Self-confidence and survival

We consider the impact of history on the survival of a monopolist selling single units in discrete time periods, whose quality is learned slowly. If the seller learns her own quality at the same rate as customers, a sufficiently bad run of luck could induce her to stop selling. When she knows her quality, a good seller never stops selling. Furthermore, a seller with positive, though imperfect, information sells for the same number of periods whether her information is private or public. We further consider the robustness of the central result when the seller's opportunities for strategic behaviour are limited.