We study production in advance in a setting where firms first source inventories that remain unobservable to rivals, and then simultaneously set prices. In the unique equilibrium, each firm occasionally holds a sale relative to its reference price, resulting in firms sometimes being left with unsold inventory. In the limit as inventory costs become fully recoverable, the equilibrium converges to an equilibrium of the game where firms only choose prices and produce to order—the associated Bertrand game (examples of which include fully asymmetric clearinghouse models). Thus, away from that limit, our work generalizes Bertrand-type equilibria to production in advance, and challenges the commonly held view associating production in advance with Cournot outcomes. The analysis involves, as an intermediate step, mapping the price-inventory game into an asymmetric all-pay contest with outside options and non-monotonic winning and losing functions. We apply our framework to public policy towards information sharing, mergers, cartels, and taxation.

We develop an aggregative games approach to study oligopolistic price competition with multiproduct firms. We introduce a new class of IIA demand systems, derived from discrete/continuous choice, and nesting CES and logit demands. The associated pricing game with multiproduct firms is aggregative and a firm's optimal price vector can be summarized by a uni‐dimensional sufficient statistic, the ι‐markup. We prove existence of equilibrium using a nested fixed‐point argument, and provide conditions for equilibrium uniqueness. In equilibrium, firms may choose not to offer some products. We analyze the pricing distortions and provide monotone comparative statics. Under (nested) CES and logit demands, another aggregation property obtains: All relevant information for determining a firm's performance and competitive impact is contained in that firm's uni‐dimensional type. We extend the model to nonlinear pricing, quantity competition, general equilibrium, and demand systems with a nest structure. Finally, we discuss applications to merger analysis and international trade.