The paper investigates the stability of a dominant cartel in the price-leadership model, where a group of firms (the cartel) sets the price and a competitive fringe follows this price. The authors show that there is a general interest in forming a cartel, as it benefits both the cartel members and the competitive fringe, with the latter reaping a disproportionate share of the benefits. However, the stability of the cartel is analyzed differently depending on whether the number of firms is finite or infinite. For a finite number of firms, each with the same cost curve, the authors prove that there always exists a stable cartel. This stability is due to the negligible impact of a firm's exit or entry on the price and profits, which makes it difficult for cartel members to defect to the competitive fringe. In contrast, for an infinite continuum of firms, the cartel is unstable because the impact of a firm's exit or entry on the price and profits is significant, leading to an incentive for firms to defect. The paper also discusses the implications of these findings for the stability of the price-leadership model and suggests that the size of the cartel relative to the competitive fringe is crucial for stability. In large finite industries, only cartels containing a small fraction of the firms are expected to be stable, as the cartel's effectiveness is limited. The authors conclude that further research is needed to determine the generality of their results, especially in more complex models and dynamic frameworks.The paper investigates the stability of a dominant cartel in the price-leadership model, where a group of firms (the cartel) sets the price and a competitive fringe follows this price. The authors show that there is a general interest in forming a cartel, as it benefits both the cartel members and the competitive fringe, with the latter reaping a disproportionate share of the benefits. However, the stability of the cartel is analyzed differently depending on whether the number of firms is finite or infinite. For a finite number of firms, each with the same cost curve, the authors prove that there always exists a stable cartel. This stability is due to the negligible impact of a firm's exit or entry on the price and profits, which makes it difficult for cartel members to defect to the competitive fringe. In contrast, for an infinite continuum of firms, the cartel is unstable because the impact of a firm's exit or entry on the price and profits is significant, leading to an incentive for firms to defect. The paper also discusses the implications of these findings for the stability of the price-leadership model and suggests that the size of the cartel relative to the competitive fringe is crucial for stability. In large finite industries, only cartels containing a small fraction of the firms are expected to be stable, as the cartel's effectiveness is limited. The authors conclude that further research is needed to determine the generality of their results, especially in more complex models and dynamic frameworks.