Prediction Markets with Intermittent Contributions

TL;DR

Prediction Markets with Intermittent Contributions tackles the challenge of data ownership and collaboration by introducing a prediction-market framework that supports online, robust forecast combination and intermittent participation. The approach combines forecasts through online linear regression, handles missing submissions with a robust correction mechanism, and distributes rewards via an in-sample online Shapley-like allocation and an out-of-sample quantile-loss score. The methodology is validated through synthetic time-invariant and time-varying scenarios and a real-world wind forecasting case, showing convergence, adaptability, and improved forecast quality under missing data. The work contributes a principled, economically grounded mechanism for fair payoff distribution and demonstrates practical viability for renewable energy forecasting contexts.

Abstract

Although both data availability and the demand for accurate forecasts are increasing, collaboration between stakeholders is often constrained by data ownership and competitive interests. In contrast to recent proposals within cooperative game-theoretical frameworks, we place ourselves in a more general framework, based on prediction markets. There, independent agents trade forecasts of uncertain future events in exchange for rewards. We introduce and analyse a prediction market that (i) accounts for the historical performance of the agents, (ii) adapts to time-varying conditions, while (iii) permitting agents to enter and exit the market at will. The proposed design employs robust regression models to learn the optimal forecasts' combination whilst handling missing submissions. Moreover, we introduce a pay-off allocation mechanism that considers both in-sample and out-of-sample performance while satisfying several desirable economic properties. Case-studies using simulated and real-world data allow demonstrating the effectiveness and adaptability of the proposed market design.

Figures (6)

• Figure 1: Market design overview
• Figure 2: Convergence of estimated weights for QR (top) and RQR (bottom) with $k=1$ and $\tau=0.5$.
• Figure 3: pay-off allocation for QR (top) and RQR (bottom) with three quantile levels $m = {0.1, 0.5, 0.9}$ and a total step reward of £100.
• Figure 4: Convergence of estimated weights for QR (top) and RQR (bottom) with $k=1$ and $\tau=0.5$ in a time-varying scenario.
• Figure 5: Bias with varying missingness rate ranging from 5% to 90%.