  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.
