We characterize mixed-strategy equilibria when capacity constrained suppliers can charge location-based prices to different customers. We establish an equilibrium with prices that weakly increase in the costs of supplying a customer. Despite prices above costs and excess capacities, each supplier exclusively serves its home market in equilibrium. Competition yields volatile market shares and an inefficient allocation of customers to firms. Even ex-post cross-supplies may restore efficiency only partly. We show that consumers may benefit from price discrimination whereas the the firms make the same profits as with uniform pricing. We use our findings to discuss recent competition policy cases and provide hints for a more refined coordinated-effects analysis.