convert free users to paying ones. Price promotions (or “sales”) are often used in freemium to induce the conversion. However …, the causal effect of exposing consumers to such inter-temporal price variation is unclear. While sales can generate …, where the base version is sold for free, so that sales form extreme price cuts on the overall product combination. We work …

of the space of all price paths in time to the space of time-constant prices is sensible since the latter in general … contains Nash equilibria. We prove that the equilibrium price of the weakest active firm tends to marginal cost as the number …