# Statistical Estimation with Strategic Data Sources in Competitive Settings

## TL;DR

This paper explores the strategic interactions among competing data aggregators in data markets, revealing the challenges in designing mechanisms for quality assurance and the implications of non-cooperative equilibria on social welfare.

## Contribution

It introduces a model analyzing competition among data aggregators, highlighting the existence of multiple or no Nash equilibria and quantifying the efficiency loss through the price of anarchy.

## Key findings

- No Nash equilibrium or infinitely many in competitive settings.
- Fundamental ambiguity in incentivizing data sources.
- Quantified social welfare loss via price of anarchy.

## Abstract

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.