Demand-side response, essential for developing low-carbon power systems, is often triggered through dynamic price signals. Consumers being exposed to such price signals depend on whether their power supply contract is based on a flat or a dynamic tariff, mimicking at least partially the dynamics of this price. In liberalized power retail markets, these two types of contracts can enter into competition for the same population. This article focuses on such interaction. Specifically, we study the retail market equilibrium when flat and dynamic tariffs compete for the same population, which is horizontally differentiated by its ability to engage in demand response. We obtain analytical results defining implicitly retailers’ best responses, equilibria of the retail market and, as a reference point, optimal offers for a regulated unique retailer, both for variable and truly dynamic tariffs. In the general case, the price competition between the two retailers imposes that the dynamic contract can only convey the dynamics of the underlying supply costs with a diminishing scaling factor dependent on the distribution of the propensity to flexibility among the population. An application to the French case based on 2023-2024 data is provided, with a focus on flexible consumers’ enrollment into dynamic tariffs and retailers’ markups. For variable tariffs (varying in time but fixed ex-ante), competition between tariffs yields lower levels of flexibility effectively triggered through tariffs, even at high flexibility potential of the population. For truly dynamic tariffs (varying in time and unknown ex-ante), the unique retailer option seems less attractive for a regulator interested in mobilizing demand-side flexibility than the retail competition between specialized retailers. This is notably the case if consumers overestimate electricity prices on average. However, with dynamic tariffs, less flexible consumers bear the cost of imperfectly forecasting the dynamic tariff levels, even though this imperfect forecast is a trait of the whole population.