The contribution of this project comes from developing a new approach to an issue central to economic theory, i.e., the determinants of market failure. Economists have compiled a taxonomy of exceptions to market efficiency. For example, optimality theorems for markets do not hold if the returns to production are increasing or if public goods are bought or sold. This project uses developments in mechanism theory and models of economies with a continuum of agents to develop a more general and more powerful anatomy of market failure. This research builds on past work by the investigators. They are capable of doing the work. The study of mechanisms is an attractive approach because of its generality. Markets are one of many different types of mechanisms for allocating resources, so markets may fail to achieve economic efficiency where some other mechanisms might not fail. The investigators have shown in their previous work that the source of mechanism failure is the presence of monopoly power due to increasing returns, externalities and public goods. In this project they characterize efficient dominant strategy mechanisms applicable to transferable or non-transferable utility and finite agent or nonatomic models. For the existence, or feasibility, of such mechanisms, homogenity of the environment is shown to be the decisive condition without which there is mechanism failure. Connections are drawn between mechanism failure and market failure. Comparisons are made between Bayesian Nash equilibrium and dominant strategy equilibrium. A special case, the double-auction model, is examined for dominant strategy properties and the findings are applied to the question of attainment of equilibrium in a market with a small number of agents. Theoretically, asymptotic properties of double-auction markets are investigated. The issue of homogeneity versus non-homogeneity in nonatomic models is addressed with special reference to the existence of Walrasian equilibrium, the characterization of Walrasian equilibria that are not perfectly competitive, and the phenomenon of monopolistic competition.
