Evolutionary Game Dynamics for Crowd Behavior in Emergency Evacuations

This paper studies the problem of a large group of individuals that has to get to a safety exit in the context of high-stress emergency evacuations. We model this problem as a discrete-state continuous-time game, where the players update their strategies to reach the exit within a defined time horizon, whilst avoiding undesirable situations such as congestion and being trampled. The proposed model builds on crowd dynamics in a two-strategy game theoretic context, which we extend to include aspects of crowd behavior originating in sociology and psychology, and in the analogous studies performed in immersive virtual environments. The main contribution of this paper is threefold: i) we propose a novel game formulation of the model in terms of the population distribution across three strategies, and provide a link with prospect theory; ii) we study the equilibria of the system and their stability via Lyapunov stability theory of nonlinear systems; iii) we extend the model to a multi-population setting, where each population represents the group of players at a certain distance from the exit.