Dealers, insiders and bandits: learning and its effects on market outcomes

This thesis seeks to contribute to the understanding of markets populated by boundedly rational agents who learn from experience. Bounded rationality and learning have both been the focus of much research in computer science, economics and finance theory. However, we are at a critical stage in defining the direction of future research in these areas. It is now clear that realistic learning problems faced by agents in market environments are often too hard to solve in a classically rational fashion. At the same time, the greatly increased computational power available today allows us to develop and analyze richer market models and to evaluate different learning procedures and algorithms within these models. The danger is that the ease with which complex markets can be simulated could lead to a plethora of models that attempt to explain every known fact about different markets. The first two chapters of this thesis define a principled approach to studying learning in rich models of market environments, and the rest of the thesis provides a proof of concept by demonstrating the applicability of this approach in modeling settings drawn from two different broad domains, financial market microstructure and search theory. In the domain of market microstructure, this thesis extends two important models from the theoretical finance literature. The third chapter introduces an algorithm for setting prices in dealer markets based on the model of Glosten and Milgrom (1985), and produces predictions about the behavior of prices in securities markets. In some cases, these results confirm economic intuitions in a significantly more complex setting (like the existence of a local profit maximum for a monopolistic market-maker) and in others they can be used to provide quantitative guesses for variables such as rates of convergence to efficient market conditions following price jumps that provide insider information. The fourth chapter studies the problem faced by a trader with insider information in Kyle’s (1985) model. I show how the insider trading problem can be usefully analyzed from the perspective of reinforcement learning when some important market parameters are unknown, and that the equilibrium behavior of an insider who knows these parameters can be learned by one who does not, but also that the time scale of convergence to the equilibrium behavior may be impractical, and agents with limited time horizons may be better off using approximate algorithms that do not converge to equilibrium behavior. The fifth and sixth chapters relate to search problems. Chapter 5 introduces models for a class of problems in which there is a search “season” prior to hiring or matching, like academic job markets. It solves for expected values in many cases, and studies the difference between a “high information” process where applicants are immediately told when they have been rejected and a “low information” process where employers do not send any signal when they reject an applicant. The most important intuition to emerge from the results