Modeling tagged pedestrian motion: a mean-field type game approach

TL;DR

This paper develops a mean-field type game model for tagged pedestrian motion, incorporating crowd interactions like congestion and crowd aversion, to assist in strategic positioning of emergency personnel.

Contribution

It introduces a novel mean-field game framework for modeling tagged pedestrian dynamics considering crowd effects, with equilibrium characterization and numerical simulations.

Findings

Equilibrium controls are characterized mathematically.

Numerical simulations demonstrate model behavior.

Crowd effects significantly influence pedestrian trajectories.

Abstract

This paper suggests a model for the motion of tagged pedestrians: pedestrians moving towards a specified targeted destination, which they are forced to reach. It aims to be a decision-making tool for the positioning of fire fighters, security personnel, and other services in a pedestrian environment. Taking interaction with the surrounding crowd into account leads to a differential nonzero-sum game model where the tagged pedestrians compete with the surrounding crowd of ordinary pedestrians. When deciding how to act, pedestrians consider crowd distribution-dependent effects, like congestion and crowd aversion. Including such effects in the parameters of the game, makes it a mean-field type game. The equilibrium control is characterized, and special cases are discussed. Behavior in the model is studied by numerical simulations.