This thesis is focused on various dynamic oligopoly pricing games in revenue management and supply chain management. The oligopoly theory has been well-developed in the literature of economics. Nevertheless, the oligopolistic models I study in this thesis bear the unique flavor of operations management---concerning the operational-level detailed decision making and strategic interaction with random effects. In a comparison fashion, I discuss below problems and concepts that have been explored, and tools and methodologies that have been applied. (1) Stochastic game and differential game. We aim to solve for Markov perfect equilibria to stochastic games of oligopoly pricing competition in various settings. The stochastic game is generally intractable. However, we are able to completely characterize equilibrium strategies of its deterministic differential counterpart. The solution schemes suggested by the differential problem then are proved to be asymptotically optimal for the original stochastic game. Chapter 1 adopts this approach to a dynamic pricing game of multiple firms selling products with fixed initial capacity over a finite horizon. Chapter 4 adopts the same methodology to a revenue management game of finite-horizon make-to-order manufacturing systems. (2) Supermodular (submodular) game and (quasi-)concave game. Chapters 1, 4 and 5 apply the theory of superrnodular games to characterize oligopolistic interaction: Chapter 5 is its application in a two-stage Stackelberg game of both multiple supplier and multiple retailer competition where each stage is a static game; Chapters 1 and 4 are its applications in deterministic differential games. Chapter 3 reveals that the property of submodularity in competition of strategic substitutes is essential in retaining the monotone property of equilibrium strategies in time in finite-horizon stochastic revenue management games. Parallelly, the theory of (quasi-) concave games can also be used to capture equilibrium policies with applications that can be found in Chapters 2 and 5. (3) Price (Bertrand) competition and quantity (Cournot) competition. A key issue in oligopoly pricing competition is the choice of strategic variables. Chapter 2 addresses the choice of intertemporal strategic variables in the revenue management game of multiple firms selling products with fixed initial capacity over a finite horizon. The concern of choosing strategic decision variable is a unique problem arising from such a revenue management setting. Moreover, Chapters 1 and 5 particularly consider price competition, Chapter 4 considers quantity competition, and Chapters 2 and 3 study both. (4) Substitutable products and complementary products. Another issue in oligopoly pricing competition is what kind of interaction the demand system exhibits among differentiated products when there is a change in the chosen decision variable of a particular firm. The effects of substitutability and complementarity in demand systems combined with the choice of strategic variable (either price or quantity) yield games of supermodularity and submodularity. Chapter 3 explores these different types of strategic interaction in revenue management settings. (Abstract shortened by UMI.)
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