This paper studies unidirectional pedestrian flow by using a lattice gas model with parallel update rules. Game theory is introduced to deal with conflicts that two or three pedestrians want to move into the same site. Pedestrians are either cooperators or defectors. The cooperators are gentle and the defectors are aggressive. Moreover, pedestrians could change their strategy. The fundamental diagram and the cooperator fraction at different system width $W$ have been investigated in detail. It is found that a two-lane system exhibits a first-order phase transition while a multilane system does not. A microscopic mechanism behind the transition has been provided. Mean-field analysis is carried out to calculate the critical density of the transition as well as the probability of games at large value of $W$. The spatial distribution of pedestrians is investigated, which is found to be dependent (independent) on the initial cooperator fraction when $W$ is small (large). Finally, the influence of the evolutionary game rule has been discussed.

• Received 9 January 2011

DOI:https://doi.org/10.1103/PhysRevE.84.036107