How does market concentration affect the potency of monetary policy? The ubiquitous monopolistic-competition framework is silent on this issue. To tackle this question we build a model with heterogeneous oligopolistic sectors. In each sector, a finite number of firms play a Bertrand dynamic game with staggered price rigidity. Following an extensive Industrial Organization literature, we focus on Markov equilibria within each sector. Aggregating up, we study monetary shocks and provide a closed form formula for the response of aggregate output, highlighting three measurable sufficient statistics: demand elasticities, market concentration, and markups. We calibrate our model to the empirical evidence on pass-through, and find that higher market concentration significantly amplifies the real effects of monetary policy. To separate the strategic effects of oligopoly from the effects this has on residual demand, we compare our model to one with monopolistic firms after modifying consumer preferences to ensure firms face comparable residual demands. Finally, the Phillips curve for our model displays inflation persistence and endogenous cost-push shocks.