  Internet tracking technologies and wearable electronics provide a vast amount
of data to machine learning algorithms. This stock of data stands to increase
with the developments of the internet of things and cyber-physical systems.
Clearly, these technologies promise benefits. But they also raise the risk of
sensitive information disclosure. To mitigate this risk, machine learning
algorithms can add noise to outputs according to the formulations provided by
differential privacy. At the same time, users can fight for privacy by
injecting noise into the data that they report. In this paper, we conceptualize
the interactions between privacy and accuracy and between user (input)
perturbation and learner (output) perturbation in machine learning, using the
frameworks of empirical risk minimization, differential privacy, and
Stackelberg games. In particular, we solve for the Stackelberg equilibrium for
the case of an averaging query. We find that, in equilibrium, either the users
perturb their data before submission or the learner perturbs the machine
learning output, but never both. Specifically, the learner perturbs if and only
if the number of users is greater than a threshold which increases with the
degree to which incentives are misaligned. Provoked by these conclusions - and
by some observations from privacy ethics - we also suggest future directions.
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. We hope that this effort will
open the door to future work in the area of differential privacy games.
