I. Introduction
Modeling the many interactions, diverse beliefs, and behaviors that are contained in a financial market is a daunting task. However, much of modern finance theory is based on careful assumptions and well-crafted theories that allow simplification to analytically tractable models often involve a single representative agent. While such models appear to push one's notions of stylized representations to the limit, they are a common part of the economics toolkit for making difficult social interactions tractable. These heroic attempts at simplifying markets have generally been unsuccessful at meeting the challenge of lining up with many empirical features of real markets. Among these are relative returns, the amount and persistence of volatility and trading volume, and cross correlations between volatility, returns, and volume. At the moment, there is no unified theoretical model capable of replicating all these facts, although some have been replicated individually.