Prediction markets and performative predictions

Abstract

In the field of performance analysis of forecasters, proper scoring rules are a class of scoring rules that incentivize truthful forecasting, assuming that the predictions themselves cannot influence the outcome of the event in question. However, in practice, there exists the phenomenon of performative predictions, where the forecaster may attempt to manipulate the world through their own prediction in a way that increases their expected score, without reflecting their true initial belief. In this work, we study this scenario where predictions influence the event they are trying to predict.We focus on the context of prediction markets, which can be considered a way of aggregating individual forecasts into a single final prediction. To do this, we model a prediction market as a game and use tools from game theory to derive properties about how much players’ optimal predictions can differ from the true probability of the event, among other theoretical properties of these models.