Failure of Equilibrium Selection Methods for Multiple-Principal, Multiple-Agent Problems with Non-Rivalrous Goods: An Analysis of Data Markets
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The advent of machine learning tools has led to the rise of data markets. These data markets are characterized by multiple data purchasers interacting with a set of data sources. Data sources have more information about the quality of data than the data purchasers; additionally, data itself is a non-rivalrous good that can be shared with multiple parties at negligible marginal cost. In this paper, we study the multiple-principal, multiple-agent problem with non-rivalrous goods. Under the assumption that the principal's payoff is quasilinear in the payments given to agents, we show that there is a fundamental degeneracy in the market of non-rivalrous goods. Specifically, for a general class of payment contracts, there will be an infinite set of generalized Nash equilibria. This multiplicity of equilibria also affects common refinements of equilibrium definitions intended to uniquely select an equilibrium: both variational equilibria and normalized equilibria will be non-unique in general. This implies that most existing equilibrium concepts cannot provide predictions on the outcomes of data markets emerging today. The results support the idea that modifications to payment contracts themselves are unlikely to yield a unique equilibrium, and either changes to the models of study or new equilibrium concepts will be required to determine unique equilibria in settings with multiple principals and a non-rivalrous good.
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