Theoretical Investigation of Prediction Markets with Aggregate Uncertainty

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 simple model of prediction markets with aggregate uncertainty that theoretically characterizes 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 about the forecast. We have also shown that the best possible prediction a prediction market can make is the direct communication equilibrium. However, prediction markets do not always converge to the direct communication equilibrium. 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.