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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. (ECON 3)--UCL, 2006