# Analysis of Cooperation Behaviors and Crowd Dynamics during Pedestrian Evacuation with Group Existence

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## Abstract

**:**

## 1. Introduction

## 2. Model Description

#### 2.1. Transition Probability

#### 2.2. Behavioral Interaction Mechanism

#### 2.3. Behavior Updating Rule

## 3. Simulation and Results

#### 3.1. Effect of the Initial Distribution Pattern

#### 3.2. Influence of the Willingness to Cooperate

#### 3.3. Influence of the Intensity of Interaction

#### 3.4. Influence of the Number and Size of Groups

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Plots of fraction of cooperation and evacuation time versus distribution pattern: (

**a**) fraction of cooperation; (

**b**) evacuation time.

**Figure 6.**Time-evolution process of fraction of cooperation with different distribution patterns: (

**a**) the clustered distribution pattern; (

**b**) the random distribution pattern.

**Figure 7.**Group members’ typical snapshots under clustered distribution at time steps 1, 2, 10, and 30: (

**a**) ts = 1; (

**b**) ts = 2; (

**c**) ts = 10; (

**d**) ts = 30.

**Figure 8.**Pedestrian behaviors’ typical snapshots under clustered distribution at time steps 1, 2, 10, and 30: (

**a**) ts = 1; (

**b**) ts = 2; (

**c**) ts = 10; (

**d**) ts = 30.

**Figure 9.**Group members’ typical snapshots under random distribution at time steps 1, 10, 30, and 50: (

**a**) ts = 1; (

**b**) ts = 10; (

**c**) ts = 30; (

**d**) ts = 50.

**Figure 10.**Pedestrian behaviors’ typical snapshots under random distribution at time steps 1, 10, 30, and 50: (

**a**) ts = 1; (

**b**) ts = 10; (

**c**) ts = 30; (

**d**) ts = 50.

**Figure 11.**Plots of fraction of cooperation and evacuation time versus r for different values of k

_{E}and k

_{B}: (

**a**) fraction of cooperation; (

**b**) evacuation time.

**Figure 12.**The relationship between fraction of cooperation and k

_{B}with different values of k

_{E}for (

**a**) r = 0.1; (

**b**) r = 0.5; and (

**c**) r = 0.9.

**Figure 13.**The relationship between evacuation time and k

_{B}with different values of k

_{E}for (

**a**) r = 0.1; (

**b**) r = 0.5; and (

**c**) r = 0.9.

**Figure 14.**Fractions of cooperation with different values of n and s for (

**a**) r = 0.1; (

**b**) r = 0.5; and (

**c**) r = 0.9.

**Figure 15.**Evacuation time with different values of n and s for (

**a**) r = 0.1; (

**b**) r = 0.5; and (

**c**) r = 0.9.

Cooperation (C) | Defection (D) | |
---|---|---|

Cooperation (C) | P_R, P_R | P_S, P_T |

Defection (D) | P_T, P_S | P_P, P_P |

Cooperation (C) | Defection (D) | |
---|---|---|

Cooperation (C) | H_R, H_R | H_S, H_T |

Defection (D) | H_T, H_S | H_P, H_P |

Parameter | Description | Value |
---|---|---|

P_R | Payoffs of out-group pedestrians when they are both cooperators | 1 |

P_S | Payoffs of cooperators when the interacting member of different groups is a defector | 0 |

P_T | Payoffs of defectors when the interacting member of different groups is a cooperator | 1.5 |

P_P | Payoffs of out-group pedestrians when they are both defectors | 0 |

H_R | Payoffs of in-group pedestrians when they are both cooperators | 1 + r |

H_S | Payoffs of cooperators when the interacting member of the same group is a defector | 0.5 |

H_T | Payoffs of defectors when the interacting member of the same group is a cooperator | 1 |

H_P | Payoffs of in-group pedestrians when they are both defectors | 0 |

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**MDPI and ACS Style**

Ma, Y.; Liu, X.; Huo, F.; Li, H.
Analysis of Cooperation Behaviors and Crowd Dynamics during Pedestrian Evacuation with Group Existence. *Sustainability* **2022**, *14*, 5278.
https://doi.org/10.3390/su14095278

**AMA Style**

Ma Y, Liu X, Huo F, Li H.
Analysis of Cooperation Behaviors and Crowd Dynamics during Pedestrian Evacuation with Group Existence. *Sustainability*. 2022; 14(9):5278.
https://doi.org/10.3390/su14095278

**Chicago/Turabian Style**

Ma, Yaping, Xiaoying Liu, Feizhou Huo, and Hui Li.
2022. "Analysis of Cooperation Behaviors and Crowd Dynamics during Pedestrian Evacuation with Group Existence" *Sustainability* 14, no. 9: 5278.
https://doi.org/10.3390/su14095278