Equilibrium Selection in Data Markets: Multiple-Principal, Multiple-Agent Problems with Non-Rivalrous Goods

The advent of data-driven tools has led to the rise of data markets. These data markets are often characterized by multiple data purchasers interacting with a set of data sources. There are several aspects of data markets that distinguish them from a typical commodity market. First, data sellers have more information about the quality of data than the data purchasers. Second, data is a non-rivalrous good that can be shared with multiple parties at negligible marginal cost. Third, the value of data is coupled, and there are strong informational externalities. Formally, this gives rise to a new class of games which we call multiple-principal, multiple-agent problem with non-rivalrous goods. 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.