Personalized pricing and advertising: An asymmetric equilibrium analysis

We study personalized price competition with costly advertising among n quality-cost differentiated firms. Strategies involve mixing over both prices and whether to advertise. In equilibrium, only the top two firms advertise, earning “Bertrand-like” profits. Welfare losses initially rise then fall with the ad cost, with losses due to excessive advertising and sales by the “wrong” firm. When firms are symmetric, the symmetric equilibrium yields perverse comparative statics and is unstable. Our key results apply when demand is elastic, when ad costs are heterogeneous, and with noise in consumer tastes.