Statistical estimation with strategic data sources in competitive settings

In this paper, we introduce a preliminary model for interactions in the data market. Recent research has shown ways in which a single central data aggregator can design mechanisms to ensure it receives high quality data from a collection of users, even when the sources have an aversion to producing and reporting such estimates to the aggregator. However, we have shown that these mechanisms often break down in more realistic models, where multiple data aggregators are in competition for the users' data. We formulate the competition that arises between the aggregators as a game, and show this game admits either no Nash equilibria, or a continuum of Nash Equilibria. 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.