Symmetric equilibrium existence and optimality in differentiated product markets

Equilibrium existence and optimality are analysed in a market for products differentiated by their variety. A game of three stages is analysed. Firms enter in the first stage, choose varieties in the second stage, and choose prices in the third stage. The existence of subgame-perfect equilibria is established. At equilibrium products are symmetrically located in the space of characteristics and are offered at equal prices. The surplus maximizing solution is characterized, and it is shown that surplus maximizing product diversity is lower than the equilibrium one.