Before revision:  A mean-field theory indicates that a new mechanism -- the dynamical reciprocity , as a counterpart to the well-known network reciprocity, is at work to foster cooperation, which is confirmed by the detailed analysis.
After revision:  A mean-field theory indicates that a new mechanism -- the dynamical reciprocity , as a counterpart to the well-known network reciprocity, is at work to foster cooperation, which is confirmed by the detailed analysis.