Abstract: Companies spend hundreds of millions of dollars annually on advertising to build and maintain awareness for their brands in competitive markets. However, awareness formation models in the marketing literature ignore the role of competition. Consequently, we lack both the empirical knowledge and normative understanding of building brand awareness in dynamic oligopoly markets. To address this gap, we propose an N-brand awareness formation model, design an extended Kalman filter to estimate the proposed model using market data for five car brands over time, and derive the optimal closed-loop Nash equilibrium strategies for every brand. The empirical results furnish strong support for the proposed model in terms of both goodness-of-fit in the estimation sample and cross-validation in the out-of-sample data. In addition, the estimation method offers managers a systematic way to estimate ad effectiveness and forecast awareness levels for their particular brands as well as competitors' brands. Finally, the normative analysis reveals an inverse allocation principle that suggests -- contrary to the proportional-to-sales or competitive parity heuristics -- that large (small) brands should invest in advertising proportionally less (more) than small (large) brands.