We study a Cournot industry in which each firm sells multiple quality-differentiated products. We use an upgrades approach, working not with the actual products but instead with upgrades from one quality to the next. The properties of single-product models carry over to the supply of upgrades, but not necessarily to the supply of complete products. Product line determinants and welfare results are presented. Strategic commitment to product lines is considered; firms may well choose to compete head-to-head.

In this book a rigorous, systematic, mathematical analysis is presented for oligopoly with multi-product firms in static as well as dynamic frameworks in the light of recent developments in theories of games, oligopoly and industrial organization. The general results derived in this book on oligopoly with multi-product firms contain, as special cases, all previous results on oligopoly with single product as well as oligopoly with product differentiation and single product firms. A constructive nu- merical method is given for finding the Cournot-Nash equilibrium, which may be extremely valuable to those who are interested in numerical analysis of the effects of various industrial policies. A sequential adjustment process is also formulated for finding the equilibrium. Dynamic adjustment processes have two versions, one with a discrete time scale and the other with a continuous time scale. The stability of the equilibrium is thoroughly investigated utilizing powerful mathematical results from the stability and linear algebra literature. The methodology developed for analyzing stability proves to be useful for dynamic analysis of economic models.

We study multiproduct firms in the contexts of unregulated monopoly, regulated monopoly and Cournot oligopoly. Using the concept of consumer surplus as a function of quantities (rather than prices), we present simple formulas for optimal prices and show that Cournot equilibrium exists and corresponds to a Ramsey optimum. We then discuss a tractable class of preferences that involve a generalized form of homotheticity. Profit-maximizing quantities are proportional to efficient quantities. We discuss optimal monopoly regulation when the firm has private information about its cost vector, and find situations where optimal regulation leaves relative price decisions to the firm.

The thesis consists of five chapters. The first of them contains introduction. Chapter 2 considers a broad class of two player symmetric games, which display a fundamental non-concavity when actions of both players are about to be the same. This implies that no symmetric equilibrium is possible. We distinguish different properties of the payoff functions, like strategic substitutes, complements and quasi-concavity, which are not necessarily imposed globally on the joint action space. A number of applications from industrial organization and applied microeconomics literature are provided. In Chapter 3 we generalize to the extent possible the known results for the case of games with one-dimensional action sets to the general case of games with action spaces that are complete lattices. We find that in the general case the scope for asymmetric equilibrium behavior is definitely broader than in the one-dimensional case, though still quite limited. Moreover, we investigate under which sufficient conditions asymmetric pure strategy Nash equilibria are always Pareto dominated by symmetric pure strategy Nash equilibria. In Chapter 4 we deal with the effects of market transparency on prices in the Bertrand duopoly model. We consider two types of strategic interaction between firms in an industry - strategic complementarities and substitutabilities. In the first case, the results are close to conventional wisdom, especially, when in the same time products are substitutes. Namely, equilibrium prices and profits are always decreasing in transparency level, while the consumer’s surplus is increasing. Considering price competition with strategic substitutes, an ambiguity in the direction of change of prices appears. This leads to ambiguity concerning equilibrium profits and surplus changes caused by increasing transparency. In Chapter 5 we provide general conditions for Cournot oligopoly with product differentiation to have monotonic reaction correspondences. We give a proof for the conditions stated by Vives (1999). Moreover we elaborate more general requirements. They allow for identifying increasing best responses even in case inverse demand is submodular, and similarly, decreasing best responses in case of supermodular inverse demand. Examples illustrating the scope of applicability of these results are provided.