Towards Data Auctions with Externalities
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The design of data markets has gained in importance as firms increasingly use predictions from machine learning models to make their operations more effective, yet need to externally acquire the necessary training data to fit such models. A property of such markets that has been given limited consideration thus far is the externality faced by a firm when data is allocated to other, competing firms. Addressing this is likely necessary for progress towards the practical implementation of such markets. In this work, we consider the case with n competing firms and a monopolistic data seller. We demonstrate that modeling the utility of firms solely through the increase in prediction accuracy experienced reduces the complex, combinatorial problem of allocating and pricing multiple data sets to an auction of a single digital (freely replicable) good. Crucially, this is what enables us to model the negative externalities experienced by a firm resulting from other firms' allocations. We obtain forms of the welfare-maximizing and revenue-maximizing auctions for such settings. We highlight how the form of the firms' private information – whether they know the externalities they exert on others or that others exert on them – affects the structure of the optimal mechanisms. We find that in all cases, the optimal allocation rules turn out to be single thresholds (one per firm), in which the seller allocates all information or none of it to a firm. We note the framework and results introduced hold more broadly for the auction of digital goods with externalities.
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