The paper examines the stability of a dominant cartel in a price-leadership model. It shows that there is a general interest in forming a cartel, even though fringe firms benefit more. With a finite number of firms, a stable dominant cartel always exists, unlike in a continuum of firms where the cartel is unstable. The paper demonstrates that when the number of firms is finite, a stable cartel can be found, as the internal and external stability conditions are satisfied. In contrast, with a continuum of firms, the cartel is unstable because fringe firms can free-ride and benefit more. The paper also shows that in large industries, the fraction of firms in a stable cartel tends to zero. The results suggest that the stability of a cartel depends on the impact of a firm's exit or entry on price and profits. The paper concludes that the key factor in the stability of a price-leadership cartel is the size of the effect on price and profits from the addition or loss of a cartel member. The analysis highlights the importance of finite versus continuum models in determining cartel stability.The paper examines the stability of a dominant cartel in a price-leadership model. It shows that there is a general interest in forming a cartel, even though fringe firms benefit more. With a finite number of firms, a stable dominant cartel always exists, unlike in a continuum of firms where the cartel is unstable. The paper demonstrates that when the number of firms is finite, a stable cartel can be found, as the internal and external stability conditions are satisfied. In contrast, with a continuum of firms, the cartel is unstable because fringe firms can free-ride and benefit more. The paper also shows that in large industries, the fraction of firms in a stable cartel tends to zero. The results suggest that the stability of a cartel depends on the impact of a firm's exit or entry on price and profits. The paper concludes that the key factor in the stability of a price-leadership cartel is the size of the effect on price and profits from the addition or loss of a cartel member. The analysis highlights the importance of finite versus continuum models in determining cartel stability.