This project consists of three parts: (1) the study of perfect competition in the context of large assignment models; (2) the development of a general equilibrium model of bankruptcy and collateral with applications to financial markets; and (3) the development of an extended notion of equilibrium in extensive form games with continuous action spaces. This research contributes a powerful new theory of competition, general insights into the impact of bankruptcy on financial markets and new insights into ways of solving a class of bargaining problems found frequently in economics. The work on characterizing competition in large assignment problems is especially exciting because it could lead to a new way of conceptualizing competition that would capture as special cases such widely used criteria as non manipulability of prices and the appropriation of agents' marginal contributions. The assignment model has a rich history as a laboratory for the development of important new theories such as linear programming and core theory. Past work by the investigator and his collaborators suggests that their study of the uniqueness of equilibrium prices in large assignment models could provide another new, powerful analytical tool for economic theory.
