UC San Diego

This dissertation contains two chapters of my research. Chapter 2 studies whether prices aggregate private information in large competitive markets. To demonstrate the existence of fully revealing equilibrium prices, the literature on common-value auctions typically assumes that the information structure satisfies a strong ordering, the so-called monotone likelihood ratio property. This assumption rules out a large number of market situations - for instance, when signals come from different sources, and thus, the signals are multidimensional. This paper provides necessary and sufficient conditions for the existence of equilibria that fully aggregate information. These conditions are an ordering on the information structure, although sufficiently weak to allow for multidimensional signals to fit naturally. In addition, the paper shows that informative equilibria exist generically whenever signals are at least as numerous as values. On the other end, when signals are scarce, relative to the values, the reverse result holds. In a context where the object has multiple characteristics and signals are specialized to specific characteristics, informative equilibria are generic as long as signals are sufficiently rich for each characteristic. Chapter 3 extends the Crawford and Sobel (1982) (CS) cheap talk model, by allowing for the possibility that the message sent by the informed expert never arrives to the decision maker. This feature introduces a novel strategic consideration because when a message does not arrive, the receiver does not know whether the message was sent and lost, or not sent at all. The paper studies equilibria under quadratic preferences. In contrast to Blume et al. (2007), equilibria continue to have the partition structure of CS when there are finitely many ways in which messages can be misinterpreted. Furthermore, this mechanism achieves the upper bound on efficiency as in the mediated mechanism by Goltsman et al. (2008)