A Tractable Mean Field Game Model for the Analysis of Crowd Evacuation Dynamics

A fixed time horizon evacuation model for a large population of confined agents is proposed within the mean field games framework. Unlike previously proposed models relying on simulations or partial differential equation analysis, the proposed model remains linear in the individual agent dynamics and quadratic in the cost functions, ultimately dictating the agents' motion. We use negative definite matrices in the cost function to reflect congestion effect during evacuations. This leads to Riccati equations that generically display a finite escape time. Therefore, we develop an existence theory for the infinite population mean field game based equilibrium dynamics, and establish its Nash property for a large but finite population of agents. Simulation results illustrating the numerical behavior of the model are presented with stress effect and different social interaction scenarios such as congestion and crowd following behavior.