This thesis consists of three empirical studies that examine the relationship between different forms of rivalry in monopoly and oligopoly airline markets and the resulting market price outcomes. The ultimate goal of this work is to empirically distinguish the concept of competition from the market structure, which is often conceived as a combination of the number of firms present in a market and their relative market share or dominance. These studies build on economic theory of imperfect competition to determine the incentives for rivalry in each context and in turn develop a measure of the intensity of competition in order to study its effect on market price outcomes. A large part of this thesis focuses on forms and instruments of rivalry that firms may deploy to maintain or expand their market dominance and restrain competition. It therefore studies the dynamics of both competitive and plausibly anticompetitive behaviour in the airline industry.