Before revision:  We present a more generalized model by introducing a novel hierarchy measure to interpolate the cooperativeness of group members in any hierarchy structure of interest. We derive the conditions under which cooperation can emerge and verify our analytical predictions by agent-based computer simulation.
After revision:  We present a more generalized modified framework in which his model is a special case, by developing and introducing a new hierarchy measure into the model to estimate the cooperation level in a set of hierarchical structures omitted in Mark's work yet common in everyday life--those with multiple leaders. We derived the conditions under which cooperation can emerge and verify our analytical predictions by agent-based computer simulation.