Modeling Behavioral Rules and Norm Evolution in Crowd Evacuation

Topic Description
During emergency evacuations, individual behavior is not entirely independent but is influenced by social norms (such as queuing and mutual assistance) and emergent, evolving rules (such as risk-avoidance priority and herding). This topic requires modeling and analyzing how behavioral rules dynamically evolve through individual interactions during the evacuation process, and exploring their impact on overall evacuation efficiency.

Solution Process

1. Problem Definition and Core Elements

• Behavioral Rules: Explicit or implicit behavioral logic followed by individuals during evacuation, for example:
  • Cooperation Rule: Actively giving way to the elderly and weak, assisting others.
  • Competition Rule: Scrambling for exits, pushing others.
  • Herding Rule: Following the movement direction of the crowd.
• Norm Evolution: Individuals dynamically adjust their own rules by observing others' behavior and environmental feedback (such as congestion levels), eventually forming behavioral patterns at the group level.
• Key Challenges: How to quantify the interactions between rules? How is the evolution process influenced by the environment (such as spatial layout, threat level)?

2. Modeling Framework Design
Step 1: Define Individual Rule Repository

• Assign an initial rule to each agent (e.g., 70% of individuals choose cooperation, 30% choose competition). Rules can be represented as strategy functions:

\[ Strategy_i = f(\text{personal attributes}, \text{environmental state}) \]

• For example:
  • Cooperation rule: Speed reduced by 20%, priority given to avoiding nearby individuals.
  • Competition rule: Speed increased by 10%, partial collision detection ignored.

Step 2: Design Interaction Mechanisms

• Individuals interact during evacuation in the following ways:
  • Direct Observation: Perceiving the behavior (e.g., whether others yield) and outcomes (e.g., whether they get closer to the exit faster) of surrounding individuals.
  • Environmental Feedback: Adjusting rule preferences based on congestion levels, casualty incidents, etc.
• For example: If an individual is repeatedly stuck in congestion due to competition, they may switch to a cooperative strategy.

Step 3: Rule Evolution Logic

• Adopt an Imitation Dynamics model:
  1. An individual randomly selects a neighbor with probability \(p\) to compare utility (e.g., movement efficiency).
  2. If the neighbor's utility is higher, they replicate that neighbor's rule with probability \(q\).
• Example utility function:

\[ U_i = \alpha \cdot \text{movement speed} - \beta \cdot \text{number of collisions} + \gamma \cdot \text{mutual assistance gain} \]

3. Simulation Implementation and Parameter Calibration
Step 1: Basic Evacuation Scenario Setup

• Construct a typical evacuation environment (e.g., a room with a single exit), set parameters such as initial crowd distribution and exit capacity.

Step 2: Introduce Dynamic Rule Updates

• Execute per time step:
  1. Individuals move according to their current rules (based on a social force model).
  2. Record individual utility (e.g., displacement increment, number of conflicts).
  3. Perform rule imitation or random exploration of new rules according to probability.

Step 3: Sensitivity Analysis of Key Parameters

• Adjust the following parameters to observe evolution outcomes:
  • Threat Level: High threat may promote the dominance of competition rules.
  • Spatial Constraints: Narrow passages may reinforce cooperation rules.
  • Information Transparency: Does visibility of others' behavior promote norm unification?

4. Results Analysis and Optimization Insights

• Evolutionary Steady-State Analysis:
  • Multiple steady states may form: universal cooperation, universal competition, or coexistence of mixed strategies.
  • For example: When exit width is insufficient, competition rules easily lead to the "arching effect" (congestion at the exit), eventually triggering a shift towards cooperation.
• Intervention Strategy Suggestions:
  • Early Guidance: Reinforce cooperative norms through broadcasts and signage to prevent the spread of competition rules.
  • Dynamic Adjustment: Temporarily allocate exits based on real-time congestion data to influence the direction of rule evolution.

5. Model Validation and Extensions

• Validation Methods:
  • Compare with actual evacuation video data to test if the rule distribution aligns with model predictions.
  • Calibrate imitation probability parameters through agent-based experiments (e.g., VR evacuation).
• Extension Directions:
  • Introduce cultural differences (e.g., collectivist vs. individualist groups).
  • Combine with rumor propagation models to study the impact of information distortion on rule evolution.

Through the above steps, the model can reveal the deep connection between behavioral rule evolution and evacuation efficiency, providing a theoretical basis for formulating dynamic crowd management strategies.