# Competitive Statistical Estimation with Strategic Data Sources

## TL;DR

This paper analyzes data markets with multiple aggregators, revealing the potential for multiple or no equilibria and highlighting the social inefficiency issues arising from free-riding and mechanism design in competitive data environments.

## Contribution

It characterizes all generalized Nash equilibria in multi-aggregator data markets and identifies conditions leading to social inefficiency, extending prior single-aggregator analyses.

## Key findings

- Multiple or no equilibria can occur in multi-aggregator data markets.
- Conditions for social inefficiency of equilibria are explicitly characterized.
- Mechanism components influencing inefficiency are identified.

## Abstract

In recent years, data has played an increasingly important role in the economy as a good in its own right. In many settings, data aggregators cannot directly verify the quality of the data they purchase, nor the effort exerted by data sources when creating the data. Recent work has explored mechanisms to ensure that the data sources share high quality data with a single data aggregator, addressing the issue of moral hazard. Oftentimes, there is a unique, socially efficient solution. In this paper, we consider data markets where there is more than one data aggregator. Since data can be cheaply reproduced and transmitted once created, data sources may share the same data with more than one aggregator, leading to free-riding between data aggregators. This coupling can lead to non-uniqueness of equilibria and social inefficiency. We examine a particular class of mechanisms that have received study recently in the literature, and we characterize all the generalized Nash equilibria of the resulting data market. We show that, in contrast to the single-aggregator case, there is either infinitely many generalized Nash equilibria or none. We also provide necessary and sufficient conditions for all equilibria to be socially inefficient. In our analysis, we identify the components of these mechanisms which give rise to these undesirable outcomes, showing the need for research into mechanisms for competitive settings with multiple data purchasers and sellers.