal is to develop a new crowd simulationmodel that can predict trends of crowd movement in thesesituations while ignoring the trajectory of a particular indi-vidual, discuss the conditions of winning and losing sides,and help to develop measures to quell incidents of crowdviolence. Not only will such a method be useful for trainingpolice officers, but it could also predict the trends of crowdmovements and provide the decision for controlling crowdviolence incidents.It is difficult to simulate realistic antagonistic crowd be-haviors because of complex influencing factors. In practice,such behaviors are closely related to antagonistic emotions[13], [14], i.e. the emotions between opposed groups, andevolutionary game theory [5], [12]. In the pursuit of morerealistic antagonistic behaviors in virtual agents, antagonis-tic emotion simulation should be incorporated into crowdsimulation models [6]. Most prior crowd simulation modelsignore antagonistic emotions and individuals’ antagonisticbehaviors. Fu et al. [15] focus on agents’ emotions for onlyone role without involving the antagonistic emotions be-tween different types of agents. Some empirical methods ofmodeling antagonistic behaviors are presented in the formof riot games [16], game theoretic models [17], and socialnetworks. These methods are based on statistical spatial-temporal analysis and role-playing dynamics in crowds andcan generate emergent social phenomena. Other models use a r X i v : . [ c s . M A ] N ov OURNAL OF L A TEX CLASS FILES, VOL. X, NO. X, NOVEMBER 2019 2 evolutionary game theory to simulate the behaviors andinteractions between different kinds of agents [12], [18].Evolutionary game theory has successfully helped explainmany complex and challenging aspects of biological andsocial phenomena in recent decades [18]. Inspired by theidea that more offspring will be produced by more fit biolog-ical organisms in a given environment, evolutionary gametheory provides us with the methodology to study strategicinteractions among agents in incidents of crowd violence[19]. There is considerable work on evaluating individuals’emotions [20], [21]. Panic, for example, destroys an individ-ual’s normal mental function, transforms the individual intoan irrational state, and can lead to unpredictable abnormalbehaviors. Furthermore, Durupinar et al. [5] point out thatagents’ emotions dominate their decision-making processin games and other behaviors. However, the relationshipbetween antagonistic emotion and antagonistic crowd be-havior has not been fully explored [15]. It is challengingto accurately model antagonistic emotions among agentsin different roles because the antagonism is complex andchanges constantly and dynamically [22]. Moreover, priormethods do not consider the effect of antagonistic emotionon evolutionary game theory despite the fact that emotioninfluences an agent’s behavior significantly. For example, Lvet al. [23] calculate emotions based on political viewpoints ofindividuals at political rallies. Their method doesn’t involveevolutionary game theory or explore the relationship be-tween evolutionary game theory and antagonistic emotion.Recent advances in crowd simulation models attemptto simulate plausible human behavior by introducing psy-chological phenomena to virtual agents [6]. Inspired bythe psychological theory in [24], which shows the char-acterization and simulation of emotional contagion, thesepsychological phenomena effectively improve the reliabilityof simulations. Fu et al. [15] integrate emotional contagionwith individual movement to obtain realistic emotions andbehaviors in a crowd during an emergency. Based on thismethod, we propose an enhanced SIS model consideringthe benefits of games and test our antagonistic emotionalcontagion method among agents in different roles. More-over, we integrate antagonistic emotional contagion withevolutionary game theory through deterrent force, whichdescribes the differences between agents more accurately.Finally, we determine antagonistic crowd behaviors com-bining antagonistic emotional contagion and evolutionarytheories.Our main contributions include: • We propose a method to simulate emotion contagionbetween antagonistic agents in different roles, whichis determined by combing the enhanced SIS andgame approaches. • We propose a kind of deterrent force, which is mod-elled by a mixture of emotional forces and physicalforces defeating the opponents, and it helps individ-uals make reasonable decisions in the games. • We integrate antagonistic emotions into an evolu-tionary game theoretic method through deterrentforce to model antagonistic crowd behaviors morerealistically.Our model can generate simulation results that are clos- est to the real-world scenarios in the overall trends of crowdmovements. We have implemented our model and tested iton several outdoor scenarios with varying ratios of differenttypes of roles. Our simulation results are compared withthe real-world videos and we evaluate the benefits of ourmodel by performing user studies. The results indicate thatthe behaviors of agents generated by our model are closer toreal-world scenes in the overall trend of crowd movementsthan those seen in other methods.The rest of this paper is organized as follows. We reviewrelated work in Section 2. We give an overview of ourmethod in Section 3. We introduce our model in Section4 and show it can be used to generate antagonistic crowdbehaviors. We describe the implementation and highlightits performance on complex scenarios in Section 5. We alsopresent results from our preliminary user studies in Section5.
ELATED W ORK
In this section, we provide a brief overview of prior works inemotional contagion, evolutionary game theory, and agent-based crowd simulation.
Emotion is a psychological parameter and has a significantinfluence on individuals in a crowd [5], [25], [26], [27].Emotional contagion is closely related to human movement[28], [29], [30]. In this subsection, we introduce some repre-sentative works about emotional contagion [4].The epidemiological susceptible-infectious-recovered(SIR) model [31] divides the individuals in a crowd intothree categories: infected, susceptible, and recovered. Theanalysis of the spread of epidemic among these three groupshas also been extended to other fields. In [32], the extendedmodel is used to simulate the spread of rumors. Some re-searchers use the epidemiological SIR model in conjunctionwith other models to describe emotion propagation underspecific situations. In [5], the epidemiological SIR modelis improved by combining it with the OCEAN (openness,conscientiousness, extroversion, agreeableness, neuroticism)personality model [33]. In [34], a qualitatively simulatedapproach to model emotional contagion is proposed forlarge-scale emergency evacuation. The method shows thatthe effectiveness of rescue guidance is influenced by theleading emotions in a crowd. Moreover, in [15], the cellularautomata model based on the SIR model (CA-SIRS) is usedto describe emotional contagion in a crowd during an emer-gency, capturing the dynamic process “susceptible-infected-recovered-susceptible.” However, in some case, people onlyneed to consider two emotional states: infected and sus-ceptible. Hill et al. [35] evaluate the spread of long-termemotional states across a social network based on the clas-sical SIS (Susceptible Infected Susceptible) model. Cai etal. [36] combine the OCEAN and SIS models to simulateemotional contagion on crowd evacuation. Song et al. [37]discuss the factors influencing individual evacuation de-cision making in the view of social contagion based onSusceptible-Infective (SI) model. Emotional contagion canalso be used in traffic simulation [38], [39], [40] and crowdqueuing simulation [41].
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Fig. 1: Overview of our ACSEE model. (a) Crowd violence occurs. Civilians, activists, and cops are specified in our modeland they can perceive environmental information. The basic attributes of these agents are introduced in Section 4.2. (b)Our antagonistic emotional contagion method consists of two components: mental emotion and external emotion. After theoutbreak of the crowd violence, the antagonistic emotions of each agent are updated at each time step (Section 4.3). (c) Wecalculate the antagonistic emotion and deterrent force of each agent. The situation of the cops and activists is determinedbased on the deterrent force, which is defined according to antagonistic emotion. The game between antagonistic copsand activists is carried out in different situations. Agents use different strategies to carry out game interactions and theirbenefits are analyzed (Section 4.4). Their strategies are evolved over time using the evolutionary learning method. (d)We present behavior control method based on deterrent force, strategy, and benefit (Section 4.5). Agents choose rationalmovement directions and actions and their positions are updated. We use step (b) to calculate the positions of all the agentsat the next time step. (e) If the crowd violence subsides, the incident ends.A thermodynamic-based emotional contagion model isintroduced by Bosse et al. [42] in the ASCRIBE system. Theauthors use a multi-agent based approach to define emo-tional contagion within groups. Their study focuses on theemotions of a collective entity rather than the emotions ofsingle individuals. Neto et al. [6] adapt the model proposedby Bosse et al. [43] into BioCrowds and cope with differentgroups of agents. Tsai et al. [44] present an emotional con-tagion model that spreads the highest level of emotion tosurrounding agents in their ESCAPES framework. In [45],dynamic emotion propagation is described from the per-spective of social psychology, combining thermodynamic-based models and epidemiological-based models.According to the behaviors of different agents in antag-onistic scenarios, we define three kinds of agents. Each kindof agents is assigned a role separately: civilians, activists,and cops. Because of the antagonism between agents withdifferent roles, the above-mentioned emotional contagionmodels can’t be directly applied to crowd violent scenes. Inthis paper, we propose antagonistic emotions. Antagonisticemotions are the opposite emotions of agents in differentroles. Different roles of agents come from opposing groupsin crowd violent scenes. In our model the emotions of copsand activists are the antagonistic emotions. Antagonisticemotional contagion is the emotional contagion process ofantagonistic agents in different roles under certain situa-tions. Our antagonistic emotional contagion method canquantitatively characterize dynamic changes in the antag- onistic emotions between different roles.
In this subsection, we summarize some representativeworks about evolutionary game theory.Evolutionary game theory has solved many biologicalproblems. For example, in [46], genome-driven evolutionarygame theory helps to explain the rise of metabolic interde-pendencies in microbial communities.Some researchers have applied evolutionary game the-ory to the recommendation system. Saab et al. [47] useclassical and spatial evolutionary game theory as a possiblesolution to the Sybil attack in recommender systems. Li et al.[48] propose a new stability analysis of repeated games andevolutionary games based on a subset of Nash equilibrium.Evolutionary game theory can help us understand thebehaviors of individuals better. Huang et al. [49] presenta model in which every mutation leads to a new gamebetween the mutants and the residents based on a evolu-tionary game theoretic approach. Evolutionary game theoryis one of the most effective approaches to understand andanalyze widespread cooperative behaviors among individ-uals [50]. In [51], the combination of evolutionary gametheory and graph theory provides an extended frameworkto investigate cooperative behavior in social systems. Queket al. [12] focus on the development of a spatial evolution-ary multiagent social network to study the macroscopic-
OURNAL OF L A TEX CLASS FILES, VOL. X, NO. X, NOVEMBER 2019 4 behavioral dynamics of civil violence due to microscopicgame-theoretic interactions between goal-oriented agents.Some previous works [12], [52] study antagonistic crowdbehaviors in crowd violence incidents based on evolution-ary game theory but do not fully consider the differencesof antagonistic emotions and deterrent forces of agentswith different roles. In this paper, we further improve theevolutionary game theoretic method. At first, game in ourmodel is established between opposing groups (cops andactivists). When these agents confront different scenariosand situations, they adopt different strategies such as defec-tion or cooperation to get higher benefits and less casualties.Evolutionary game theory is a modeling approach of strate-gic interactions among agents in crowd violent incidentsbased on natural selection mechanism. Natural selectionmechanism means that more offspring will be producedby more fit biological organisms in a given environment.We use evolutionary game theory to analyze the strategiesand benefits of agents. Our model incorporates antagonisticemotions into evolutionary game theory to describe thedifferences between agents, which estimates situations ofantagonistic scenes more accurately.
Agent-based model is a kind of versatile method can sim-ulate complex scenarios. In an agent-based model, all theagents are endowed with greater autonomy and have theirown inherent attributes and properties. Agents can receiveinformation from the surrounding environment, which willinfluence their actions and decisions [53]. They have sep-arate velocities and moving directions. Hence, an agent-based model can produce complex crowd behaviors. In con-trast to agent-based models, flow-based and particle-basedmodels cannot accurately describe the differences betweenagents [54]. A flow-based model is mainly used to simulatehigh-density crowds and has no individuals or groups.A particle-based model cannot model high-level decision-making behaviors. Therefore, we integrate the proposedmodel with an agent-based method. In this subsection, wesummarize this kind of methods.An agent-based approach is the most common wayto simulate crowd movements [55]. Kountouriotis et al.[54] use the agent-based model to simulate thousands ofagents in real time, which integrates a high level of indi-vidual parametrization, such as group behaviors betweenfriends and between a leader and a follower. Luo et al.[56] introduce a novel framework for proactive steering inagent-based crowd simulation. The Social Forces Model iscombined with an agent-based method to simulate crowds[57]. In this model, repulsive and tangential forces of eachagent are introduced to avoid collisions with surroundingagents and obstacles. However, all the agents share the sameattributes and move with the same speed, which doesn’tconform to real-world scenarios.Some agent-based methods are used to simulate crowdmovements in emergency scenarios. In these scenarios, theemotional state of an agent is a very important influencingfactor in simulating realistic behaviors. Shendarkar et al.[58] present a novel crowd simulation model for emergencyresponse using BDI (belief, desire, intention) agents. Luo et al. [59] describe the human-like decision-making processbased on various physiological, emotional, and social groupattributes for agents under normal and emergency situa-tions. Aydt et al. [60] propose an emotion model integratedwith an agent-based method in serious games based onmodern appraisal theory. In contrast to the above meth-ods, which don’t involve antagonistic scenes or emotionsbetween agents in different roles, our method focuses onantagonistic emotions and the relationship between antago-nistic emotions and evolutionary game theory.TABLE 1: The parameters used in our ACSEE model.
Notation Description PR The radius of perceived range e exi External emotion of agent ie mei Mental emotion of agent i ∆ e exi,j ( t ) The increase in the strength of agent i ’s externalemotion received from agent j at time t ∆ e exc ( t ) The increment of external emotion of agent c attime t ∆ bene i ( t ) The difference of the benefits of the games at time t and t − for agent i ∆ e mei ( t ) The increment of the mental emotion of agent i attime t ∆ e i ( t ) The increment of the total emotion of agent i attime te i ( t ) The total emotion of agent i at time tT a c If the emotion value of an activist exceeds thethreshold T a c , role transition from activist tocivilian occurs. T c a If the emotion value of a civilian less than thethreshold T c a , role transition from civilian toactivist occurs. f i ( t ) The deterrent force of agent i at time tF i ( t ) The total deterrent force of agents of the same typefor agent i at time t ˆ F i ( t ) The total deterrent force of his or her opponents inthe cells neighboring agent i at time t ∆ F i The difference of the total deterrent forces betweencops and activists that agent i can perceive at time tP die The death probability T warn The early warning threshold warn time
The time of early warning T warn time The time of early warning threshold
VERVIEW OF OUR APPROACH
In this section, we introduce some basic and importantconcepts about crowd behavior simulation and crowd emo-tional contagion. We also give an overview of our method.
Crowd behavior simulation can be defined as a process ofemulating or simulating the movement of large amount ofentities, characters or agents [61]. At a broad level, crowdmovement is governed by psychological status of individu-als and their surrounding environment [22]. When humansform a crowd, interaction becomes an essential part of theoverall crowd movement [5]. For agent-based methods ofcrowd simulation used in this paper, each agent is as-sumed as an independent decision-making entity, which hasknowledge of the environment and a desired goal position
OURNAL OF L A TEX CLASS FILES, VOL. X, NO. X, NOVEMBER 2019 5 at each step of the simulation. The interactions betweenan agent with others or with the environment are oftenperformed at a local level [62]. A typical crowd simulationmodel can be defined as in Equation 1. P t represents thepositions of all the agents in the scene at time t and P t +1 is the positions of all the agents at time t + 1 , which can beinduced by crowd simulation model f . P t +1 = f ( P t ) (1) Crowd simulation research has recently taken a new di-rection for modeling emotion of individuals to generatebelievable, heterogeneous crowd behaviors. Emotion of anagent can greatly affect its ability to perceive, learn, behave,and communicate within the surrounding environment [5].The emotion owned by one agent provides informationabout other agents’ behavioral intentions and modulateshis or her behavioral decision-making process. Based ontheir appraisal of the environment, emotions of the agentsin a crowd are updated dynamically at different time. Inantagonistic scenes, such emotional changes become moreobvious and play a vital role in crowd interaction behaviors.As shown in Equation 2, the emotion values of all the agents E t +1 at time t + 1 can be computed according to theirrelative positions P t and emotions of the agents E t at time t . E t +1 = g ( E t , P t ) (2) This paper mainly discusses the influence of antagonisticemotions on agents’ behaviors, whose purpose is to com-pute and update the status of all the agents at differenttime steps according to their emotions and roles. The crowdemotion is fully integrated into crowd behavior simulation,also with considering the confrontation between agentswith different roles, such as civilians, activists, and cops.Given the positions P t , the emotions E t , and the roles R t of all the agents at time t , our crowd simulation modelACSEE ( P t , E t ) estimates the positions P t +1 , the emotions E t +1 , and the roles R t +1 of all the agents at next time stepas Equation 3. { P t +1 , E t +1 , R t +1 } = ACSEE ( f ( P t − ) , g ( E t − , P t − ) , R t )= ACSEE ( P t , E t , R t ) (3) ODEL
We present a novel A ntagonistic C rowd behavior S imulationmodel (ACSEE) based on E motional contagion and E volutionary game theories. Our model consists of threeimportant modules: antagonistic emotional contagion, an-tagonistic evolutionary gaming, and behavior control. Theantagonistic emotional contagion method is designed bycombining the enhanced SIS and game approaches. Usingthe antagonistic emotions of agents, we define their deter-rent forces in Section 4.4. The enhanced evolutionary game theoretic approach is determined based on the deterrentforces of agents. Our ACSEE model computes the behaviorof each agent by modeling the influence from antagonisticemotional contagion and evolutionary game theories. Theflowchart of our ACSEE model is presented in Figure 1. For convenience, the important parameters used in theACSEE model and their descriptions are listed in Table 1.
In this section, we mainly describe the role of different kindsof agents and the assumptions we formulated.
Crowd violence incidents are often caused by some serioussocial contradictions, where a certain amount of activistschallenge or break the normal and peaceful social orderor stability in different ways of violence such as large-scale gathering, group activities, and physical conflicts. Weclassify the agents in the crowd under such situations ascivilians, activists, or cops based on their roles according to[12], [63].Civilians are neutral agents in the environment and poseno danger to the central authority. In general, civilians arevulnerable groups and do not participate in confrontation.The cops do their best to protect civilians while the activistspersecute them. However, civilians may change their roles ifconditions are favorable to express their anger and frustra-tion publicly. For example, because of the instigation of thesurrounding activists, the civilians may turn into activiststo participate in the riot. Activists aim to create havoc andfuel the ongoing unrest while avoiding being defeated bycops. Cops maintain public order by suppressing activistsand play a key role in preventing terrorist attack. In real-world scenarios, cops and activists can represent any two an-tagonistic groups [13]. Civilians can also represent onlookersand neutral parties.
Antagonistic crowds arise for many complex influencingfactors. The simulation of antagonistic crowd behaviorsconsidering all the influencing factors is an insoluble prob-lem. From the observations of the real antagonistic crowdbehaviors, we formulate the following assumptions to makethis problem solvable. • Emotions of cops are positive while those of activistsare negative. Civilians are neutral agents. The pro-cess of emotional contagion can change their emo-tions. Cops with high positive emotions will makethe agents around them more positive. Activists withhigh negative emotions will make the agents aroundthem more negative. Civilians don’t actively affectthe emotions of surrounding agents [5]. • An agent can maintain a perceived range that iscentered around it. We regard the perceived rangeof an agent as a circular area with a fixed radius PR [5], [64]. OURNAL OF L A TEX CLASS FILES, VOL. X, NO. X, NOVEMBER 2019 6 • Agents use different strategies to interact with theiropposing agents. Agents’ strategies refer to the ac-tions taken during the games. According to the en-countered situation, activists and cops can adopt oneof two different strategies: cooperation or defection[12], [65]. The cooperation strategy of activists meansaccepting peaceful settlements and running awayfrom the cops. The activists with defection strategywill revolt aggressively and instigate civilians torevolt. The cops with cooperation strategy keep awayfrom large gatherings of activists to protect civilians.The defection strategy of cops means pursuing ac-tivists. • The agent may be classified as death. Dead agentsare subdued by their opponents and pose no threatany more. It doesn’t mean biological death.
Since emotion has an important influence on people’s be-havior decision-making, accurate emotion modeling is es-sential and fundamental for a crowd simulation model[5]. In this section, we present our antagonistic emotionalcontagion module. Emotions in our model incorporate theantagonism between agents in different roles. e i denotes theemotion of agent i . e i ∈ ( − , and e i (cid:54) = 0 . There are twodifferent types of emotion: positive emotion and negativeemotion. When the emotion value is greater than 0, theemotion is positive. The higher the emotion value of anagent, the more positive his/her emotion. When the emotionvalue is less than 0, the emotion of the agent becomesnegative. The lower the emotion value of an agent, the morenegative his/her emotion. When an emotion value is closerto 0, the agent is regarded as being in a peaceful state and heor she tends to be conservative. The descriptions of differentemotion values of different roles are listed in Table 2.TABLE 2: The descriptions of different emotion values ofdifferent roles Descriptions of emotion EmotionCloser to Closer to Closer to − Roles Cops high morale;brave in subduingthe activists peaceful low morale;afraid of activists;dare not to fight with activistsActivists escape from copsnot challenging cops peaceful arrogant and attack copsCivilians brave;not fear of activists peaceful uneasy, suffering,fear of activists, and obeyed
In such an antagonistic game scenario, individuals willbe influenced by external and internal stimuli. Externalstimuli mainly come from the external environment andare often accepted by individuals passively. Internal stimulicome from the subjective perception and judgment of indi-viduals by themselves. Both the internal and external stimuliin the antagonistic scenarios are able to produce emotions,so the emotion of an agent e i consists of two parts. The firstpart is the external emotion e exi , which is influenced bysurrounding agents. The second part is the mental emotion e mei [66], which is determined by an agent’s own subjectiveconsciousness. Therefore, the final emotion value is definedas follows [67], [68]: e i = e exi + e mei (4) Our method for calculating external emotion is inspired bythe emotional contagion model in [15]. An agent can beaffected by others in his or her perceived range. The increasein the strength of external emotion of agent i ( ∆ e exi,j ( t ) )received from agent j at time t is defined as: ∆ e exi,j ( t ) = [1 − − L )) ] × e i ( t ) × A j,i × B i,j (5)where L represents the distance between agent i and j , e i denotes the emotion of agent i , A j,i is the intensity ofemotion received by i from sender j , and B i,j is the intensityof emotion which is sent from i to receiver j .Civilians can only passively receive the emotional conta-gion from surrounding agents and cannot actively influenceothers. The increment of external emotion of agent o attime t is denoted as ∆ e exo ( t ) . ∆ e exo ( t ) includes emotionalinfluences received from all the cops and activists in theperceived range of agent o . ∆ e exo ( t ) is defined as follows: ∆ e exo ( t ) = k (cid:88) i =1 ∆ e exo,c i ( t ) + n (cid:88) j =1 ∆ e exo,a j ( t ) (6)where ∆ e exo,c i ( t ) and ∆ e exo,a j ( t ) denote the increase in thestrength of the external emotion transmitted from cop c i and activist a j to agent o . Each agent establishes game play with agents in the oppos-ing group who are in his or her perceived range. Becausecivilians are neutral members and remain peaceful, weassume that no game interaction will occur between civilianagents. The benefits of each game are determined accordingto the method outlined in Section 4.4. Mental emotion isdefined as the difference between the benefits of two gamesand the mental emotion of civilians is a constant [69].The difference between the benefits of the games at time t and t − for agent i is denoted as ∆ bene i ( t ) = bene i ( t ) − bene i ( t − . The threshold that leads to emotional fluctua-tions is δ . The relationship between the increment of mentalemotion and the difference between the benefits at time t isdefined by: ∆ e mei ( t ) = rand ( − . , . , | ∆ bene i ( t ) | < δ . δ +exp( δ/ ∆ bene i ( t )) , ∆ bene i ( t ) ≥ δ − . δ +exp(∆ bene i ( t ) /δ ) , ∆ bene i ( t ) ≤ − δ (7)In Equation 7, | ∆ bene i ( t ) | < δ means that the differencebetween benefits fails to reach the emotional fluctuationthreshold δ . Therefore, there is little change in the emotionof agent i . In this case, the mental emotion value is a randomnumber on the interval (-0.01, 0.01). ∆ bene i ( t ) ≥ δ meansthat the benefit at time t is higher than that at time t − . Thebenefit increase makes the cops more positive and activistsmore negative. ∆ bene i ( t ) ≤ − δ means that the differencebetween the benefits of time t and t − is higher than theemotional fluctuation threshold δ . The benefit at time t islower than that at time t − . The benefit decrease makescops more negative and activists more positive. OURNAL OF L A TEX CLASS FILES, VOL. X, NO. X, NOVEMBER 2019 7
Our emotion updating method for agents is presented inFigure 2. The mental and external emotions of each agentare updated according to the evolution of the games andchanges in agents’ locations. The external emotion of anagent is determined by the emotional contagion (externalstimulus) of surrounding cops and activists. The differencesbetween the benefits of games (internal stimulus), which isdefined in Section 4.3.2, lead to the changes in the mentalemotions of cops and activists.Fig. 2: Emotion updating method. The benefit of thegame between cops and activists is the internal stimulus,which leads to the changes in mental emotions. Emotionalcontagion among different kinds of agents is the externalstimulus, which leads to the changes in external emotions.The increment of the total emotion ( ∆ e o ( t ) ) of agent o attime t is defined as follows: ∆ e o ( t ) = ∆ e exo ( t ) + ∆ e meo ( t ) (8)For each time step, the total emotion value is updated.At time t , the total emotion value of agent o is defined asfollows: e o ( t ) = e o ( t −
1) + ∆ e o ( t ) (9) In our model an agent establishes game play with all theagents from the opposing group within his or her perceivedrange, according to game theory. When agents confront dif-ferent scenarios and situations, they adopt different strate-gies and get varying benefits. They aim to maximize theirbenefits and minimize casualties according to the currentsituation. In this subsection, we present the evolutionarygame theoretic module of our model, which is used toanalyze the strategies and benefits of agents.At first, agents estimate surrounding situations based onthe deterrent forces of the agents in their perceived range.Deterrent force is a kind of power by which an agent canbeat his or her opponents and is closely related to the agent’sbehavior. Emotion plays a crucial role in agents’ deterrentforces [70]. The deterrent force of agent i is defined in thefollowing equation: f i ( t ) = sin (cid:16) | e i ( t ) | · π (cid:17) (10) where e i ( t ) is the emotion of agent i at time t . The morepositive or negative the emotion of an agent is, the greaterthe deterrent force the agent possesses [70]. The total deter-rent forces are defined as follows: F i ( t ) = (cid:88) k ∈ A f k ( t ) (11) ˆ F i ( t ) = (cid:88) ˆ k ∈ ˆ A f ˆ k ( t ) (12)where the set A denotes agents of the same type in theperceived range of agent i and the set of the opposing agentsin the perceived range of agent i is ˆ A .The situation is defined according to the difference be-tween the total deterrent forces of cops and activists per-ceived by agent i , which is expressed in Equation 13, asfollows. ∆ F i = F i ( t ) − ˆ F i ( t ) (13)Under different situations, the benefits gained during thegames are different. The benefit matrix is defined accordingto varying situations. In contrast, the benefit matrix definedin [12] is based on the number of cops and activists andassumes that the deterrent forces of all the agents are thesame. Instead, we define the benefit matrix based on thedeterrent forces of cops and activists. We fully account forthe differences between the deterrent forces of all the agents,which conforms to real-world scenes. The benefit matrixcorresponding to different situations is shown in Table 3.TABLE 3: Benefit matrix of cops and activists. ∆ F denotesthe situations of cops and activists. ∆ F > means that thetotal deterrent force of the cops is higher than that of theactivists. ∆ F < and ∆ F = 0 are defined in a similarway. Activists and cops can adopt two different strategies:cooperation or defection. We list the benefits of cops andactivists corresponding to different situations. For example,the ratio of the benefits of the cops using a cooperationstrategy to the activists using a cooperation strategy is 1:4when ∆ F > . The ratio of the benefits of the cops usinga cooperation strategy to the activists using a defectionstrategy is 2:2 when ∆ F > [12] Situations Benefit Strategy of activistsCooperation Defection ∆ F > Strategyofcops Cooperation 1,4 2,2Defection 3,3 4,1 ∆ F < Cooperation 4,1 3,3Defection 2,2 1,4 ∆ F = 0 Cooperation 3,3 0,5Defection 5,0 1,1
When the total deterrent force of the cops is higherthan that of the activists ( ∆ F > ), if both groups adopta strategy of cooperation, cops miss an opportunity to makearrests. Compared with activists, cops reap fewer benefits. Ifboth groups defect, cops gain the upper hand because theyhave a higher total deterrent force and therefore reap morebenefits. If cops cooperate and activists defect, both groups’ OURNAL OF L A TEX CLASS FILES, VOL. X, NO. X, NOVEMBER 2019 8 benefits remain relatively neutral. Cops should defect toconfront activists while activists should cooperate to avoidchallenging cops and inviting casualties. If cops defect andactivists cooperate, cops exert dominance over activists andactivists avoid direct conflict. Therefore, both groups obtainbenefits. When the total deterrent force of cops is less than orequal to that of activists ( ∆ F < or ∆ F = 0 ), their benefitsare defined similarly.After a game, the strategies of cops and activists areupdated according to the results of that game. Each agent isdefined by a binary string. This string encodes the strategybits in different situations. This string suggests the strategiesan agent should adopt when ∆ F = 0 , when ∆ F > , andwhen ∆ F < . Then the effectiveness or benefit of eachstrategy is calculated. The more beneficial strategy is chosenand it will be passed on to the offspring in an attempt tocreate a better strategy. The behavior control method of agents is determined byantagonistic emotional contagion and evolutionary gametheoretic approaches. In this section, we present some rulesabout how agents determine their positions at the next timestep and their living states.Agents determine their positions at the next time stepbased on the cellular automaton model [15]. A cellularspace of M × N cells is defined and each agent occupiesone cell. At each time step, agents choose to move to theirneighboring cells or stay still.Whether an agent moves or not depends on the deterrentforces exhibited by his or her neighboring agents. For a copor an activist, this is divided into the following possiblecases according to real-world videos: • If the total deterrent force of agents in the opposinggroup is higher than that of agents of the same typein agent i ’ s neighboring cells, he or she has to move.The moving direction of agent i is determined bythe expected benefits of his or her neighboring cells.At first, the neighboring cells around agent i will bechecked to find the empty ones (an empty cell meansthat there is not an agent in it). Then the expectedbenefits of all the empty cells are calculated. The cellwith the highest benefit is the position to which agent i will move. • Next we consider the situation where the total de-terrent force of the opposing agents is less than thatof agents of the same type in agent i ’s neighboringcells. If agent i ’s strategy is defection, he or she willmove to the nearest opposing agent (i.e. attack theopposing agent). If agent i ’s strategy is cooperation,he or she will stay away from opposing agents andmove to the nearest civilian. If agent i is a cop, he orshe will protect the civilian. If agent i is an activist,he or she will attack the civilian. In this case, agent i may also choose to stay still. • Agent i with no neighbors chooses to move. Themoving direction is the same as the situation wherethe total deterrent force of the opposing agents is lessthan that of agents of the same type. • Civilians move to safer positions where there aremore cops around them.The agent with a defection strategy attacks his or heropponents. The agent may be dead. A dead agent in thiscase means being subdued by his or her opponents andtherefore posing no threat to these opponents. It doesn’tmean real death. At each time step, the death probability ofeach agent is calculated and denoted as P die . In contrast tothe definition in [12], which is based on the number of copsand activists, we define P die based on the total deterrentforces of cops and activists. P die = 1 − exp (cid:32) ln . · (cid:80) F i (cid:80) (cid:95) F i (cid:33) (14)where (cid:80) F i represents the total deterrent force of agents ofthe same type, and (cid:80) (cid:98) F i represents the total deterrent forceof his or her opponents in the cells neighboring agent i . (cid:80) F i (cid:80) (cid:95) F i denotes the total deterrent force of the cop-to-activistratio within the perceived range of agent i . ln . is set toensure a plausible value ( P die = 0 . ) when (cid:80) F i = (cid:80) (cid:95) F i [12], [71].Each agent has an early warning threshold T warn . Whenthe value of P die exceeds the threshold T warn , the valueof warn time increases by 1. When the value of warn time exceeds the threshold T warn time , the agent will die. Becausethe endurance of each agent is different, the values of thethresholds T warn and T warn time are also different for eachagent. MPLEMENTATION AND PERFORMANCE
We have implemented our model using Visual C++ to sim-ulate antagonistic crowd behaviors based on Unity3D . Thecomputing environment is a common PC with a quadcore2.50 GHz CPU,16 GB memory, and an Nvidia GeForce GTX1080 Ti graphics card.TABLE 4: List of parameter values used in our simulation
Scenario Number of agents Size of 2-D Grid Ta c Tc a EmotionCivilians Activists Cops Civilians Activists CopsNo.1:Activists attackcivilians 80 50 40 20 ×
20 squares 0.1 -0.5 0.1 -0.5 0.5No.2:Role transitions 80 50 70 20 ×
20 squares 0.1 -0.5 0.1 -0.5 0.5No.3:Cops encirclingactivists 80 50 70 20 ×
20 squares 0.1 -0.5 0.1 -0.5 0.5No.4:Real-world 1 10 50 30 20 ×
20 squares 0.1 -0.5 0.1 -0.5 0.5No.5:Real-world 2 80 50 30 20 ×
20 squares 0.1 -0.5 0.1 -0.5 0.5No.6:Real-world 3 3 14 40 20 ×
20 squares 1 -1 0.1 -0.1and-0.3 0.9No.7:Real-world 4 0 30 100 40 ×
40 squares 1 -1 0 -0.2 0.8No.8:Real-world 5 100 30 100 40 ×
40 squares 1 -1 0.1 -0.9and-0.2 0.9No.9:ACSEE vs. CVM 80 50 30 20 ×
20 squares 0.1 -0.5 0.1 -0.5 0.5
We run a series of experiments involving varying rolenumber ratios in outdoor scenarios. The parameter val-ues in different scenarios used in the simulation runs arelisted in Table 4. The perceived range PR of agents is 10, T warn ∈ [0 . , . , and T warn time ∈ [8 , . Figures 3, 6, OURNAL OF L A TEX CLASS FILES, VOL. X, NO. X, NOVEMBER 2019 9 (a) (b) (c) (d)(e) (f) (g) (h)Fig. 3: The numbers of three types of agents at different time steps according to different initial R ca (the ratio of cops toactivists): (a) R ca is 0 (0 cops), (b) R ca is 0.6 (30 cops), (c) R ca is 0.8 (40 cops), (d) R ca is 1 (50 cops), (e) R ca is 1.2 (60 cops),(f) R ca is 1.4 (70 cops), and (g) R ca is 1.6 (80 cops). (h) Active ratio curves for different initial R ca s . (a) shows a steep dropin the number of civilians. The number of activists remains the same because there are no cops to fight with the activists.We can see from (a) to (g) that the number of dead activists increases as R ca increases. When R ca is 1.2, all the activistshave been subdued by cops. The time required for all the activists to be subdued by cops decreases as R ca increases. Thecivilian survival time lengthens and there are more surviving civilians as R ca increases. We can see that there is an initialrise in the number of civilians in (f) and (g) because the total deterrent force of the cops is much higher than that of theactivists. Some activists change their roles (from activist to civilian). (h) shows the overview of active ratios (ratios of theactivists to the sum of the activists and civilians) corresponding to different R ca s . An inverse relationship between theactive ratio and the R ca is presented. Therefore, increasing the ratio of cops can help subdue activists.7, 9, and 12 report the results of 200 runs. The average ofthe 200 runs is the final result. We investigate the effect ofvarying role number ratios on the crowd violence results(in Section 5.1). By analyzing the simulation results, we findthat our model can account for many emergent phenomena(discussed in Section 5.3). Next, we study how differentimportant factors influence crowd violence. In Section 5.4we show the impact of emotional contagion on the resultsof crowd violence. We compare the different simulationresults with or without considering emotional contagion.In Section 5.5, the relationship between the deterrent forceand the strategy is revealed. The strategies adopted by eachagent in different situations are analyzed. In Section 5.6,our simulation results are compared with the real-worldvideos and the simulation results generated by differentmodels. The real-world videos are chosen from the publicdataset and real antagonistic events. More details aboutcomparisons can be seen in the supplementary video. Userstudies are performed to evaluate our method in Section 5.7. We investigate the effects of varying ratios of agents indifferent roles on the results of crowd violence. By analyzinga large number of real-world antagonistic videos, we selectseveral representative values of R ca (the ratio of cops to Fig. 4: The positions of all the agents at the 168th frame( R ca is 1). The green, purple, and blue circles representcivilians, activists, and cops, respectively. The stronger thecolor intensity of a circle, the higher the deterrent force ofthe agent.activists). In this section the initial R ca s are 0, 0.6, 0.8, 1, 1.2,1.4, and 1.6. The initial numbers of civilians and activists are80 and 50, respectively. The initial emotion values of all theactivists and cops are -0.5 and 0.5, respectively.We can learn from Figure 3 that the number of differentkinds of agents determines the outcome of crowd violenceto some extent. When we increase the ratio of cops, they can OURNAL OF L A TEX CLASS FILES, VOL. X, NO. X, NOVEMBER 2019 10 (a) (b) (c)(d) (e) (f)(g) (h) (i)Fig. 5: Some fascinating emergent phenomena our model uncovers. (a), (b), and (c) are the simulations of activists attackingcivilians. (d), (e), and (f) are the simulations of role transitions. (g), (h), and (i) are the simulations of cops encircling activists.The green, purple, blue, and grey circles are civilians, activists, cops, and dead agents, respectively. The stronger the colorintensity of a circle, the higher the deterrent force of the agent.subdue activists quickly, stabilize the situation, and reducecivilian casualties. When R ca is 1, it means that the initialtotal deterrent force of the cops is equal to that of theactivists. Both cops and activists have the same probabilityof winning. However, in the end, the cops fail which meansthat all the cops are subdued by the activists. We offer adetailed explanation in the following analysis.Figure 4 shows the positions of all the agents at the 168thframe when R ca is 1. At this time step, the numbers of copsand activists are the same. Activists with strong deterrentforces are mainly located in the upper right corner of thescene. Some cops with weak deterrent forces are amongthe crowd of activists (upper right corner of the scene).Some surrounding civilians turn into activists because ofthe incitement of the activists with high deterrent forces.The cops with strong deterrent forces are in the upper leftcorner of the scene, which makes it difficult for them torescue the cops in the upper right corner. When the copswith weak deterrent forces are killed by the activists withstrong deterrent forces, there are fewer cops left. Finally, allthe activists get together to attack the remaining cops andthe activists win.We learn from Figure 4 that activists participate incollective behavior to create regions of low cop-to-activistratios, which reduces the chances of activist death. Theconglomeration of scattered activists into small groups andthe amalgamation of small groups into large ones makeit difficult to wipe them out [71]. Although the numberof agents determines the outcome of crowd violence to a certain extent, some take advantage of agents’ spatialdistributions to affect the outcome of crowd violence. In this section we analyze the impact of agent parameterson the result of crowd violence. We choose two parameterswhich have great influences on the simulation results: PR (the radius of perceived range) and A or B in Equation5. In Equation 5, A j,i is the strength attribute by whichan emotion is received by i from sender j and B i,j is thestrength attribute by which an emotion is sent from i toreceiver j . We discuss the relationship between active ratios(ratios of activists to the sum of the activists and civilians)and the parameters. The initial numbers of the civilians,activists, and cops are 80, 50, and 70, respectively. The initialemotions of the civilians, activists, and cops are 0.1, -0.5, and0.5, respectively. The initial total deterrent force of the copsis higher than that of the activists.We show active ratios according to various values of PR in Figure 6. We assume that all individuals have the same PR . When PR of agents are different, the results of activeratios are also different. With the increase of PR , agents canmore accurately estimate the situations. Therefore, the hightotal deterrent force of cops plays a role in defeating theactivists. The active ratio decreases with the increase of PR .In addition, we also discuss the relationship betweenthe values of A or B and active ratios in Figure 7. A and OURNAL OF L A TEX CLASS FILES, VOL. X, NO. X, NOVEMBER 2019 11
Fig. 6: Active ratios corresponding to different
PRs (theradius of perceived range). The active ratio decreases withthe increase of PR . When PR is greater than 10, the activeratio tends to be stable. We choose PR = 10 in this paper.Fig. 7: Active ratios corresponding to different values of A .The active rate decreases with the increases of A . When A is greater than 0.8, the active ratio tends to be stable. Wechoose A = 0 . in this paper. B are very important parameters for emotional contagionin Equation 5. The values of them are positively correlatedwith the values of emotional contagion. We suppose all thestrength attributes of A between any two individuals are thesame and those of B between any two individuals are thesame. The relationship between the active ratio and A is thesame as that between the active ratio and B . We take A asan example to discuss this relationship. As the value of A increases, agents’ emotions also increase and the differencebetween the total deterrent forces of cops and activists isgreater. Due to the high deterrent force of cops, more andmore activists are subdued by cops. Therefore when thevalue of A increases, the active rate decreases. Our model can simulate many emergent phenomena thatconform to real-world scenes. Figures 5a, 5b, and 5c show Fig. 8: Simulation of antagonistic crowd behavior using 3Dcharacter models.that activists with strong deterrent forces attack civilians. Atthe top left corner of this scene, there are a lot of civilians.Many activists are at the lower right corner of Figure 5a.Agents of the same type gather together according to [72].Therefore, it is reasonable that agents of the same typegather together. The number of activists is larger than that ofthe cops. We can see from Figure 5a that the total deterrentforce of the activists is stronger than that of the cops.Activists attack civilians (Figure 5b) and more and morecivilians die (Figures 5b and 5c).At the lower right corner of Figure 5d, there are plenty ofcops with high deterrent forces near the highlighted activistand his deterrent force is weak. If he continues to resist,he will die. He therefore transitions roles (from activistto civilian). When all the other activists die, he survives(Figure 5f). When the number of surrounding activists islarge enough, it may impel civilians to become activists [73].In Figure 5g, there are many more cops than activists.The total deterrent force of the cops is much stronger thanthat of the activists. At first, the cops divide the activistsinto two groups (Figure 5g) and prevent the activists fromgathering together to form a larger group. Next, the copseliminate these two groups of activists individually. Thereare some activists in the left side of the scene (the firstgroup). Cops encircle these activists and more activists willdie. When all the activists on the left side are eliminated,the cops return to the activists on the right side of the scene(the second group). These activists are encircled by the cops.Finally, all the activists are killed by the cops and the copswin.Figure 8 shows the simulation of antagonistic crowdbehavior using 3D character models. The activists with highdeterrent forces on the left of the scene are not afraid ofthe cops with low deterrent forces. In the upper left cornerof the scene, the activists with high deterrent forces attacka civilian. The civilian runs away from the activists. In themiddle and lower part of the scene, the cop with a highdeterrent force attacks the activist and he runs away fromthe cop.
The impact of emotional contagion on the results of crowdviolence is presented in Figure 9. The initial numbers ofcivilians, activists, and cops are 80, 50, and 40, respectively.In Figure 9a, the initial emotion values of the cops are higherthan those of the activists. At the 53rd time step, the number
OURNAL OF L A TEX CLASS FILES, VOL. X, NO. X, NOVEMBER 2019 12 (a) (b)Fig. 9: The changes in the number of civilians, activists,and cops: (a) considering emotional contagion and (b) notconsidering emotional contagion.(a) (b)Fig. 10: Simulation results (a) considering emotional con-tagion and (b) not considering emotional contagion. In (a)the deterrent forces of the agents are different and the sametypes of agents are more likely to gather together. In (b) thedeterrent forces of all the agents are the same and the sametype of agents are dispersed.of activists is zero. All the activists have been wiped out bythe cops. At first the number of civilians increases becausethe total deterrent force of the cops is much higher thanthat of the activists. Some activists change their role (fromactivist to civilian). In Figure 9b, all the agents withoutemotion have the same deterrent force. At the 41st time step,the number of cops is zero and the activists win.We can learn from Figure 9 that the emotion module ofour model can describe the differences observed betweenthe agents. In our model, the deterrent forces of all theagents are different according to their emotions. The greaterthe absolute value of an agent’s emotion, the higher thedeterrent force of that agent. Although the number of agentsis small, it is still possible to overcome a larger group ofopponents by improving the emotions and deterrent forcesof them. Therefore, our model can simulate situations inwhich agents overcome their more numerous opponents.Figure 10 shows simulation results with and withoutconsidering emotion. In Figure 10a the deterrent forces ofthe agents are different. The stronger the color intensity ofa circle, the higher the deterrent force of the agent. Becauseof emotional contagion, the same types of agents are morelikely to gather together, which is similar to what happens inreal-world scenarios [72]. In Figure 10b the deterrent forcesof all the agents are the same and the same type of agentsare more dispersed.Figure 11 shows the heat maps of antagonistic emotion. (a) (b)(c) (d)Fig. 11: The heat maps of antagonistic emotion: (a) heatmap at the 5th time step, (b) heat map at the 17th time step,(c) heat map at the 27th time step, and (d) heat map at the42th time step. The red area represents the emotions of thecops. The blue area represents the emotions of the activists.The stronger the color intensity, the larger the value of theemotion.Fig. 12: Cooperation ratios of cops and activists at differenttime steps: (a) when the total deterrent force of the activistsis higher than that of the cops; (b) when the total deterrentforce of the activists is equal to that of the cops; (c) when thetotal deterrent force of the activists is less than that of thecops.Different colors represent different types of agents’ emo-tions. The stronger the color intensity, the larger the valueof the emotion. At first, the emotions of the cops and theactivists are very weak. Later, as a result of the confrontationbetween cops and activists, both types of emotions increase.Since the initial emotions of the cops are higher than thoseof activists, the overall emotional scope of the cops becomeswider and wider and that of the activists becomes smallerand smaller. Finally, all the activists are wiped out by thecops and there is no blue area on the map.
We present the relationship between deterrent force andstrategy selection in this subsection. We analyze the strat-egy (cooperation or defection) adopted by each agent withrespect to their different deterrent forces.Figure 12 shows the overview of cooperation ratios (theratio of the number of agents adopting a cooperation strat-egy to the total number of this type of agents) in relation to
OURNAL OF L A TEX CLASS FILES, VOL. X, NO. X, NOVEMBER 2019 13 different deterrent forces. When the total deterrent force ofthe activists is higher than that of the cops (Figure 12a),most of the cops adopt a cooperation strategy to avoidcausalities and conserve their fighting forces. When the totaldeterrent force of the activists is equal to that of the cops,the cooperation ratios of cops and activists are almost thesame from the 5th time step to the 45th time step. After the45th time step, the cops defeat the activists. More and morecops adopt defection strategy, the cooperation ratio of thecops decreases, and the cooperation ratio of the activistsincreases. When the total deterrent force of the activistsis less than that of the cops, the cooperation ratio of theactivists is higher than that of the cops.In summary, the agent with a higher deterrent force ismore likely to adopt a defection strategy and the agent witha lower deterrent force is more likely to adopt a cooperationstrategy.
To validate our approach, we compare our simulation re-sults with those generated by the CVM [12] and ABEC [74]models and real-world videos. Main goal of our model isto predict trends of crowd movements in these situationswithout explicitly modeling the trajectory of a particularindividual. Simulation results obtained by our model areclosest to the real-world scenes in the overall trends ofcrowd movements.The real scenes shown in Figures 13a and 13c are chosenfrom the public web dataset [75]. The real scenes of Figures13e, 13g, and 13i are chosen from real antagonistic incidentson YouTube. For the real-world scenarios in Figure 13, weuse different colors to distinguish different roles of indi-viduals. The green, purple, and blue circles and cylindersrepresent civilians, activists, and cops, respectively. The redarrows are the dominant paths of crowd movements. Copsand activists in this case represent two opposing groups.Civilians in this case represent onlookers and neutrals.There are no deaths of activists or cops in these scenes.The scenes can be simulated by increasing the values ofthe thresholds of T warn and T warn time for our model. Theparameter values used in the simulation runs are listed inTable 4. More details can be seen in the supplementaryvideo.We use the dominant path and entropy metric to quan-titively evaluate our simulation results. Dominant pathis defined based on collectiveness of crowd movements.Collectiveness, which indicates the degree to which indi-viduals acting as a unit, is a fundamental and universalmeasurement for various crowd systems, including crowdsin antagonistic scenes [76]. Individuals locally coordinatetheir movements and behaviors with their neighbors, andthen the crowd is self-organized into collective movementswithout external control. The method proposed in [77] isused to calculate the collectiveness of our simulation results.When the collectiveness of individual movements in a cer-tain area is significantly higher than that of surroundingarea, a small group of agents with similar movements isformed. The center of the group is determined according tothe average of the positions of all the agents in this group.The trajectory of the group center forms its dominant path (a) (b)(c) (d)(e) (f)(g) (h)(i) (j)Fig. 13: Comparisons between real scenes and our simula-tion results. (a), (c), (e), (g), and (i) are five real antagonisticscenes. (b), (d), (f), (h), and (j) are our corresponding simula-tion results generated by our ACSEE model. The red arrowsare the dominant paths of crowd movements.and can be treated as the movement trend of the wholegroup. Using this method, we can get the dominant paths ofthe real-world videos. We use entropy metric [78], angularerror (AE) [79], and inter-group distance metric (IDM) [80]to evaluate our crowd simulation results. They are usedto evaluate the errors of trajectories, movement directions,and distances between each group, respectively. These threeevaluation methods complement each other, which are usedto evaluate our results more comprehensively.An entropy metric [78] is adopted to evaluate the errorbetween the dominant paths of simulation results and thatof the real-world videos. A lower entropy value implies ahigher similarity between the simulation results and thereal-world scenarios. Table 5 shows the entropy metric of OURNAL OF L A TEX CLASS FILES, VOL. X, NO. X, NOVEMBER 2019 14 the simulation results achieved by the CVM, ABEC, andACSEE (ours) models on different scenarios in Figure 13.The simulation results obtained by our model conform tothe real-world videos best.The angular error (AE) [79] between the movementdirection of the simulation result ( V x , V y ) and that of theground-truth ( V xgt , V ygt ) is also used to evaluate our crowdsimulation method. This AE is defined in Equation 15.The inter-group distance metric (IDM) [80] compares thedifference in the average distances between each pair ofclustered agents. Tables 6 and 7 show the AE and IDM ofour simulation results on different scenarios in Figure 13.Tables 5, 6, and 7 show that our method consistentlyoutperforms the CVM and ABEC models. Compared withthe CVM model, our ACSEE model considers the agents’ an-tagonistic emotions and accurately describe the differencesbetween agents’ deterrent forces. Compared with the ABECmodel only considering emotional contagion in antagonisticscenarios, our method considers not only antagonistic emo-tion, but also the relationship between antagonistic emotionand evolutionary game theory. The agent is able to choose amore reasonable strategy according to the situation. AE = cos − (( V x · V xgt + V y · V ygt ) / (cid:112) V x + V y (cid:112) V xgt + V ygt ) (15) TABLE 5: Entropy metric for our simulation algorithms ondifferent scenarios from Figure 13. A lower entropy valueimplies higher similarity between the simulation results andthe real-world scenarios. Simulations with an entropy scoreless than . are considered very visually similar to thesource data and those with a score greater than . arevisually very different [78]. Scene No. 2 (Figure 13c) is toolarge and chaotic and the collectiveness of crowd movementis not so obvious. Therefore, the entropy value of Scene No.2 is larger than . , but this value is far less than . . Scene No. 1 2 3 4 5ACSEE
ABEC 0.232 1.320 0.268 0.139 0.180CVM 0.259 1.369 0.270 0.151 0.187
TABLE 6: AE for the simulation algorithms on differentscenes from Figure 13. A lower value for AE implies highersimilarity with respect to the real-world crowd videos. Wereport mean and variance of AE at different time steps.
Scene No. 1 2 3 4 5ACSEE
ABEC 0.214/0.155 0.463/3.027 0.999/12.822 0.500/0.002 0.558/0.006CVM 1.329/20.709 1.579/1.500 1.464/14.452 0.948/0.007 0.856/0.062
The simulation result generated by our model is com-pared with those of the CVM [12] and ABEC [74] models inFigure 14. More details can be seen in the supplementaryvideo. In contrast to the CVM and ABEC models, ourmethod can better quantify the differences of the deterrentforces of all the agents. Besides, we also integrate antag-onistic emotional contagion into evolutionary game theory TABLE 7: IDM (pixel) for our simulation algorithms ondifferent scenes from Figure 13. Lower numbers are better.
Scene No. 1 2 3 4 5ACSEE
ABEC 31 32 21 18 35CVM 40 42 32 49 63 to estimate situations of antagonistic scenes more accurately,which helps agents make reasonable strategies in the games.Therefore our simulation result is the most similar to thereal-world scenario.
In this section we describe user studies conducted to demon-strate the perceptual benefits of our ACSEE model com-pared to other models in simulating antagonistic crowdbehaviors.
Experiment Goals & Expectations : Our main goal is tomeasure how close the crowd movement tendencies gener-ated using different models are to those observed in real-world videos. We hypothesize that in both studies, agentssimulated with our ACSEE model will exhibit overall moreplausible antagonistic crowd movements than other models.Therefore, participants will strongly prefer our model to theother models.
Experimental Design : Two user studies were conductedbased on a paired-comparison design. In each study, partic-ipants were shown pre-recorded videos in a side-by-sidecomparison of simulation results generated by differentmodels and a real-world video. In particular, we askedthe users to compare the crowd movement tendencies gen-erated by different crowd simulation models with thoseobserved in real-world videos. The studies had no timeconstraints and the participants were free to take breaksbetween the benchmarks. We encouraged the users to watchthese videos as many times as they wanted and finally givea stable score.
Comparison Methods : The first study compares ourACSEE model considering emotion with our model thatdoes not consider emotion. The second study compares ourmodel with the CVM [12] and ABEC [74] models.
Environments : We use outdoor scenarios without ob-stacles. In these scenarios, the green, purple, blue, andgrey circles are civilians, activists, cops, and dead agents,respectively.
Metrics : Participants were shown two pre-recordedvideos in a side-by-side comparison of the simulation resultand a real-world video. We asked the users to first watchthe real-world video and then rate each simulation resulton a scale of 1 - 5 in terms of the similarity of movementtendencies between the real-world video and the simulationresult video. A score of 1 indicates most dissimilar and ascore of 5 indicates most similar movement tendencies.
Results : There are 39 participants (20 female) with amean age of . ± . years in these studies. We measurethe mean and the variance of their scores and then computethe p-values using a two-tailed t-test. The means of their OURNAL OF L A TEX CLASS FILES, VOL. X, NO. X, NOVEMBER 2019 15 (a) Real scenario (b) CVM result(c) ABEC result (d) Our resultFig. 14: Comparisons between the real scenario and sim-ulation results of different crowd simulation models. Thesimulation result obtained by our model conform to the real-world video best.Fig. 15: User evaluation of simulation scenes. (a) Compari-son of simulation results considering emotion and withoutconsidering emotion. (b) Comparison of simulation resultsgenerated by the CVM, ABEC, and ACSEE models. Partic-ipants were asked to rate each simulation result on a scaleof 1 - 5 in terms of the similarity of movement tendenciesbetween the real-world videos and the simulation resultvideos. We can see from the results that our simulationresults are most similar to real-world scenarios.scores for our model without emotion and with emotionare . ± . and . ± . , respectively. The meansof their scores for the CVM, ABEC, and ACSEE modelsare . ± . , . ± . , and . ± . , respectively.The p-value for Figure 15a comparison is . e − . The p-values for the comparison of the CVM and ACSEE modelsand that of the ABEC and ACSEE models in Figure 15bare . e − and . e − , respectively. We observe thatthe antagonistic crowd behavior simulations generated byour ACSEE model score much higher than the other modelsat a statistically significant rate (p-value < ONCLUSION AND L IMITATIONS
We present a new model for antagonistic crowd behaviorsimulation integrated with emotional contagion and evolu-tionary game theory. Our approach builds on well-knownpsychological theories to present a comprehensive and an-tagonistic emotional contagion model. Based on the emo-tional calculation method, we propose the deterrent force todetermine the situation of cops and activists. According tothe situation, an enhanced evolutionary game theoretic ap-proach incorporated with antagonistic emotional contagionis determined. Finally, we present a behavior control deci-sion method based on the antagonistic emotional contagionand evolutionary game theoretic approaches.Our proposed model is verified by simulations. We in-vestigate the impact of different factors (number of agents,emotion, strategy, etc.) on the outcome of crowd violence.Our model is compared with real-world videos and previ-ous approaches. Results show that our proposed model canreliably generate realistic antagonistic crowd behaviors.However, our model still has several limitations. Al-though our simulation results are closer to the real-worldscenes in the overall trend of crowd movement, the antago-nistic emotions in a crowd violent scene cannot be obtaineddirectly or inferred accurately. One of the main reasons isthat the quality of most of the real videos is poor, sincethey are often captured by moving phones. At present,there is no effective methods to identify and quantify theemotion values of all the individual in such videos withpoor quality. Thus, the initial state of our model is setempirically according to real-world videos, which is time-consuming and not very accurate. In the future, we planto use the latest wearable equipment to collect these dataand provide a new method that can quickly and accuratelyobtain the initial state. Moreover, the strategies and benefitscalculated by our antagonistic evolutionary game theoreticapproach are the ideal situations. Game theory assumesthat all individuals are rational. However, some people inreal scenes are irrational and extreme, which doesn’t fullysatisfy the precondition of game theory. In practice, peopledo not necessarily adopt the optimal strategy because ofthe limitations of perception and other complex factors.Our current calculation result is optimal, which is onlyone of the possible results. In fact, it is impossible for allsimulation results to be consistent with the real results. Wewill continue to improve our prediction results consideringmore actual situations of antagonistic crowds. At present,the behavior control in our model is proposed based onthe cellular automata [15]. Other more complex behavioralcontrol methods will be further considered.
CKNOWLEDGMENTS
This work was supported by National Natural ScienceFoundation of China under Grant Number 61672469,61772474, 61822701, 61872324, Program for Science & Tech-nology Innovation Talents in Universities of Henan Province(20HASTIT021, 18HASTIT020) and Youth Talent PromotionProject in Henan Province (2019HYTP022).
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Chaochao Li is a Ph.D candidate in the Schoolof Information Engineering of Zhengzhou Uni-versity, China, and his research interest is com-puter graphics and computer vision. He got hisB.S. degree in computer science and technologyfrom the School of Information Engineering ofZhengzhou University.
Pei Lv is an associate professor in School ofInformation Engineering, Zhengzhou University,China. His research interests include video anal-ysis and crowd simulation. He received his Ph.Din 2013 from the State Key Lab of CAD&CG,Zhejiang University, China. He has authoredmore than 20 journal and conference papers inthese areas, including IEEE TIP, IEEE TCSVT,IEEE TACACM MM, etc.
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Dinesh Manocha ∼ dm Hua Wang was born in 1982. She receivedher PhD degree in Computer Science fromthe Institute of Computing Technology, ChineseAcademy of Sciences, in 2015. She is currentlyan associate professor of Zhengzhou Universityof Light Industry, Zhengzhou, China. Her mainresearch interests include traffic animation andenvironment modeling.
Yafei Li is an assistant professor in the School ofInformation Engineering, Zhengzhou University,Zhengzhou, China. He received the PhD degreein computer science from Hong Kong BaptistUniversity, in 2015. He held a visiting position inthe Database Research Group with Hong KongBaptist University. His research interests spanmobile and spatial data management, location-based services, and urban computing. He hasauthored more than 20 journal and conferencepapers in these areas, including IEEE TKDE,IEEE TSC, ACM TWEB, ACM TIST, PVLDB, IEEE ICDE, WWW, etc.
Bing Zhou is currently a professor at the Schoolof Information Engineering, Zhengzhou Univer-sity, Henan, China. He received the B.S. andM.S. degrees from Xi’an Jiao Tong Universityin 1986 and 1989, respectively,and the Ph.D.degree in Beihang University in 2003, all incomputer science. His research interests covervideo processing and understanding, surveil-lance, computer vision, multimedia applications.