Multiproduct-Firm Oligopoly: An Aggregative Games Approach

Abstract

This paper introduces a new class of demand systems to study oligopolistic pricing games with multiproduct rms. We focus on the class of demand systems that can be derived from discrete/continuous choice with iid type 1 extreme-value taste shocks. We also show that these demand systems are integrable with quasi-linear preferences. The pricing game is aggregative and payo functions are uni-modal, although not necessarily quasi-concave. Firms’ tting-in and best-response functions can be entirely summarized by a uni-dimensional sucient statistic, called the iota-markup. This allows us to show that, under fairly weak conditions, the pricing game has a Nash equilibrium. Under stronger conditions, this equilibrium is unique. We also provide an algorithm which exploits the aggregative nature of the game to compute the pricing equilibrium with multiproduct rms and CES demands. The algorithm always converges. As an application, we derive a number of results on the dynamic optimality of myopic merger policy under dierentiated Bertrand competition.

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