Evacuation of pedestrians from a single room by using snowdrift game theories

Dong-Mei Shi and Bing-Hong Wang
Phys. Rev. E 87, 022802 – Published 4 February 2013

Abstract

Game theory is introduced to simulate the complicated interaction relations among the conflicting pedestrians in a pedestrian flow system, which is defined on a square lattice with the parallel update rule. Modified on the traditional lattice gas model, each pedestrian can move to not only an empty site, but also an occupied site. It is found that each individual chooses its neighbor randomly and occupies the site with the probability W(xy)=11+exp[(PxUx)/κ], where Px is the x's payoff representing his personal energy, and Ux is the average payoff of its neighborhood indicating the potential well energy if he stays. Two types of pedestrians are considered, and they interact with their neighbors following the payoff matrix of snowdrift game theory. The cost-to-benefit ratio r=c/(2bc) (where b is the perfect payoff and c is the labor cost) represents the fear index of the pedestrians in this model. It is found that there exists a moderate value of r leading to the shortest escape time, and the situation for large values of r is better than that for small ones in general. In addition, the pedestrian flow system always arrives at a consistent state in which the two types of walkers have the same number and evolve by the same law irrespectively of the parameters, which can be interpreted as the self-organization effect of pedestrian flow. It is also proven that the time point of the onset of the steady state is unrelated to the scale of the pedestrians and the square lattice. Meanwhile, the system exhibits different dynamics before reaching the consistent state: the number of the two types of walkers oscillates when PC>0.5 (i.e., probability to change the present strategy), while no oscillation happens for PC0.5. Finally, it is shown that a smaller density of pedestrians ρ induces a shorter average escape time.

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  • Received 28 October 2012

DOI:https://doi.org/10.1103/PhysRevE.87.022802

©2013 American Physical Society

Authors & Affiliations

Dong-Mei Shi1,* and Bing-Hong Wang2,†

  • 1Department of Physics, Bohai University, Jinzhou Liaoning, 121000, People's Republic of China
  • 2Department of Modern Physics and Nonlinear Science Center, University of Science and Technology of China, Hefei Anhui, 230026, People's Republic of China

  • *sdm21@mail.ustc.edu.cn
  • bhwang@ustc.edu.cn

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Vol. 87, Iss. 2 — February 2013

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