Game theoretic modeling of helping behavior in emergency evacuations

We study the collective helping behavior in a room evacuation scenario in which two volunteers are required to rescue an injured person. We propose a game theoretic model to study the evolution of cooperation in rescuing the injured persons. We consider the existence of committed volunteers who do not change their decision to help the injured persons. With the committed volunteers, all the injured persons can be rescued depending on the payoff parameters. In contrast, without the committed volunteers, rescuing all the injured persons is not achievable on most occasions because some lonely volunteers often fail to find peers even for low temptation payoff. We have quantified various collective helping behaviors and summarized those collective patterns with phase diagrams. In the context of emergency evacuations, our study highlights the vital importance of the committed volunteers to the collective helping behavior.