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In this paper, we introduce a preliminary model for interactions in the datamarket. Recent research has shown ways in which a data aggregator can designmechanisms for users to ensure the quality of data, even in situations wherethe users are effort-averse (i.e. prefer to submit lower-quality estimates) andthe data aggregator cannot observe the effort exerted by the users (i.e. thecontract suffers from the principal-agent problem). However, we have shown thatthese mechanisms often break down in more realistic models, where multiple dataaggregators are in competition. Under minor assumptions on the properties ofthe statistical estimators in use by data aggregators, we show that there iseither no Nash equilibrium, or there is an infinite number of Nash equilibrium.In the latter case, there is a fundamental ambiguity in who bears the burden ofincentivizing different data sources. We are also able to calculate the priceof anarchy, which measures how much social welfare is lost between the Nashequilibrium and the social optimum, i.e. between non-cooperative strategic playand cooperation.

Statistical Estimation with Strategic Data Sources in Competitive Settings