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. For each of these cases we provide conditions to secure the existence of exclusively asymmetric equilibria. Moreover we consider the case of convex payoff functions. 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 strategic complemantarities with action spaces that are complete lattices. One key issue addressed is the extent to which all equilibria tend to be symmetric for the general case of multi-dimensional (i.e. only partially ordered) strategy spaces. We find that the scope for asymmetric equilibrium behavior is definitely broader than in the one-dimensional case, though still quite limited. Another key question investigated here is whether asymmetric pure strategy Nash equilibria are always Pareto dominated by symmetric pure strategy Nash equilibria. While this need not hold in general for games with strategic complementarities, we identify different sufficient conditions that guarantee that such dominance holds. In Chapter 4 we deal with the effects of market transparency on prices in the Bertrand duopoly model. The analysis is intuitive and simple when we consider two types of strategic interaction between firms in an industry - strategic complementarities and substitutabilities. We present also traditional comparative statics analyses, demanding additionally some other regularity conditions, to cover those problems, when neither of these situations is the case. 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. For a special case when supermodularity holds, but products are not substitutes, the result on profits is not valid anymore. 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.

This thesis deals with different forms of strategic complementarities in industrial organization problems. Chapter 2 is an attempt to develop a unified approach to endogenous heterogeneity by constructing a general class of two-player symmetric games that possess only asymmetric pure-strategy Nash equilibria. These classes of games are characterized in some abstract sense by two general properties: payoff non-concavities and some form of strategic substitutability. While the second characteristic allows to show the existence of pure strategy Nash equilibria, the second precludes these equilibria to be symmetric. Other two classes of games that always possess asymmetric, but never symmetric, pure-strategy equilibria, although they are not of strategic substitutes are also studied. This chapter also generalizes a number of models dealing with two-stage games, with long term investment decisions in the first stage and product market competition in the second stage. Chapter 3 investigates the effects of forward looking behaviour in technology adoption. The setup is an overlapping generations model where agents choose between two alternative networks taking into consideration both the installed base and the expected base. The latter element is the distinctive feature of the approach. It is shown that a unique equilibrium exists, on which agents coordinate their expectations. While exhibiting hysteresis, the equilibrium adoption path does not comply with technologies locking in. Network choices are characterized both in terms of their long run properties and the expected time of adoption. Chapter 4 studies the problem of a monopolist who produces a good with network externalities and faces the possibility of selling a new higher quality. Within the vertical product differentiation it identifies the necessary and sufficient conditions for quality improvement to take place when a good, produced by a monopolist, exhibits positive network externalities. When network effects are not very strong, the monopolist produces both the high and the low quality and thus quality improvement takes place. In this case, he will use an introductory pricing strategy for the quality that benefits from network externalities, not maximizing however the network size. As the network effect becomes more important, the monopolist will have an incentive to practise introductory pricing and produce both qualities. Finally, if the network externality is higher than the intrinsic quality differential, quality improvement does not take place. Chapter 5 deals with the problem of an incumbent producing a low quality good with network externalities that faces the threat of entry by a higher quality good. In the framework of a vertical product differentiation model, it is identified a necessary and sufficient condition under which quality improvements are spontaneously adopted along, in spite of the existence of network effects. This condition says that the intensity of network effects on consumers' preferences should not exceed twice the differential of intrinsic qualities existing between the two variants. Finally, chapter 6 is concerned with the optimal path of prices of a monopolist who operates in a network industry for a finite horizon. Agents obtain intrinsic utility from the good and from the fact that in the past there have been other consumers using it. It is observed that the monopolist has an incentive to introduce the good at initially low prices and to increase the price as the time goes by. This chapter concludes with a necessary and sufficient condition under which the initial price, and only the initial one is zero. This condition is related both with the intensity of the preferences for the network and with the time horizon of the monopolist.