Impact of Committed Minorities: Unveiling Critical Mass of Cooperation in the Iterated Prisoner's Dilemma Game

TL;DR

This study explores how small committed minorities can trigger widespread cooperation in the Iterated Prisoner's Dilemma, revealing tipping points and conditions under which minority influence leads to full cooperation across different population structures.

Contribution

It uncovers the mechanisms and critical thresholds by which committed minorities promote cooperation in repeated social dilemma games, considering various strategies and network topologies.

Findings

Unconditional cooperators can induce full cooperation under weak imitation.

Conditional cooperators employing Tit-for-Tat or extortion strategies promote cooperation under strong imitation.

Excessive density of conditional cooperators can hinder cooperation in structured populations.

Abstract

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.