  The critical mass effect is a prevailing topic in the study of complex
systems. Recent research has shown that a minority of zealots can effectively
drive widespread cooperation in social dilemma games. However, achieving a
critical mass of cooperation in the prisoner's dilemma requires stricter
conditions. The underlying mechanism behind this effect remains unclear,
particularly in the context of repeated interactions. This paper aims to
investigate the influence of a committed minority on cooperation in the
Iterated Prisoner's Dilemma game, a widely studied model of repeated
interactions between individuals facing a social dilemma. In contrast to
previous findings, we identify tipping points for both well-mixed and
structured populations. Our findings demonstrate that a committed minority of
unconditional cooperators can induce full cooperation under weak imitation
conditions. Conversely, a committed minority of conditional cooperators, who
often employ Tit-for-Tat or extortion strategies, can promote widespread
cooperation under strong imitation conditions. These results hold true across
various network topologies and imitation rules, suggesting that critical mass
effects may be a universal principle in social dilemma games. Additionally, we
discover that an excessive density of committed conditional cooperators can
hinder cooperation in structured populations. This research advances our
understanding of the role of committed minorities in shaping social behavior
and provides valuable insights into cooperation dynamics.
