  Machine learning algorithms have reached mainstream status and are widely
deployed in many applications. The accuracy of such algorithms depends
significantly on the size of the underlying training dataset; in reality a
small or medium sized organization often does not have the necessary data to
train a reasonably accurate model. For such organizations, a realistic solution
is to train their machine learning models based on their joint dataset (which
is a union of the individual ones). Unfortunately, privacy concerns prevent
them from straightforwardly doing so. While a number of privacy-preserving
solutions exist for collaborating organizations to securely aggregate the
parameters in the process of training the models, we are not aware of any work
that provides a rational framework for the participants to precisely balance
the privacy loss and accuracy gain in their collaboration. In this paper, by
focusing on a two-player setting, we model the collaborative training process
as a two-player game where each player aims to achieve higher accuracy while
preserving the privacy of its own dataset. We introduce the notion of Price of
Privacy, a novel approach for measuring the impact of privacy protection on the
accuracy in the proposed framework. Furthermore, we develop a game-theoretical
model for different player types, and then either find or prove the existence
of a Nash Equilibrium with regard to the strength of privacy protection for
each player. Using recommendation systems as our main use case, we demonstrate
how two players can make practical use of the proposed theoretical framework,
including setting up the parameters and approximating the non-trivial Nash
Equilibrium.
