Oligopolistic price competition with a continuous demand

Demand functions in two related models of oligopolistic price competition with homogeneous products are derived from a set of economically plausible axioms. These axioms represent weaker assumptions about consumer behavior compared to the classic Bertrand model. In both models, firms do not necessarily face a discontinuous demand at an equilibrium price level. Hence, firms may charge an equilibrium price that is above their marginal cost (earning a strictly positive profit). The equilibrium price is lower when there are more firms and/or consumers are more sensitive to price changes. In the limit, when consumers are highly sensitive to price changes, both models converge to the classic Bertrand model.