On convergence of forecasts in prediction markets

TL;DR

This paper introduces a dynamic prediction market model demonstrating that if some agents make accurate forecasts, the market's aggregated predictions converge to the true conditional expectations of future values.

Contribution

It provides a theoretical proof that market forecasts converge to true expectations given the presence of agents with correct or asymptotically correct predictions.

Findings

Market forecasts converge to true conditional expectations.

Presence of correct agents ensures convergence.

The model applies to sequences of random vectors.

Abstract

We propose a dynamic model of a prediction market in which agents predict the values of a sequence of random vectors. The main result shows that if there are agents who make correct (or asymptotically correct) next-period forecasts, then the aggregated market forecasts converge to the next-period conditional expectations of the random vectors.