Incentivizing Data Collaboration: A Mechanism Design Approach

We study the problem of incentivizing strategic agents to truthfully contribute high-quality data in collaborative learning settings, where each agent benefits from improved estimation based on others’ data. Each agent privately observes the quality of their data, and agents may misreport it if not incentivized properly. We cast this problem with a Bayesian mechanism design framework in which the platform aims to find the optimal data-sharing mechanism that jointly determines allocations and payments to maximize both estimation accuracy and platform revenue. We prove that the optimal mechanism that incentivizes truthful reporting takes the form of a personalized threshold and pricing mechanism, in which each agent is allocated the learned estimator if their reported quality exceeds a (personalized) threshold and is charged a price based on the relevance of other agents' data in the learning task. We analyze this mechanism in a canonical Gaussian mean estimation task, derive a closed-form solution to the optimal mechanism, and highlight how data correlation affects the mechanism. We further extend the model to allow agents to exert costly efforts to improve their data quality before collaboration. We show that "free-riding" is mitigated as the optimal data-sharing mechanism induces a supermodular game: each agent is incentivized to exert more effort when others exert more. Finally, we show that equilibrium efforts form a complete lattice, and in the highest-effort equilibrium, each agent increases effort as other agents' data becomes more relevant in the learning task.