Comment: 42 pages, 11 figuresIn a refreshing mathematical investigation, Mark (2018) shows that status hierarchy may facilitate the emergence of cooperation in groups. Despite the contribution, the present paper notes that there are limitations in Mark's model that makes it less realistic than it could in explaining real-world experiences. Consequently, 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 in these groups, and verified our analytical predictions in agent-based computer simulations. In so doing, not only does our model elaborate on its predecessor and support Mark's general prediction. For theory, our work further reveals two novel phenomena of group cooperation: Both the relative number of cooperators to defectors in groups and the assortativity among these different roles can backfire
they are not always the higher, the better for cooperation to thrive. For methodology, the hierarchy measure developed and our model using the measure may also be applied in future research on a wide range of related topics.