Statistical estimation with strategic data sources in competitive settings

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 principalagent 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.

Optimal contract design for effort-averse sensors

“…By contrast, the work presented here focuses on influencing the underlying effort invested by the participating sensors in order to improve the quality of estimates determined by averaging. This paper is closer, in essence, to the studies in (Chen, Gupta, and Huang, 2016;Dobakhshari, Li, and Gupta, 2016;Gao et al, 2015;Han, Zhang, Luo, Hu, and Veeravalli, 2016;Koutsopoulos, 2013;Luo, Tan, and Xia, 2014;Westenbroek, Dong, Ratliff, and Sastry, 2017;Yang, Xue, Fang, and Tang, 2012;Zhao et al, 2014), where the sensors are assumed to incur a cost that is proportional to the time or the energy dedicated to a sensing task. How-ever, those studies differ in several ways from the framework formulated in this paper.…”

Competitive Statistical Estimation With Strategic Data Sources

“…Furthermore, the work in the paper is a significant extension of our prior work [22] where we considered strategic data sources with a specific exponential function mapping effort to query response quality. In the present work, we characterize equilibria and the price of anarchy for a much broader class of games between data buyers where the data sources' effort functions can be any non-negative, strictly decreasing, convex, and twice continuously differentiable function.…”

“…Due to the wide variety of estimators data aggregators can use, as well as effort-to-variance functions that characterize data sources, it is difficult to provide interesting general bounds on the price of anarchy, a widely used metric for the inefficiency of equilibria [27]. However, when both are specified, the price of anarchy can be explicitly calculated [22].…”

Perspective in Supply Chain Risk Management

“…The optimal strategies for keeping supply chain enterprises from competing with each other and improving this system have been given by many scientists, shown in Refs. [24] (Shengdong , Romuold (2016) [25] , Tyler Westenbrok (2019) [26] the inventory model for the supply chain that consists of supplier and retailer has been constructed according to two cases of their cooperative and competitive, respectively. Then, the Nash equilibrium point's existence has been proven under some certain constraints, when the non-cooperative game makes sense between their interactions.…”