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

... In this paper, information markets are introduced as a promising mechanism for predicting uncertain outcomes. Information markets are markets that are specially designed for aggregating information and making predictions on future events. A generic model of information markets is proposed. We derive some fundamental properties on when information markets can converge to the direct communications equilibrium, which aggregates all information across traders and is the best possible prediction for the event under consideration