Crowd simulation has received increased attention in virtual reality, games, urban modeling, and pedestrian dynamics. One of the most important tasks in crowd simulation is to generate realistic crowd behaviors. Physical methods[1, 2], psychology principles[3, 4], or approaches from other relatively matured disciplines [5, 6] are leveraged into the crowd simulation to improve the similarity between simulation results and real-world crowd movements. As pointed out in , emotion has a great influence on crowd behavior and it often invokes an agent to implement either a positive or a negative behavioral response. Thus, the emotion modeling in crowd simulation is always the main focus in latest research work. However, the emotional aspects of antagonistic crowds behaviors among different roles of people are left unexplored . Analyzing the emotions of antagonistic crowds behaviors is indeed extremely important, as it can help us understand evolution process of antagonistic crowd behaviors and predict trends of crowd movement.
In this paper, we mainly deal with the problem of simulating antagonistic crowd behaviors. Such behaviors are associated with acts of violation and destruction and are typically carried out as a sign of defiance against a central authority or an indication of conflict between opposing groups . Our goal is to develop a new crowd model that can predict trends of crowd movement in these situations while ignoring the trajectory of a particular individual, discuss the conditions of winning and losing sides, and help to develop measures to quell incidents of crowd violence. Not only will such a method be useful for training police officers, but it could also predict the development trend of the antagonistic scenes and provide the strategic basis for controlling crowd violence incidents.
It is difficult to simulate realistic antagonistic crowd behaviors because of complex influencing factors. In practice, such behaviors are closely related to antagonistic emotion , i.e. the emotion between opposed groups, and evolutionary game theory [4, 9]. In the pursuit of more realistic antagonistic behaviors in virtual agents, antagonistic emotion simulation should be incorporated into crowd simulation models . Most prior crowd simulation models ignore antagonistic emotion and individuals’ antagonistic behaviors. Some empirical methods of modeling antagonistic behaviors are presented in the form of riot games , game theoretic models , and social networks. These methods are based on statistical spatial-temporal analysis and role-playing dynamics in crowds and can generate emergent social phenomena. Other models use evolutionary game theory to simulate the behaviors and interactions between different kinds of agents [9, 14]. Evolutionary game theory has successfully helped explain many complex and challenging aspects of biological and social phenomena in recent decades . Inspired by the idea that fitter biological organisms will tend to produce more offspring, evolutionary game theory provides us with the methodology to study strategic interactions among agents in incidents of crowd violence . There is considerable work on evaluating individuals’ emotions [16, 17]. Panic, for example, destroys an individual’s normal mental function, transforms the individual into an irrational state, and can lead to unpredictable abnormal behavior . Furthermore, Durupinar et al.  point out that agents’ emotions dominate their decision-making process in games and for other behaviors. However, the relationship between antagonistic emotion and antagonistic crowd behavior has not been fully explored . It is challenging to accurately model antagonistic emotions among agents in different roles because the antagonism is complex and changes constantly and dynamically . Moreover, prior methods do not consider the effect of antagonistic emotion on evolutionary game theory despite the fact that emotion influences an agent’s behavior significantly.
Recent advances in crowd simulation models attempt to simulate plausible human behavior by introducing psychological phenomena to virtual agents . Inspired by the psychological theory in , which shows the characterization and simulation of emotional contagion, these psychological phenomena effectively improve the reliability of simulations. In , an enhanced susceptible-infectious-recovered (SIR) model integrates emotional contagion with individual movement, and realistic emotions and behaviors in crowd during an emergency can be obtained. We propose many improvements to this enhanced SIR model  and test the antagonistic emotional contagion method among agents in different roles. Moreover, we combine emotional contagion and evolutionary game theories to propose an antagonistic crowd behavior simulation model.
Our main contributions include:
We propose an antagonistic emotional contagion method that considers the antagonism between agents in different roles. It is determined by combining the enhanced SIR and game approaches.
We integrate antagonistic emotions into evolutionary game to estimate the situation of the antagonistic scene more accurately, which helps individuals make reasonable decisions in the games.
Our model can generate simulation results that tend to be closer to the real-world scenes in the overall trend of crowd movement. We have implemented our model and tested it on several outdoor scenarios with varying ratios of different types of roles. Our simulation results are compared with the real-world videos and we evaluate the benefits of our model by performing user studies. Our results indicate that the behaviors of agents generated by our model are closer to real-world scenes in the overall trend of crowd movement than those seen in other methods.
The rest of this paper is organized as follows. We review related work in Section 2. We give preliminary in Section 3. We introduce our model in Section 4 and show it can be used to generate antagonistic crowd behaviors. We describe the implementation and highlight its performance on complex scenarios in Section 5. We also present results from our preliminary user studies in Section 5.
2 Related Work
In this section, we provide a brief overview of prior works in emotional contagion, evolutionary game theory, and crowd simulation.
2.1 Emotional contagion
The epidemiological susceptible-infectious-recovered (SIR) model  divides the individuals in a crowd into three categories: infected, susceptible, and recovered. The analysis of the spread of epidemic among these three groups has also been extended to other fields. In , the extended model is used to simulate the spread of rumors. Some researchers use the epidemiological SIR model in conjunction with other models to describe emotion propagation under specific situations. The cellular automata model is used to simulate the spread of infectious diseases in . In , the epidemiological SIR model is improved by combining it with the OCEAN model . In , a qualitatively simulated approach to modeling emotional contagion is proposed for large-scale emergency evacuation. These methods show that the effectiveness of rescue guidance is influenced by the leading emotions in a crowd. Moreover, in , the cellular automata model based on the SIR model (CA-SIRS) is used to describe emotional contagion in a crowd during an emergency.
A thermodynamic-based emotional contagion model is introduced by Bosse et al.  in the ASCRIBE system. The authors use a multi-agent-based approach to define emotional contagion within groups. Their study focuses on the emotions of a collective entity rather than the emotions of single individuals. Neto et al.  adapt the model of Bosse et al.  into BioCrowds and cope with different groups of agents. Tsai et al.  present an emotional contagion model that spreads the highest level of emotion to surrounding agents in their ESCAPES framework. In , dynamic emotion propagation is described from the perspective of social psychology, combining thermodynamic-based models and epidemiological-based models.
There is antagonism between agents in different roles in crowd violence incidents. These emotional contagion models can’t be directly applied to crowd violence scenes, but our antagonistic emotional contagion method can quantitatively characterize dynamic changes in the antagonistic emotions between different roles.
2.2 Evolutionary game theory
Evolutionary dynamics is characterized by the interplay of mutation, selection, and random drift . Evolutionary experiments in microbes provide powerful demonstrations of all these forces at work . In this subsection, we summarize some representative works about evolutionary game theory.
Evolutionary game theory has solved many biological problems. For example, in , genome-driven evolutionary game theory helps explain the rise of metabolic interdependencies in microbial communities.
Some researchers have applied evolutionary game theory to the recommendation system. Saab et al.  use classical and spatial evolutionary game theory as a possible solution to the Sybil attack in recommender systems. Li et al.  propose a new stability analysis of repeated games and evolutionary games based on a subset of Nash equilibrium.
Evolutionary game theory helps us understand the behavior of individuals. Huang et al.  present a model in which each mutation generates a new evolutionary game characterized by a benefit matrix with an additional row and an additional column. Evolutionary game theory is one of the most effective approaches to understanding and analyzing widespread cooperative behaviors among individuals . In , the combination of evolutionary game theory and graph theory provides an extended framework to investigate cooperative behavior in social systems. Quek et al.  focus on the development of a spatial evolutionary multiagent social network to study the macroscopic-behavioral dynamics of civil violence due to microscopic game-theoretic interactions between goal-oriented agents.
2.3 Crowd simulation
There is extensive work on interactive crowd simulation for games, animation, and virtual reality. This work includes multi-agent simulation techniques for computing collision-free trajectories and navigation based on social forces , rule-based methods , cellular automata models , geometric optimization , vision-based steering , personality models , energy models , etc. Other classes of simulation algorithms are based on data-driven methods [48, 49] and simulation parameter estimation from real-world crowd data . Macroscopic approaches directly attempt to govern the global behaviors of crowds by computing velocity fields based on analyzing the environment description , manually designing velocity fields , or applying the continuum theory for the flow of crowds to crowd simulation .
Cellular automation approaches such as  and  discretize floor space into cells, where each agent can occupy exactly one cell. Such approaches are computationally inexpensive and thus support large crowds. Our model simulates antagonistic crowd behaviors by using a combination of cellular automation and multi-agent methods.
|The radius of perceived range|
|External emotion of agent|
|Mental emotion of agent|
|The increase in the strength of agent ’s external emotion received from agent at time|
|The increment of external emotion of agent at time|
|The difference of the benefits of the games at time and for agent|
|The increment of the mental emotion of agent at time|
|The increment of the total emotion of agent at time|
|The total emotion of agent at time|
|If the emotional value of an activist exceeds the threshold , role transition from activist to civilian occurs.|
|If the emotional value of a civilian less than the threshold , role transition from civilian to activist occurs.|
|The deterrent force of agent at time|
|The total deterrent force of the agents of the same type for agent at time|
|The total deterrent force of the agents in the opposing group for agent at time|
|The difference of the total deterrent forces between cops and activists that agent can perceive at time|
The probability of death
|The early warning threshold|
|The time of early warning|
|The time of early warning threshold|
In this section, we will introduce some basic and important concepts about crowd behavior simulation and crowd emotion contagion.
Crowd behavior simulation can be defined as a process of emulating or simulating the movement of large amount of entities, characters or agents . At a broad level, crowd movement is governed by psychological status of individuals and their surrounding environment . When humans form a crowd, interaction becomes an essential part of the overall crowd movement . For agent-based methods of crowd simulation used in this paper, each agent is assumed as an independent decision-making entity, which has knowledge of the environment and a desired goal position at each step of the simulation. The interactions between an agent with others or with the environment are often performed at a local level . A typical crowd simulation model can be defined as in Equation 1. represents the positions of all the agents in the scene at time , is the positions of all the agents at time , which can be induced by crowd simulation model .
Crowd simulation research has recently gained a new direction of modeling emotion of individuals to generate believable, heterogeneous crowd behaviors, considering the emotion of an agent in the crowd can greatly affect its ability to perceive, learn, behave, and communicate within the surrounding environment. The emotion owned by one agent provides the information about others agents’ behavioral intentions and modulate their behavioral decision making processes. Based on their appraisal of the environment, the emotion of each agent in the crowd will be updated dynamically at different time. In antagonistic scenes, such emotional changes become more obvious and will play a vital important role in crowd interaction behaviors. As shown in Equation 2, the emotional values of all the agents at the time can be computed according to their relative positions and emotions of the agents at the time .
This paper mainly discusses the influence of antagonistic emotions on agents’ antagonistic behaviors, whose purpose is to compute and update the status of all the agents at different time steps according to their emotions and roles. The crowd emotion is fully integrated into crowd behavior simulation, also with considering the confrontation between agents with different roles, such as civilians, activists, and cops. Given the positions , the emotions , and the roles of all the agents at time , our crowd simulation model estimates the positions , the emotions , and the roles of all the agents at next frame as Equation 3.
4 ACSEE Model
We present a novel Antagonistic Crowd behavior Simulation model (ACSEE) based on Emotional contagion and Evolutionary game theories. Our model consists of three important modules: antagonistic emotional contagion, situation estimation for evolutionary game, and behavior control. The antagonistic emotional contagion method is designed by combining the enhanced SIR and game approaches. Using the antagonistic emotions of agents, we define their deterrent forces in Section 4.4. The enhanced evolutionary game approach is determined based on the deterrent forces of agents. Our ACSEE model computes the behaviors of each agent by modeling the influence from antagonistic emotional contagion and evolutionary game theories. The flowchart of our ACSEE model is presented in Figure 1.
4.1 Symbols and Notations
For convenience, the important parameters used in the ACSEE model and their descriptions are listed in Table I.
4.2 Agent modeling in antagonistic scenes
In this section, we mainly describe the role of different kinds of agents and the assumptions we formulated to solve this problem.
4.2.1 Civilians, activists, and cops
Crowd violence incidents are often caused by some serious social contradictions, where a certain amount of activists challenge or break the normal and peaceful social order and stability in different ways of violence such as large-scale gathering, group activities and physical conflicts. We classify the agents in the crowd under such situations as civilians, activists, or cops based on their roles according to[9, 59].
Civilians are neutral agents in the environment and pose no danger to the central authority. In general, civilians are vulnerable groups and do not participate in confrontation. The cops will do their best to protect civilians while the activists will persecute them. However, civilians may change their roles if conditions are favorable to express their anger and frustration publicly. Fox example, through the incitement of the surrounding activists, the civilians may turn into activists to participate in the riot. Activists aim to create havoc and fuel the ongoing unrest while avoiding to be defeated by cops. Cops maintain public order by destroying activists and play a key role in determining the success of terrorist attack suppression. In real-world scenarios, cops and activists can represent any two antagonistic groups . Civilians can also represent onlookers and neutrals. The role of cops, activists, and civilians are shown in Figure 2.
Antagonistic crowds arise for many complex influencing factors. The simulation of antagonistic crowd behaviors considering all the influencing factors is an insoluble problem. From observations of the real antagonistic crowd behaviors, we formulate the following assumptions to make this problem solvable.
We use a metric to calculate emotion values (Section 4.3.3) and use them to perform role transitions between activists and civilians as we show in Figure 2. The role of cops is fixed and will not change. If the emotional value of an activist exceeds the threshold , role transition from an activist to a civilian occurs. If the emotional value of a civilian becomes less than the threshold , role transition from a civilian to an activist occurs .
Agents use different strategies to interact with their opposing agents. Agents’ strategies refer to the actions taken during the games. According to the situation encountered, activists and cops can adopt one of two different strategies: cooperation or defection [9, 61]. The cooperation strategy of activists means not challenging cops, accepting peaceful settlements, and running away from the cops. The defection strategy of activists means revolting aggressively and instigating civilians to revolt. The cooperation strategy of cops means keeping away from large gatherings of activists to protect civilians. The defection strategy of cops means pursuing activists.
The agent may be classified as dead. A dead agent in this case means being subdued by his or her opponents and therefore posing no threat to these opponents. It doesn’t mean biological death.
4.3 Antagonistic emotional contagion module
Considering the emotion has an important influence on people’s behavior decision-making, accurate emotion modeling is very essential and fundamental for a crowd simulation model. In this section, we present our antagonistic emotional contagion module. Emotions in our model incorporate the antagonism between agents in different roles. denotes the emotion of agent . and . There are two different types of emotion: positive emotion and negative emotion. When the emotional value is greater than 0, the emotion is positive. The higher the emotional value of an agent, the more positive the emotion. When the emotional value is less than 0, the emotion of the agent is negative. The lower the emotional value of an agent, the more negative the emotion. When an emotional value is closer to 0, the agent is regarded as being in a peaceful state and he or she tends to be conservative. The descriptions of different emotional values of different roles are listed in Table II.
|Descriptions of emotion||Emotion|
|Closer to||Closer to||Closer to|
|peaceful||arrogant and attack cops|
In such an antagonistic game scenario, individuals will be influenced by external and internal stimuli. External stimuli mainly comes from the external environment and is often accepted by individuals passively. Internal stimuli comes from the subjective perception and judgment of individuals by themselves. Both the internal and external stimuli in the antagonistic scenarios is able to produce emotions, so the emotion of an agent consists of two parts. The first part is the external emotion , which is influenced by surrounding agents. The second part is the mental emotion , which is determined by an agent’s own subjective consciousness. Therefore, the final emotional value is defined as follows:
4.3.1 External emotion
Our method for calculating external emotion is inspired by the emotional contagion model in . An agent can be affected by agents in his or her perceived range. The increase in the strength of external emotion of agent () received from agent at time is defined as:
where represents the distance between agent and , denotes the emotion of agent , is the intensity of emotion received by from sender , and is the intensity of emotion which is sent from to receiver .
Civilians can only passively receive the emotional contagion from surrounding agents and cannot actively influence others. The increment of external emotion of agent at time is denoted as . includes emotional influences received from all the cops and activists in the perceived range of agent . is defined as follows:
where and denote the increase in the strength of the external emotion transmitted from cop and activist to agent .
4.3.2 Mental emotion
Each agent establishes game play with agents in the opposing group who are in his or her perceived range. Because civilians are neutral members and remain peaceful, we assume that no game interaction will occur between civilian agents. The benefits of each game are determined according to the method outlined in Section 4.4. Mental emotion is defined as the difference of the benefits between two games and the mental emotion of civilians is a constant .
The difference of the benefits of the games at time and for agent is denoted as . The threshold that leads to emotional fluctuations is . The relationship between the increment of mental emotion and the difference between the benefits at time is defined by:
In Equation 7, means that the difference between benefits fails to reach the emotional fluctuation threshold . Therefore, there is little change in the emotion of agent . In this case, the mental emotional value is a random number on the interval (-0.01, 0.01). means that the benefit at time is higher than the benefit at time . The benefit increase makes the cops more positive and activists more negative. means that the difference between the benefits of time and is higher than the emotional fluctuation threshold . The benefit at time is lower than the benefit at time . The benefit decrease makes cops more negative and activists more positive.
4.3.3 Emotion updating
Our emotion updating method for agents is presented in Figure 3. The mental and external emotions of each agent are updated according to the evolution of the games and changes in agents’ locations. The external emotion of an agent is determined by the emotional contagion (external stimulus) of surrounding cops and activists. The differences of the benefits of the games (internal stimulus), which is defined in Section 4.3.2, lead to the changes in the mental emotions of cops and activists.
The increment of the total emotion () of an agent at time is defined as follows:
For each time step, the total emotional value is updated. At time , the total emotional value of agent is defined as follows:
4.4 Situation estimation for evolutionary game method
In our model an agent establishes game play with all the agents from the opposing group within his or her perceived range, according to game theory. When agents confront different scenarios and situations, they adopt different strategies and get varying benefits. They aim to maximize their benefits and minimize casualties according to the current situation. In this subsection, we present the evolutionary game module of our model, which is used to analyze the strategies and benefits of agents.
At first, agents estimate the surrounding situation based on the deterrent forces of the agents in their perceived range. Deterrent force is a kind of power by which an agent can beat his or her opponents and is closely related to the agent’s behavior. Emotion plays a crucial role in agents’ deterrent forces [64, 65, 66]. The deterrent force of agent is defined in the following equation:
where is the emotion of agent . The more positive or negative the emotion of an agent is, the greater the deterrent force an agent possesses . The total deterrent forces are defined as follows:
where the set denotes agents of the same type in the perceived range of agent and the set of the opposing agents in the perceived range of agent is .
The situation is defined according to the difference between the total deterrent forces of cops and activists perceived by agent , which is expressed by Equation 13, as follows.
Under different situations, the benefits gained during the games are different. The benefit matrix is defined according to varying situations. In contrast, the benefit matrix defined in  is based on the number of cops and activists and assumes that the deterrent forces of all the agents are the same. Instead, we define the benefit matrix based on the deterrent forces of cops and activists. We fully account for the differences in the deterrent forces of each agent, which conform to real-world scenes. The benefit matrix corresponding to different situations is shown in Table III.
|Comparison of deterrent force||Benefit||Strategy of activists|
|Strategy of cops||Cooperation||1,4||2,2|
When the total deterrent force of the cops is higher than that of the activists (), if both groups adopt a strategy of cooperation, cops miss an opportunity to make arrests. Compared with activists, cops reap fewer benefits. If both groups defect, cops gain the upper hand because they have a higher total deterrent force and therefore reap more benefits. If cops cooperate and activists defect, both groups’ benefits remain relatively neutral. Cops should defect to confront activists while activists should cooperate to avoid challenging cops and inviting casualties. If cops defect and activists cooperate, cops exert dominance over activists and activists avoid direct conflict. Therefore, both groups obtain benefits. When the total deterrent force of cops is less than or equal to that of activists ( or ), their benefits are defined similarly.
After a game, the strategies of cops and activists are updated according to the results of that game. Each agent is defined by a binary string. This string encodes the strategy bits in different situations. This string suggests the strategies an agent should adopt when , when , and when . Then the effectiveness or benefit of each strategy is calculated. The more beneficial strategy is chosen and it will be passed on to the offspring in an attempt to create a better strategy.
4.5 Behavior control module
The behavior control methods of agents are determined by antagonistic emotional contagion and evolutionary game approaches. In this section, we present some rules about how agents determine their positions at the next time step and their living states.
Agents determine their positions at the next time step based on the cellular automaton model . A cellular space of cells is defined and each agent occupies one cell. At each time step, agents choose to move to their neighboring cells or to stay still.
Whether an agent moves or not depends on the deterrent forces exhibited by his or her neighboring agents. For a cop or an activist, this is divided into the following possible cases according to real-world videos:
If the total deterrent force of agents in the opposing group is higher than that of the same type of agents in agent ’ s neighboring cells, he or she has to move. The moving direction of agent is determined by the expected benefits of his or her neighboring cells. At first, the neighboring cells around the agent will be checked to find the empty ones (an empty cell means that there is not an agent in it). Then the expected benefits of all the empty cells are calculated. The cell with the highest benefit will be the position to which agent will move.
Next we consider the situation where the total deterrent force of the opposing agents is less than that of agents of the same type in agent ’s neighboring cells. If agent ’s strategy is defection, he or she will move to the nearest opposing agent (i.e. will attack the opposing agent). If agent ’s strategy is cooperation, he or she will stay away from opposing agents and move to the nearest civilian. If agent is a cop, he or she will protect the civilian. If agent is an activist, he or she will attack the civilian. In this case, agent may also choose to stay still.
Any agent with no neighbors will choose to move. The moving direction will be the same as the situation where the total deterrent force of the opposing agents is less than that of agents of the same type.
Civilians will move to safer positions where there are more cops around them.
The agent with a defection strategy attacks his or her opponents. The agent may be dead. A dead agent in this case means being subdued by his or her opponents and therefore posing no threat to these opponents. It doesn’t mean real death. At each time step, the probability of death of each agent is calculated and denoted as . In contrast to the definition in , which is based on the number of cops and activists, we define based on the total deterrent forces of cops and activists.
where represents the total deterrent force of agents of the same type, and represents the total deterrent force of his or her opponents in the cells neighboring agent .
Each agent has an early warning threshold . When the value of exceeds the threshold , the value of will increase by 1. When the value of exceeds the threshold , the agent will die. Because the endurance of each agent is different, the values of the thresholds and are also different for each agent.
5 Implementation and performance
We have implemented our model using Visual C++ to simulate antagonistic crowd behaviors based on Unity3D . The computing environment is a common PC with a quadcore 2.50 GHz CPU,16 GB memory, and an Nvidia GeForce GTX 1080 Ti graphics card.
|Scenario||Number of agents||Size of 2-D Grid||Emotion|
|No.2:Role transitions||80||50||70||2020 squares||0.1||-0.5||0.1||-0.5||0.5|
|No.4:Real-world 1||10||50||30||2020 squares||0.1||-0.5||0.1||-0.5||0.5|
|No.5:Real-world 2||80||50||30||2020 squares||0.1||-0.5||0.1||-0.5||0.5|
|No.6:Real-world 3||3||14||40||2020 squares||1||-1||0.1||
|No.7:Real-world 4||0||30||100||4040 squares||1||-1||0||-0.2||0.8|
|No.8:Real-world 5||100||30||100||4040 squares||1||-1||0.1||
|No.9:ACSEE vs. CVM||80||50||30||2020 squares||0.1||-0.5||0.1||-0.5||0.5|
We run a series of experiments involving varying role number ratios in outdoor scenarios. The parameter values in different scenarios used in the simulation runs are listed in Table IV. The perceived range of agents is 5, , and . We investigate the effect of varying role number ratios on the crowd violence results (in Section 5.1). By analyzing the simulation results, we find that our model can account for many emergent phenomena (discussed in Section 5.2). Next, we study how different important factors influence crowd violence. In Section 5.3 we show the impact of emotional contagion on the results of crowd violence. We compare the different simulation results with or without considering emotional contagion. In Section 5.4, the relationship between the deterrent force and the strategy is revealed. The strategy adopted by each agent in different situations is analyzed. In Section 5.5, our simulation results are compared with the real-world videos and the simulation results generated by the civil violence model(CVM) . The real-world videos are chosen from the public dataset and real antagonistic events. More details about comparisons can be seen in the supplementary video. User studies are performed to evaluate our method in Section 5.6.
5.1 The impact of ratios of agents in different roles on the result of crowd violence
We investigate the effects of varying ratios of agents in different roles on the results of crowd violence. By analyzing a large number of real-world antagonistic videos, we select several representative values of (the ratio of cops to activists). In this section the initial s are 0, 0.6, 0.8, 1, 1.2, 1.4, and 1.6. The initial numbers of civilians and activists are 80 and 50, respectively. The initial emotional values of all the activists and cops are -0.5 and 0.5, respectively.
We can learn from Figure 4 that the number of different kinds of agents determines the outcome of crowd violence to some extent. When we increase the ratio of cops, they can subdue activists quickly, stabilize the situation, and reduce civilian casualties. When is 1, it means that the initial total deterrent force of the cops is equal to that of the activists. Both cops and activists have the same probability of winning. However, in the end, the cops fail which means that all the cops are subdued by the activists. We offer a detailed explanation in the following analysis.
Figure 5 shows the positions of all the agents at the 168th frame when is 1. At this time step, the numbers of cops and activists are the same. The deeper the color of a circle, the higher the deterrent force of the agent. Activists with strong deterrent forces are mainly located in the upper right corner of the scene. Some cops with weak deterrent forces are among the crowd of activists (upper right corner of the scene). The cops with strong deterrent forces are in the upper left corner of the scene, which makes it difficult for them to rescue the cops in the upper right corner. When the cops with weak deterrent forces are killed by the activists with strong deterrent forces, there are fewer cops left. Finally, all the activists get together to attack the remaining cops and the activists win.
We learn from Figure 5 that activists participate in collective behavior to create regions of low cop-to-activist ratios. This reduces the chances of activist death. The conglomeration of scattered activists into small groups and the amalgamation of small groups into large ones make it difficult to wipe them out . Although the number of agents determines the outcome of crowd violence to a certain extent, some take advantage of agents’ spatial distributions to affect the outcome of crowd violence.
5.2 Emergent phenomena uncovered by our model
Our model can simulate many emergent phenomena that conform to real-world scenes. Figures 6a, 6b, and 6c show that activists with strong deterrent forces attack civilians. At the top left corner of this scene, there are a lot of civilians. Many activists are at the lower right corner of Figure 6a. Agents of the same type gather together according to . Therefore, it is reasonable that agents of the same type gather together. The number of activists is larger than that of the cops. We can see from Figure 6a that the total deterrent force of the activists is stronger than that of the cops. Activists attack civilians (Figure 6b) and more and more civilians die (Figures 6b and 6c).
At the lower right corner of Figure 6d, there are plenty of cops with high deterrent forces near the highlighted activist and his deterrent force is weak. If he continues to resist, he will die. He therefore transitions roles (from activist to civilian). When all the other activists die, he survives (Figure 6f). When the number of surrounding activists is large enough, it may impel civilians to become activists .
In Figure 6g, there are many more cops than activists. The total deterrent force of the cops is much stronger than that of the activists. At first, the cops divide the activists into two groups (Figure 6g) and prevent the activists from gathering together to form a larger group. Next, the cops eliminate these two groups of activists individually. There are some activists in the left side of the scene (the first group). Cops encircle these activists and more activists will die. 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 of the activists are killed by the cops and the cops win.
Figure 7 shows the simulation of antagonistic crowd behavior using 3D character models. The activists with high deterrent forces on the left of the scene are not afraid of the cops with low deterrent forces. In the upper left corner of the scene, the activists with high deterrent forces attack a civilian. The civilian runs away from the activists. In the middle and lower part of the scene, the cop with a high deterrent force attacks the activist and he runs away from the cops.
5.3 The impact of emotional contagion on the result of crowd violence
The impact of emotional contagion on the results of crowd violence is presented in Figure 8. The initial numbers of civilians, activists, and cops are 80, 50, and 40, respectively. In Figure 8a, the initial emotion values of the cops are higher than those of the activists. At the 53rd time step, the number of activists is zero. All the activists have been wiped out by the cops. At first the number of civilians increases because the total deterrent force of the cops is much higher than that of the activists. Some activists change their role (from activist to civilian). In Figure 8b, all the agents without emotion 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 8 that the emotion module of our model can describe the differences observed between the agents. In our model, the deterrent forces of all the agents are different according to their emotions. The greater the absolute value of an agent’s emotion, the higher the deterrent force of that agent. Although the number of agents is small, it is still possible to overcome a larger group of opponents by improving the emotions and deterrent forces of each agent. Therefore, our model can simulate situations in which agents overcome their more numerous opponents.
Figure 9 shows simulation results with and without considering emotion. In Figure 9a the deterrent forces of the agents are different. The deeper the color of a circle, the higher the deterrent force of the agent. Because of emotional contagion, the same types of agents are more likely to gather together, which is similar to what happens in real-world scenarios . In Figure 9b the deterrent forces of all the agents are the same and the same type of agents are more dispersed.
Figure 10 shows the heat maps of antagonistic emotion. Different colors represent different types of agents’ emotions. The deeper the color, the larger the value of the emotion. At first, the emotions of the cops and the activists are very weak. Later, as a result of the confrontation between cops and activists, both types of emotions increase. Since the initial emotions of the cops are higher than those of activists, the overall emotional scope of the cops becomes wider and wider and the overall emotion scope of the activists becomes smaller and smaller. Finally, all the activists are wiped out by the cops and there is no blue area on the map.
5.4 The influence of deterrent force on strategy selection
We present the relationship between deterrent force and strategy selection in this subsection. We analyze the strategy (cooperation or defection) adopted by each agent with respect to their different deterrent forces.
Figure 11 shows the overview of cooperation ratios (the ratio of the number of agents adopting a cooperation strategy to the total number of this type of agent) in relation to different deterrent forces. When the total deterrent force of the activists is higher than that of the cops (Figure 11a), most of the cops adopt a cooperation strategy to avoid causalities and conserve their fighting forces. When the total deterrent force of the activists is equal to that of the cops, the cooperation ratios of cops and activists are almost the same from the 5th time step to the 45th time step. After the 45th time step, the cops defeat the activists. More and more cops adopt defection strategies, the cooperation ratio of the cops decreases, and the cooperation ratio of the activists increases. When the total deterrent force of the activists is less than that of the cops, the cooperation ratio of the activists is higher than that of the cops.
In summary, the agent with a higher deterrent force is more likely to adopt a defection strategy and the agent with a lower deterrent force is more likely to adopt a cooperation strategy.
To validate our approach, we compare the simulation results both with the simulation results generated by other models and real-world videos. Main goal of our model is to predict trends of crowd movement in these situations without explicitly modeling the trajectory of a particular individual. Simulation results obtained by our model tend to be closer to the real-world scenes in the overall trend of crowd movement.
The real scenes shown in Figures 12a and 12c are chosen from the public web dataset . The real scenes of Figures 12e, 12g, and 12i are chosen from real antagonistic incidents on YouTube. Cops and 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 of the thresholds of and for our model. The parameter values used in the simulation runs are listed in Table IV. More details can be seen in the supplementary video.
We use the main path and entropy metric to quantitively evaluate our simulation results. Main path is defined based on collectiveness of crowd movements. Collectiveness, which indicates the degree to which individuals acting as a unit, is a fundamental and universal measurement for various crowd systems, including crowds in antagonistic scenes . Individuals locally coordinate their movements and behaviors with their neighbors, and then the crowd is self-organized into collective motions without external control [73, 74]
. According to collectiveness of crowd movements, we find a main path from the starting point to the destination and a large number of individuals move along this path with long duration and low variance[75, 76]. The main path is able to represent the overall movement trend of crowds. Then we use the entropy metric  to evaluate the main paths of our simulation results and real-world crowd scenarios. A lower value of the entropy metric implies higher similarity with respect to the real-world crowd scenarios. Table V shows the entropy metric of our simulation results on different scenarios in Figure 12. The simulation results obtained by our model tend to conform to the real-world videos.
Our model is compared with the CVM model . Figure 13a shows our simulation results and Figure 13b shows those produced by the CVM model. Because of our use of emotional contagion, our model tends to cluster the same types of agents more easily, which is more reasonable for crowd violence scenes . More agents choose to move in our model, which simulates the chaotic scenes more naturally.
5.6 User Studies
In this section, we describe our user studies, which are conducted to demonstrate the perceptual benefits of our ACSEE model compared to other models in simulating antagonistic crowd behaviors.
Experiment Goals Expectations: Our main goal is to measure how close the antagonistic crowd behaviors generated by our ACSEE model are to those observed in real-world scenes compared with other models. We hypothesize that in both studies, agents simulated with our ACSEE model will exhibit overall plausible antagonistic crowd behaviors compared to other models. Therefore, participants will strongly prefer our model to the other models.
Experimental Design: Two user studies are conducted based on a paired-comparison design. In each study, participants are shown pre-recorded videos in a side-by-side comparison of simulation results generated by our model and the other model. In particular, we asked the users to compare the crowd movements generated by different crowd simulation models with those observed in real-world videos.
Comparison Methods: The first study compares our ACSEE model considering emotion with our model not considering emotion. The second study compares our model with the CVM model .
|(a) Our result||(b) CVM result|
Environments: We use outdoor scenarios without obstacles. In these scenarios, the green, purple, blue, and grey circles are civilians, activists, cops, and dead agents, respectively.
Metrics: The participants answer a question about whether the behaviors of agents conform to those exhibited in real-world scenes. It is an Agree/Disagree question and participants weight their evaluation using a seven-point Likert scale with values labeled “Strongly disagree,” “Disagree,” “Slightly disagree,” “Neutral,” “Slightly agree,” “Agree,” and “Strongly agree.” We convert the participant responses to a scale of 1 (Strongly Disagree) 7 (Strongly Agree) .
Results: There are 19 participants (13 male) with a mean age of
years in these studies. We measure the mean and the variance of their scores and then compute the p-values using a two-tailed t-test. The means of their scores for our model without emotion and with emotion areand , respectively. The means of their scores for the CVM and ACSEE models are and , respectively. The p-values for Figure 14a and Figure 14b comparisons are and , respectively. We observe that the antagonistic crowd behavior simulations generated by our ACSEE model score much higher than the other models, at a statistically significant rate (p-value0.05). The result indicates that the addition of emotion improves the perceptual similarity of our simulation to the antagonistic crowd behaviors in real-world scenes. Our model gets higher scores than the CVM model, as detailed in Figure 14b. Participants indicate their preference for our ACSEE model.
6 Conclusion and Limitations
We present a new model for antagonistic crowd behavior simulation integrated with evolutionary game theory and emotional contagion. Our approach builds on well-known psychological theories to present a comprehensive and antagonistic emotional contagion model. Based on the emotional calculation method, we propose using the deterrent force to determine the situation of cops and activists. According to the situation, an enhanced evolutionary game approach incorporated with antagonistic emotional contagion is determined. Finally, we present a behavior control decision method based on the antagonistic emotional contagion and evolutionary game approaches.
Our proposed model is verified by simulations. We investigate 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 previous approaches. Results show that our proposed model can reliably generate realistic antagonistic crowd behaviors.
However, our model still has several limitations. Although our simulation results are closer to the real-world scenes in the overall trend of crowd movement, the antagonistic emotions in a crowd violence scene cannot be obtained directly. One of the main reasons is that the quality of most of the real videos is poor, since they are often captured by moving phones. At present, there is no effective methods to identify and quantify the emotional values of all the individual in such videos with poor quality. Thus, the initial state of our model is set empirically according to real-world videos, which is time-consuming and not very accurate. In the future, we plan to use the latest wearable equipment to collect these data and provide a new method that can quickly and accurately obtain the initial state. Moreover, the strategies and benefits calculated by our antagonistic evolutionary game method are the ideal situation. Game theory assumes that all individuals are rational. However, some people in real scenes are irrational and extreme, which does not fully satisfy the precondition of game theory. In practice, people do not necessarily adopt the optimal strategy because of the limitations of perception and other complex factors. Our current calculation result is optimal, which is only one of the possible results. In fact, it is impossible for all simulation results to be consistent with the real results. We will continue to improve our prediction results considering more actual situations of antagonistic crowds. At present, our model is proposed based on the cellular automata model . We will extend our model to the social force model  for better crowd control.
-  . Helbing, D., . Farkas, I., and . Vicsek, T., “Simulating dynamical features of escape panic,” Nature, vol. 407, no. 6803, pp. 487–90, 2000.
-  M. Zucker, J. Kuffner, and M. Branicky, “Multipartite RRTs for rapid replanning in dynamic environments,” in Proc. IEEE Conf. Robotics and Automation, 2007, pp. 1603–1609.
-  G. Zhang, D. Lu, and L. Hong, “Strategies to utilize the positive emotional contagion optimally in crowd evacuation,” IEEE Transactions on Affective Computing, vol. PP, no. 99, pp. 1–1, 1949.
-  F. Durupinar, U. Gudukbay, A. Aman, and N. I. Badler, “Psychological parameters for crowd simulation: from audiences to mobs,” IEEE Transactions on Visualization and Computer Graphics, vol. 22, no. 9, pp. 2145–2159, 2016.
-  J. Bruneau, A.-H. Olivier, and J. Pettre, “Going through, going around: A study on individual avoidance of groups,” IEEE Transactions on Visualization and Computer Graphics, vol. 21, no. 4, pp. 520–528, 2015.
-  S. J. Guy, J. Chhugani, S. Curtis, P. Dubey, M. Lin, and D. Manocha, “PLEdestrians: a least-effort approach to crowd simulation,” in Proc. ACM SIGGRAPH/Eurographics Symp. Comput. Animation, 2010, pp. 119–128.
-  G. Zhang, D. Lu, and H. Liu, “Strategies to utilize the positive emotional contagion optimally in crowd evacuation,” IEEE Transactions on Affective Computing, pp. 1–1, 2018.
-  Y. Zhang, L. Qin, R. Ji, S. Zhao, Q. Huang, and J. Luo, “Exploring coherent motion patterns via structured trajectory learning for crowd mood modeling,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 27, no. 3, pp. 635–648, March 2017.
H. Y. Quek, K. C. Tan, and H. A. Abbass, “Evolutionary game theoretic approach
for modeling civil violence,”
IEEE Transactions on Evolutionary Computation, vol. 13, no. 4, pp. 780–800, 2009.
-  H. Situngkir, “On massive conflict: Macro-micro link,” Social Science Electronic Publishing, vol. 1, no. 4, pp. 1–12, 2004.
-  A. B. F. Neto, C. Pelachaud, and S. R. Musse, “Giving emotional contagion ability to virtual agents in crowds,” in Proc. Intelligent Virtual Agents, 2017, pp. 63–72.
-  S. Parikh and C. Cameron, “Riot games: A theory of riots and mass political violence,” in Proc. 7th Wallis Inst. Conf. Political Economy, New York: Univ. Rochester, Oct. 2000.
-  R. B. Myerson, Game theory : analysis of conflict. Harvard University Press, 1997.
-  S. Y. Chong, J. Humble, G. Kendall, J. Li, and X. Yao, Iterated Prisoner’s Dilemma and Evolutionary Game Theory, 2007.
-  J. Li, G. Kendall, and R. John, “Computing nash equilibria and evolutionarily stable states of evolutionary games,” IEEE Transactions on Evolutionary Computation, vol. 20, no. 3, pp. 460–469, 2016.
-  Á. Gómez, L. López-Rodríguez, H. Sheikh, J. Ginges, L. Wilson, H. Waziri, A. Vázquez, R. Davis, and S. Atran, “The devoted actor’s will to fight and the spiritual dimension of human conflict,” Nature Human Behaviour, vol. 1, pp. 673–679, 2017.
-  H. Jiang, Z. Deng, M. Xu, X. He, T. Mao, and Z. Wang, “An emotion evolution based model for collective behavior simulation,” in Proc. Symp. Interactive 3D Graphics and Games, 2018, pp. 10:1–10:6.
-  E. J. Johnson and A. Tversky, “Affect, generalization, and the perception of risk,” Journal of Personality Social Psychology, vol. 45, no. 1, pp. 20–31, 1983.
-  L. Fu, W. Song, W. Lv, and S. Lo, “Simulation of emotional contagion using modified SIR model: A cellular automaton approach,” Physica A Statistical Mechanics Its Applications, vol. 405, pp. 380–391, 2014.
-  S. Kim, S. J. Guy, D. Manocha, and M. C. Lin, “Interactive simulation of dynamic crowd behaviors using general adaptation syndrome theory,” in Proc. Symp. Interactive 3D Graphics and Games, 2012, pp. 55–62.
-  S. Huerre, J. Lee, M. Lin, and C. O’Sullivan, “Simulating believable crowd and group behaviors,” in Proc. ACM SIGGRAPH Asia, 2010, pp. 1–92.
-  C. M. D. Melo, J. Gratch, and P. J. Carnevale, “Humans vs. computers: Impact of emotion expressions on people s decision making,” IEEE Transactions on Affective Computing, vol. 6, no. 2, pp. 127–136, 2017.
-  J. Rao, J. Sun, Y. Zhang, J. Tang, W. Yu, Y. Chen, and A. C. M. Fong, “Quantitative study of individual emotional states in social networks,” IEEE Transactions on Affective Computing, vol. 3, no. 2, pp. 132–144, 2012.
-  W. O. Kermack and A. G. Mckendrick, “Contributions to the mathematical theory of epidemics,” Bulletin of Mathematical Biology, vol. 53, no. 1, pp. 33–55, 1991.
-  Zhao, Laijun, Cui, Hongxin, Qiu, Xiaoyan, Wang, Xiaoli, and Wang, “SIR rumor spreading model in the new media age,” Physica A Statistical Mechanics Its Applications, vol. 392, no. 4, pp. 995–1003, 2013.
-  S. H. White, A. M. D. Rey, and G. R. S nchez, “Modeling epidemics using cellular automata,” Applied Mathematics Computation, vol. 186, no. 1, pp. 193–202, 2007.
-  F. Durupinar, N. Pelechano, J. Allbeck, U. Gudukbay, and N. I. Badler, “How the ocean personality model affects the perception of crowds,” IEEE Computer Graphics and Applications, vol. 31, no. 3, pp. 22–31, 2011.
-  J. H. Wang, S. M. Lo, J. H. Sun, Q. S. Wang, and H. L. Mu, “Qualitative simulation of the panic spread in large-scale evacuation,” Simulation, vol. 88, no. 12, pp. 1465–1474, 2012.
-  T. Bosse, R. Duell, Z. A. Memon, J. Treur, and C. N. V. D. Wal, “A multi-agent model for mutual absorption of emotions,” In Proc. 23th EuropeanConf. Mod. and Sim., 2009.
-  T. Bosse, R. Duell, Z. A. Memon, J. Treur, and N. van der Wal, “A multi-agent model for emotion contagion spirals integrated within a supporting ambient agent model,” in Proc. Principles of Practice in Multi-Agent Systems, 2009, pp. 48–67.
-  J. Tsai, N. Fridman, E. Bowring, M. Brown, S. Epstein, S. Marsella, S. Marsella, A. Ogden, I. Rika, and A. Sheel, “ESCAPES: evacuation simulation with children, authorities, parents, emotions, and social comparison,” in Proc. Autonomous Agents and Multiagent Systems, 2011, pp. 457–464.
-  J. Tsai, E. Bowring, S. Marsella, and M. Tambe, “Empirical evaluation of computational fear contagion models in crowd dispersions,” Autonomous Agents and Multi-Agent Systems, vol. 27, no. 2, pp. 200–217, 2013.
-  M. A. Nowak and K. Sigmund, “Evolutionary dynamics of biological games,” Science, vol. 303, no. 5659, pp. 793–9, 2004.
-  S. Paterson, T. Vogwill, A. Buckling, R. Benmayor, A. J. Spiers, N. R. Thomson, M. Quail, F. Smith, D. Walker, and B. Libberton, “Antagonistic coevolution accelerates molecular evolution.” Nature, vol. 464, no. 7286, pp. 275–8, 2010.
-  A. R. Zomorrodi and D. Segr , “Genome-driven evolutionary game theory helps understand the rise of metabolic interdependencies in microbial communities.” Nature Communications, vol. 8, no. 1, pp. 1563–1574, 2017.
-  F. Saab, A. Kayssi, I. Elhajj, and A. Chehab, “Playing with sybil,” ACM Sigapp Applied Computing Review, vol. 16, no. 2, pp. 16–25, 2016.
-  J. Li, G. Kendall, and R. John, “Computing nash equilibria and evolutionarily stable states of evolutionary games,” IEEE Transactions on Evolutionary Computation, vol. 20, no. 3, pp. 460–469, 2016.
-  W. Huang, B. Haubold, C. Hauert, and A. Traulsen, “Emergence of stable polymorphisms driven by evolutionary games between mutants,” Nature Communications, vol. 3, no. 2, pp. 919–925, 2012.
-  M. H. Vainstein, C. Brito, and J. J. Arenzon, “Percolation and cooperation with mobile agents: Geometric and strategy clusters,” Physical Review E, vol. 90, no. 2, pp. 860–877, 2014.
-  J. Li, C. Zhang, Q. Sun, Z. Chen, and J. Zhang, “Changing the intensity of interaction based on individual behavior in the iterated prisoner s dilemma game,” IEEE Transactions on Evolutionary Computation, vol. 21, no. 4, pp. 506–517, 2017.
-  C. K. Goh, H. Y. Quek, K. C. Tan, and H. A. Abbass, “Modeling civil violence: An evolutionary multi-agent, game theoretic approach,” in Proc. Evolutionary Computation, IEEE Congress on, 2006, pp. 1624–1631.
-  D. Helbing and P. Molnar, “Social force model for pedestrian dynamics,” Physical Review E, vol. 51, no. 5, p. 4282, 1995.
-  C. W. Reynolds, “Flocks, herds and schools: A distributed behavioral model,” ACM SIGGRAPH Computer Graphics, vol. 21, no. 4, pp. 25–34, 1987.
-  J. Li, S. Fu, H. He, H. Jia, Y. Li, and Y. Guo, “Simulating large-scale pedestrian movement using ca and event driven model: Methodology and case study,” Physica A Statistical Mechanics Its Applications, vol. 437, pp. 304–321, 2015.
-  I. Karamouzas and M. Overmars, “Simulating and evaluating the local behavior of small pedestrian groups,” IEEE Transactions on Visualization and Computer Graphics, vol. 18, no. 3, pp. 394–406, 2012.
-  J. Ondrej, J. Pettre, A.-H. Olivier, and S. Donikian, “A synthetic-vision based steering approach for crowd simulation,” ACM Transactions on Graphics, vol. 29, pp. 123:1–123:9, 2010.
-  S. A. Stuvel, N. Magnenatthalmann, D. Thalmann, A. F. V. D. Stappen, and A. Egges, “Torso crowds,” IEEE Transactions on Visualization and Computer Graphics, vol. PP, no. 99, pp. 1823–1837, 2016.
-  S. Kim, A. Bera, A. Best, R. Chabra, and D. Manocha, “Interactive and adaptive data-driven crowd simulation,” in Proc. IEEE Virtual Reality Conf., Mar. 2016, pp. 29–38.
-  H. Wang, J. Ondřej, and C. O Sullivan, “Trending paths: A new semantic-level metric for comparing simulated and real crowd data,” IEEE Transactions on Visualization and Computer Graphics, vol. 23, no. 5, pp. 1454–1464, 2017.
-  G. Berseth, M. Kapadia, B. Haworth, and P. Faloutsos, “Steerfit: Automated parameter fitting for steering algorithms,” in Proc. ACM SIGGRAPH/Eurographics Symp. Comput. Animation, 2014, pp. 113–122.
-  J. Pettr, H. Grillon, and D. Thalmann, “Crowds of moving objects:navigation planning and simulation,” in Proc. IEEE Conf. Robotics and Automation, 2008, pp. 1–7.
X. Jin, J. Xu, C. C. L. Wang, S. Huang, and J. Zhang, “Interactive control of large-crowd navigation in virtual environments using vector fields,”IEEE Computer Graphics Applications, vol. 28, no. 6, pp. 37–46, 2008.
-  A. Golas, R. Narain, S. Curtis, and M. C. Lin, “Hybrid long-range collision avoidance for crowd simulation,” IEEE Transactions on Visualization and Computer Graphics, vol. 20, no. 7, pp. 1022–1034, 2014.
-  S. Wolfram, “Cellular automata as models of complexity,” Nature, vol. 311, no. 5985, pp. 419–424, 1984.
-  S. Roy, A. Ray, and S. Das, “A cellular automaton that solves distributed spanning tree problem,” Journal of Computational Science, vol. 26, 2018.
-  F. M. Nasir and M. S. Sunar, “A survey on simulating real-time crowd simulation,” in International Conference on Interactive Digital Media, 2016.
-  S. Patil, J. van den Berg, S. Curtis, M. C. Lin, and D. Manocha, “Directing crowd simulations using navigation fields,” IEEE Transactions on Visualization and Computer Graphics, vol. 17, no. 2, pp. 244–254, Feb 2011.
-  T. Bosse, R. Duell, Z. A. Memon, J. Treur, and C. N. V. D. Wal, “A multi-agent model for emotion contagion spirals integrated within a supporting ambient agent model,” in International Conference on Principles of Practice in Multi-agent Systems, 2009.
-  F. Bu and J. Sun, “The psychological behaviour research of individuals in mass violence events,” in Proceedings of the 8th International Conference on Intelligent Computing Theories and Applications, ser. ICIC, 2012, pp. 625–632.
-  X. Wang, N. Liu, S. Liu, Z. Wu, M. Zhou, J. He, P. Cheng, C. Miao, and N. M. Thalmann, “Crowd formation via hierarchical planning,” in ACM SIGGRAPH Conference on Virtual-Reality Continuum and ITS Applications in Industry, 2016, pp. 251–260.
-  S. Schutte, “Violence and Civilian Loyalties: Evidence from Afghanistan,” JOURNAL OF CONFLICT RESOLUTION, vol. 61, no. 8, pp. 1595–1625, SEP 2017.
-  I. Funahashi, “Kayika vedana (physical emotion) and cetasika vedana (mental emotion),” vol. 10, pp. 510–511, 01 1962.
-  R. W. Picard, “Affective computing,” Igi Global, vol. 1, no. 1, pp. 71–73, 2012.
-  J. T. Pickett, S. P. Roche, and G. Pogarsky, “TOWARD A BIFURCATED THEORY OF EMOTIONAL DETERRENCE,” CRIMINOLOGY, vol. 56, no. 1, pp. 27–58, FEB 2018.
-  S. Sciara and G. Pantaleo, “Relationships at risk: How the perceived risk of ending a romantic relationship influences the intensity of romantic affect and relationship commitment,” MOTIVATION AND EMOTION, vol. 42, no. 1, pp. 137–148, FEB 2018.
-  M. Khadjavi, “On the Interaction of Deterrence and Emotions,” JOURNAL OF LAW ECONOMICS & ORGANIZATION, vol. 31, no. 2, pp. 287–319, MAY 2015.
-  L. J. Carlson and R. Dacey, “The use of fear and anger to alter crisis initiation,” CONFLICT MANAGEMENT AND PEACE SCIENCE, vol. 31, no. 2, pp. 168–192, APR 2014.
-  J. M. Epstein, “Modeling civil violence: An agent-based computational approach,” in Proceedings of the National Academy of Sciences of the United States of America, vol. 99, no. Suppl 3, 2002, pp. 7243–7250.
-  G. L. Bon, “Scientific literature: The crowd. a study of the popular mind,” Science, vol. 5, pp. 734–735, 2005.
-  P. Sunita and C. Charles, “Riot games: A theory of riots and mass political violence,” in Proc. Wallis ins. Conf. Political Economy, 2000.
R. Mehran, A. Oyama, and M. Shah, “Abnormal crowd behavior detection using
social force model,” in
Proc. IEEE Conf. Comput. Vis. Pattern Recognit, 2009, pp. 935–942.
B. Zhou, X. Tang, H. Zhang, and X. Wang, “Measuring crowd collectiveness,” in
Proc. Computer Vision and Pattern Recognition, 2013, pp. 3049–3056.
-  M. Moussaid, S. Garnier, G. Theraulaz, and D. Helbing, “Collective information processing and pattern formation in swarms, flocks and crowds,” Topics in Cognitive Science, vol. 1, 05 2010.
-  C. W. Reynolds, “Flocks, herds and schools: A distributed behavioral model,” in Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques, ser. SIGGRAPH ’87, 1987, pp. 25–34.
-  N. P. Hummon and P. Dereian, “Connectivity in a citation network: The development of dna theory ,” Social Networks, vol. 11, no. 1, pp. 39–63, 1989.
-  J. Shao, C. L. Chen, and X. Wang, “Scene-independent group profiling in crowd,” in Computer Vision and Pattern Recognition, 2014, pp. 2227–2234.
-  S. J. Guy, J. V. D. Berg, W. Liu, R. Lau, M. C. Lin, and D. Manocha, “A statistical similarity measure for aggregate crowd dynamics,” Acm Transactions on Graphics, vol. 31, no. 6, pp. 1–11, 2012.
-  T. Randhavane, A. Bera, and D. Manocha, “F2fcrowds: Planning agent movements to enable face-to-face interactions,” Presence Teleoperators Virtual Environments, vol. 26, no. 2, pp. 228–246, 2017.