Multiproduct-Firm Oligopoly: An Aggregative Games Approach

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.