Prediction Markets with Intermittent Contributions

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.

💡 Research Summary

This paper proposes a novel prediction market framework designed to facilitate collaboration among self-interested agents in forecasting tasks, particularly addressing the challenges posed by data ownership issues and competitive interests. The core innovation lies in a market design that accommodates “intermittent contributions,” allowing sellers (forecast providers) to freely enter and exit the market at will, which reflects real-world practical constraints.

The market operates through a central operator who manages interactions between clients (who need forecasts) and sellers. The operator’s first key task is to optimally combine individual forecasts into a single, aggregated prediction. To achieve this, the authors employ an online learning approach based on Linear Regression (LR) models, one for each quantile level of interest. The primary methodological advancement is the extension of a Robust Linear Regression model to an online setting. This model learns not only the optimal convex combination weights for forecasts but also a linear correction matrix that compensates for missing forecasts from any seller. When a seller’s prediction is absent, the model uses correlations learned among other available forecasts to impute the missing information, allowing for continuous and reliable forecast aggregation despite irregular participation.

The second critical component is a two-tiered payoff allocation mechanism that distributes the client’s utility (reward) among sellers fairly and incentivizes both consistent participation and accurate forecasting. The total reward for a seller is a weighted sum of an in-sample and an out-of-sample component. The in-sample allocation uses a time-varying, online version of the Shapley value. This evaluates the marginal contribution of each seller’s forecast to the overall quality of the aggregated prediction over time, rewarding long-term informational value and consistency. The out-of-sample allocation directly rewards instantaneous forecasting accuracy by scoring each seller’s individual forecast against the actual outcome using a quantile scoring function (pinball loss). A parameter (δ) allows the market operator to balance the emphasis between historical contribution (in-sample) and immediate performance (out-of-sample).

The paper validates the proposed framework through comprehensive case studies using both simulated data and real-world wind power generation data. The results demonstrate that the adaptive robust linear regression model effectively maintains high forecasting accuracy even with frequent seller dropouts, outperforming standard methods. Furthermore, the dual payoff mechanism is shown to satisfy desirable economic properties (like budget balance) while effectively incentivizing sellers. This work provides a practical and theoretically sound solution for improving forecast accuracy in domains like renewable energy, where collaboration is essential but hindered by proprietary data and competitive concerns, by creating a market that is both adaptive to participation patterns and fair in reward distribution.