A Cramér-von Mises Approach to Incentivizing Truthful Data Sharing

Modern data marketplaces and data sharing consortia increasingly rely on incentive mechanisms to encourage agents to contribute data. However, schemes that reward agents based on the quantity of submitted data are vulnerable to manipulation, as agents may submit fabricated or low-quality data to inflate their rewards. Prior work has proposed comparing each agent's data against others' to promote honesty: when others contribute genuine data, the best way to minimize discrepancy is to do the same. Yet prior implementations of this idea rely on very strong assumptions about the data distribution (e.g. Gaussian), limiting their applicability. In this work, we develop reward mechanisms based on a novel, two-sample test inspired by the Cram\'er-von Mises statistic. Our methods strictly incentivize agents to submit more genuine data, while disincentivizing data fabrication and other types of untruthful reporting. We establish that truthful reporting constitutes a (possibly approximate) Nash equilibrium in both Bayesian and prior-agnostic settings. We theoretically instantiate our method in three canonical data sharing problems and show that it relaxes key assumptions made by prior work. Empirically, we demonstrate that our mechanism incentivizes truthful data sharing via simulations and on real-world language and image data.

Data Sharing for Mean Estimation Among Heterogeneous Strategic Agents

We study a collaborative learning problem where $m$ agents estimate a vector $\mu\in\mathbb{R}^d$ by collecting samples from normal distributions, with each agent $i$ incurring a cost $c_{i,k} \in (0, \infty]$ to sample from the $k^{\text{th}}$ distribution $\mathcal{N}(\mu_k, \sigma^2)$. Instead of working on their own, agents can collect data that is cheap to them, and share it with others in exchange for data that is expensive or even inaccessible to them, thereby simultaneously reducing data collection costs and estimation error. However, when agents have different collection costs, we need to first decide how to fairly divide the work of data collection so as to benefit all agents. Moreover, in naive sharing protocols, strategic agents may under-collect and/or fabricate data, leading to socially undesirable outcomes. Our mechanism addresses these challenges by combining ideas from cooperative and non-cooperative game theory. We use ideas from axiomatic bargaining to divide the cost of data collection. Given such a solution, we develop a Nash incentive-compatible (NIC) mechanism to enforce truthful reporting. We achieve a $\mathcal{O}(\sqrt{m})$ approximation to the minimum social penalty (sum of agent estimation errors and data collection costs) in the worst case, and a $\mathcal{O}(1)$ approximation under favorable conditions. We complement this with a hardness result, showing that $\Omega(\sqrt{m})$ is unavoidable in any NIC mechanism.