A Note on Prediction Markets

TL;DR

This paper examines how prediction markets aggregate private information through sequential betting, analyzing convergence of probabilities and the impact of private knowledge on collective predictions.

Contribution

It revisits theoretical results on probability updates in prediction markets, especially focusing on two individuals with different private information and their probability convergence behavior.

Findings

Probabilities tend to converge to a limit, which may differ from pooled private information.

Sequential updates can lead to convergence or divergence depending on private information.

Theoretical analysis supported by illustrative examples.

Abstract

In a prediction market, individuals can sequentially place bets on the outcome of a future event. This leaves a trail of personal probabilities for the event, each being conditional on the current individual's private background knowledge and on the previously announced probabilities of other individuals, which give partial information about their private knowledge. By means of theory and examples, we revisit some results in this area. In particular, we consider the case of two individuals, who start with the same overall probability distribution but different private information, and then take turns in updating their probabilities. We note convergence of the announced probabilities to a limiting value, which may or may not be the same as that based on pooling their private information.