Impact of committed minorities: Unveiling critical mass of cooperation in the iterated prisoner's dilemma game

The critical mass effect is a prevailing topic in the study of complex systems. Recent research indicates that a committed minority of cooperators, unwavering in their beliefs and consistently maintaining cooperation, can effectively foster widespread cooperation in social dilemma games. However, achieving a critical mass of cooperation in the one-shot prisoner's dilemma requires stricter conditions. The underlying mechanism behind this effect remains unclear, particularly in the context of repeated interactions. This work 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 confronting 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 employ extortion strategy, can promote widespread cooperation under strong imitation conditions. These results are consistent across various network topologies and imitation rules, suggesting that critical mass effects may be a universal principle in social dilemma games. Moreover, we discovered that an excessive density of committed extortioners 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.