Date of Award
Doctor of Philosophy
My thesis consists of two separate essays on economic theory. The title of the first essay (chapter 1) is "Learning and Nash Equilibria in 3 x 3 Symmetric Games" and the title of the second essay (chapter 2) is "General Equilibrium Theory with Monopolistic Competition: An Introductory Analysis.";Chapter 1 explores the dynamic implications of learning models by studying fictitious play in 3 x 3 symmetric games. The basic model consists of two persons playing a symmetric normal form game with only three pure strategies repeatedly, and choosing their strategies in each period to maximize their expected payoffs in the stage game. After each play of the game each person forms his belief about his opponent's next strategy choice according to rules defined by fictitious play. It is shown that for a reasonably wide class of 3 x 3 symmetric games the sequence of beliefs generated by fictitious play inevitably converges to a mixed-strategy Nash equilibrium. For games that do not belong to this class, the limiting outcomes of fictitious play with identical initial beliefs are characterized. Finally, replacing fictitious play with another more sophisticated learning process yields stronger convergence results for fictitious play. These results provide useful references for future work in this area.;Chapter 2 provides an introduction to general equilibrium theory with monopolistic competition. A model of an economy with monopolistic competitive firms is constructed and studied. Each monopolistic firm perceives a demand function for its output which satisfies certain consistency condition in equilibrium. Three basic questions in equilibrium theory are addressed in the context of the model: existence, uniqueness and pareto compatibility of monopolistic competitive equilibria. Using fairly standard assumptions, it is shown that an infinite number of monopolistic competitive equilibria exists which are supported by different systems of perceived demand functions. Fixing the perceived demand functions, however, the number of equilibria (with different prices and allocations) is generically finite. Also, different equilibria supported by different systems of perceived demand functions are in general pareto incompatible.
Chan, Wing-yiu, "Two Essays On Economic Theory" (1994). Digitized Theses. 2338.