In this work, we develop a new model for competition in markets with differentiated products. In addition, we present a consumer model designed to produce a flexible nonlinear inverse demand system that resembles the classical Multinomial Logit model, and discuss several extensions. We characterize firms competition in quantities based on the inverse demand system. The model is applied to the Spanish newspaper industry. This is a highly competitive two-sided market whose revenues are generated from sales and to a larger extent from advertising driven by its circulation. We then characterize the Perfect Equilibrium by conditional moment conditions, and estimate the parameters using the Generalized Method of Moments.