This thesis consists of three essays. The first essay describes a model in which a dominant player can be endogenously determined. The model is developed in the context of Cournot and Stackelberg equilibria. Cournot equilibria are obtained in games where players move simultaneously (or sequentially but unobservably), and the extensive form strategy spaces of these players are isomorphic to each other. Stackelberg equilibria, on the other hand, are obtained as the perfect equilibria of perfect information games in which the players move sequentially, with the dominant player or the leader firm moving first and the other player moving second. Thus, the question of how to model an industry -- Cournot or Stackelberg -- is answered by examining timing and information conditions both of which are presumed exogenous. Firm sizes and technologies and demand characteristics are, in this context irrelevant. What we do instead, is to note that if demand is resolved over time, then firms may face a trade-off between making decisions before the uncertainty in demand is revealed and thereby establishing a "leadership" position, or waiting until after resolution of demand in order to avoid production mistakes. The sequentially rational Nash equilibrium of the resulting game is examined. It is shown that in a market with one large firm (i.e., a firm whose output affects price) and a nonatomic continuum of small firms (i.e., firms whose individual outputs do not affect price), the only equilibrium of the game described above, with nontrivial but small uncertainty, is a Stackelberg equilibrium with the large firm as the endogenously determined dominant player. The difference between a large and a small firm is also embodied in their respective cost functions.
The second essay answers the question of whether markets with one large firm and several small but atomic firms can be approximated by or can approximate a Stackelberg equilibrium. This is answered by establishing that the equilibrium correspondence of a family of games, each of which has one large firm and several small firms, and the number of small firms increases to infinity, is continuous.
The third essay adapts the model developed in the first essay to a model of noncooperative general exchange in which the traders are in the same strategic position with respect to each other. Thus a noncooperative game is defined in an exchange economy such that a price-setting monopolist is determined endogenously in equilibrium, and this is the unique sequentially rational Nash equilibrium.
