Much evidence supports that financial markets have the ability to aggregate information. When tied to a random variable, a financial market can forecast the value of the random variable. It then becomes a prediction market. We establish a model of prediction markets with aggregate uncertainty, and theoretically characterize some fundamental properties of prediction markets. Specifically, we have shown that a prediction market is guaranteed to converge to an equilibrium, where traders have consensus on the forecast. The best possible prediction a prediction market can make is the direct communication equilibrium. However, prediction markets do not always converge to it. We have proved that a sufficient condition for the convergence to the direct communication equilibrium under our model is that the private information of each trader, conditioned on the state of the world, is identically and independently distributed. Furthermore, if this condition is satisfied, the prediction market converges in at most two rounds. 1

The capacity of markets to aggregate information has been conclusively demonstrated but the limitations of that capacityhave still not been fully explored. In this paper, we demonstrate the existence of #information traps". These traps appear to be a sort of equilibrium in which information existing in the market does not become revealed in prices. The foundation for the equilibrium is a pattern of misaligned beliefs in which each person's actions are based upon mistaken beliefs about the information held by others. The mistakes, themselves, haveatype of mutual compatibility and cannot become revealed by the price discovery process because individuals have no incentives or resources to adjust. Attempts to probe the nature of the phenomena involved two period markets with a contingent claim instrument, experienced participants, and unlimited short selling opportunities. # The authors gratefully acknowledge the #nancial support for this research whichwas provided by the Caltech...

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?

Citing recent successes in forecasting elections, movies, products, and other outcomes, prediction market advocates call for widespread use of market-based methods for government and corporate decision making. Though theoretical and empirical evidence suggests that markets do often outperform alternative mechanisms, less attention has been paid to the magnitude of improvement. Here we compare the performance of prediction markets to conventional methods of prediction, namely polls and statistical models. Examining thousands of sporting and movie events, we find that the relative advantage of prediction markets is surprisingly small, as measured by squared error, calibration, and discrimination. Moreover, these domains also exhibit remarkably steep diminishing returns to information, with nearly all the predictive power captured by only two or three parameters. As policy makers consider adoption of prediction markets, costs should be weighed against potentially modest benefits.

In this paper we study information revelation on asset markets with endogenous and exogenous information. Our results indicate that superior information can only be exploited in the beginning of trading. Information disseminates on the market and informational advantages are counter-balanced over time. This result holds true for both, exogenous and precise endogenous information. Vague endogenous information, however, has no impact on individual payoff. Furthermore, we find that excessive trading decreases individual earnings.

The results of an asset market experiment, in which 64 subjects trade two assets on eight markets in a computerized continuous double auction, indicate that objectively irrelevant information influences trading behavior. Moreover, positively and negatively framed information leads to a particular trading pattern, but leaves trading prices and trading volume una#ected. In addition, we provide support for the disposition e#ect. Participants who experience a gain sell their assets more rapidly than participants who experience a loss, and positively framed subjects generally sell their assets later than negatively framed subjects.

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

The capacity of markets to aggregate information has been conclusively demonstrated but the limitations of that capacity havestill not been fully explored. In this paper, we demonstrate the existence of \information traps". These traps appear to be a sort of equilibrium in which information existing in the market does not become revealed in prices. The foundation for the equilibrium is a pattern of misaligned beliefs in which each person's actions are based upon mistaken beliefs about the information held by others. The mistakes, themselves, have atype of mutual compatibility and cannot become revealed by the price discovery process because individuals have no incentives or resources to adjust. Attempts to probe the nature of the phenomena involved two period markets with a contingent claim instrument, experienced participants, and unlimited short selling opportunities.