  In this paper, we introduce a preliminary model for interactions in the data
market. Recent research has shown ways in which a data aggregator can design
mechanisms for users to ensure the quality of data, even in situations where
the users are effort-averse (i.e. prefer to submit lower-quality estimates) and
the data aggregator cannot observe the effort exerted by the users (i.e. the
contract suffers from the principal-agent problem). However, we have shown that
these mechanisms often break down in more realistic models, where multiple data
aggregators are in competition. Under minor assumptions on the properties of
the statistical estimators in use by data aggregators, we show that there is
either 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 of
incentivizing different data sources. We are also able to calculate the price
of anarchy, which measures how much social welfare is lost between the Nash
equilibrium and the social optimum, i.e. between non-cooperative strategic play
and cooperation.
