Multiproduct-Firm Oligopoly: An Aggregative Games Approach
我们发展了一种加总博弈方法，用以研究多产品企业间的寡头价格竞争。我们引入了一类新的IIA需求系统，该类需求系统由离散/连续选择推导而来，并将CES需求与logit需求嵌套其中。与之相关的多产品企业定价博弈具有加总性，企业的最优价格向量可由一个一维充分统计量——ι加成——加以概括。我们利用嵌套不动点论证证明了均衡的存在性，并给出了均衡唯一性的条件。在均衡中，企业可能选择不提供某些产品。我们分析了定价扭曲，并给出了单调比较静态结果。在(嵌套)CES与logit需求下，得到另一种加总性质：决定企业绩效与竞争影响的所有相关信息都包含在该企业的一维类型之中。我们将模型扩展至非线性定价、数量竞争、一般均衡以及具有嵌套结构的需求系统。最后，我们讨论了该模型在并购分析与国际贸易中的应用。
英文原文
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.