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In recent years, data have played an increasingly important role in the economy as a good in its own right. In many settings, data aggregators cannot directly verify the quality of the data they purchase, nor the effort exerted by data sources when creating the data. Recent work has explored mechanisms to ensure that the data sources share high-quality data with a single data aggregator, addressing the issue of moral hazard. Oftentimes, there is a unique, socially efficient solution. In this paper, we consider data markets where there is more than one data aggregator. Since data can be cheaply reproduced and transmitted once created, data sources may share the same data with more than one aggregator, leading to free-riding between data aggregators. This coupling can lead to nonuniqueness of equilibria and social inefficiency. We examine a particular class of mechanisms that have received study recently in the literature, and we characterize all the generalized Nash (GN) equilibria of the resulting data market. We show that, in contrast to the single-aggregator case, there is either infinitely many GN equilibria or none. We also provide necessary and sufficient conditions for all equilibria to be socially inefficient. In our analysis, we identify the components of these mechanisms that give rise to these undesirable outcomes, showing the need for research into mechanisms for competitive settings with multiple data purchasers and sellers.

Competitive Statistical Estimation With Strategic Data Sources