We analyze a two‐stage quantity setting oligopolistic price discrimination game. In the first stage, firms choose capacities and in the second stage they simultaneously choose the share that they assign to each segment. At the equilibrium, the firms focus more on the high‐valuation customers. When the capacities in the first stage are endogenous, the deadweight loss does not vanish with the level of price discrimination, as it does in one‐stage games and monopoly. Moreover, the quantity‐weighted average price increases with the level of price discrimination as opposed to the established results in the literature for one‐stage games.