Modeling pedestrian evacuation by means of game theory

Pedestrian evacuation is studied based on a modified lattice model. The payoff matrix in this model represents the complicated interactions between selfish individuals, and the mean force imposed on an individual is given by considering the impacts of neighbors, walls, and defector herding. Each passer-by moves to his selected location according to the Fermi function, and the average velocity of pedestrian flow is defined as a function of the motion rule. Two pedestrian types are included: cooperators, who adhere to the evacuation instructions; and defectors, who ignore the rules and act individually. It is observed that the escape time increases as fear degree increases, and the system remains smooth for a low fear degree, but exhibits three stages for a high fear degree. We prove that the fear degree determines the dynamics of this system, and the initial density of cooperators has a negligible impact. The system experiences three phases, a single phase of cooperator, a mixed two-phase pedestrian, and a single phase of defector sequentially as the fear degree upgrades. The phase transition has been proven basically robust to the changes of empty site contribution, wall's pressure, and noise amplitude in the motion rule. It is further shown that pedestrians derive the greatest benefit from overall cooperation, but are trapped in the worst situation if they are all defectors. (paper: interdisciplinary statistical mechanics)