Essays on Information and Markets

Abstract

This thesis provides new equilibrium existence results for markets with information asymmetries and relates them in a novel way to the role of economic intermediation. Under atomless uncertainty, single market linear price equilibria are known not to exist prevalently even when agents are risk averse expected utility maximizers. The notion of prevalence involves essentially picking an economy at random. Bypassing the nonexistence problem is one of the achievements of the nonlinear price decentralization theory. This thesis contributes by reconciling the nonlinear price decentralization theory to a large extent with certain competitive market structures. We do this in Chapter 1 by defining linear price equilibrium with multiple markets and establishing its existence. Each market has its own price vector (linear functional), and agents’ involvement in various markets is heterogeneous. As a result, price differences across markets may prevail in equilibrium. We present an example in which single market linear price equilibrium does not exist but certain corresponding equilibrium with two markets does. Our equilibrium with multiple markets has a more standard economic interpretation than equilibrium with nonlinear prices used in nonlinear decentralization theory. Our framework can potentially accommodate even more nonlinearities if economic intermediaries are explicitly introduced into the model.

Despite the nonexistence problem, single market linear price equilibrium with infinitely many states is still known to exist under restrictive assumptions on the information structure. In Chapter 2, we introduce two new results on the existence of single market linear price (Radner) equilibrium with infinitely many states under economically meaningful conditions. Our first result requires that agents have independent information, while the second assumes that the total endowment of the economy is common knowledge.

In Chapter 3, we explore how economic agents can test the scope of their knowledge and, in particular, the informational content of equilibrium prices under asymmetric information. We show that one can go far in arguing that equilibrium prices tend to be fully revealing.