According to economic theory, supported by empirical and laboratory evidence, the equilibrium price of a financial security reflects all of the information regarding the security's value. We investigate the dynamics of the computational process on the path toward equilibrium, where information distributed among traders is revealed stepby -step over time and incorporated into the market price. We develop a simplified model of an information market, along with trading strategies, in order to formalize the computational properties of the process. We show that securities whose payoffs cannot be expressed as a weighted threshold function of distributed input bits are not guaranteed to converge to the proper equilibrium predicted by economic theory. On the other hand, securities whose payoffs are threshold functions are guaranteed to converge, for all prior probability distributions. Moreover, these threshold securities converge in at most n rounds, where n is the number of bits of distributed information. We also prove a lower bound, showing a type of threshold security that requires at least n/2 rounds to converge in the worst case.

The novel idea of setting up Internet-based virtual markets, information markets, to aggregate dispersed information and predict outcomes of uncertain future events has empirically found its way into many domains. But the theoretical examination of information markets has lagged relative to their implementation and use. This paper proposes a simple theoretical model of information markets to understand their information dynamics. We investigate and provide initial answers to a series of research questions that are important to understanding how information markets work, which are: (1) Does an information market converge to a consensus equilibrium? (2) If yes, how fast is the convergence process? (3) What is the best possible equilibrium of an information market? and (4) Is an information market guaranteed to converge to the best possible equilibrium?

Sigatures are on file in the Graduate School. iii In almost all walks of life, predicting uncertain future events plays an essential role in decision-making processes. However, information related to future events frequently exists only as dispersed opinions, insights, and intuitions of individuals. Each individual only knows a little, but aggregating the dispersed information together may make considerable contribution to decision making. This is typical in many domains including business, politics, and entertainment. Therefore, how to aggregate such dispersed information for useful decision support is a crucial task. Markets have shown great potential as one of the most effective mechanisms for gathering distributed information and generating accurate forecasts, often surpassing many existing methods in practice. This research studies information markets, markets that are specially designed for information aggregation and forecasting, from four different perspectives: theoretical examination, experimental evaluation, empirical analysis, and design.

with aggregate uncertainty