DP11539 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 demand systems, derived from discrete/continuous choice, and nesting CES and logit demand systems. 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 iota-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 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. Finally, we re-visit classic questions in static and dynamic merger analysis, and study the impact of a trade liberalization on the inter- and intra-firm size distributions, productivity and welfare.