  Data is the new oil; this refrain is repeated extensively in the age of
internet tracking, machine learning, and data analytics. Social network
analysis, cookie-based advertising, and government surveillance are all
evidence of the use of data for commercial and national interests. Public
pressure, however, is mounting for the protection of privacy. Frameworks such
as differential privacy offer machine learning algorithms methods to guarantee
limits to information disclosure, but they are seldom implemented. Recently,
however, developers have made significant efforts to undermine tracking through
obfuscation tools that hide user characteristics in a sea of noise. These
services highlight an emerging clash between tracking and data obfuscation. In
this paper, we conceptualize this conflict through a dynamic game between users
and a machine learning algorithm that uses empirical risk minimization. First,
a machine learner declares a privacy protection level, and then users respond
by choosing their own perturbation amounts. We study the interaction between
the users and the learner using a Stackelberg game. The utility functions
quantify accuracy using expected loss and privacy in terms of the bounds of
differential privacy. In equilibrium, we find selfish users tend to cause
significant utility loss to trackers by perturbing heavily, in a phenomenon
reminiscent of public good games. Trackers, however, can improve the balance by
proactively perturbing the data themselves. While other work in this area has
studied privacy markets and mechanism design for truthful reporting of user
information, we take a different viewpoint by considering both user and learner
perturbation.
