  In this paper, we study network games where players are involved in
information aggregation processes subject to the differential privacy
requirement for players' payoff functions. We propose a Laplace
linear-quadratic functional perturbation mechanism, which perturbs players'
payoff functions with linear-quadratic functions whose coefficients are
produced from truncated Laplace distributions. For monotone games, we show that
the LLQFP mechanism maintains the concavity property of the perturbed payoff
functions and produces a perturbed NE whose distance from the original NE is
bounded and adjustable by Laplace parameter tuning. We focus on
linear-quadratic games, which is a fundamental type of network games with
players' payoffs being linear-quadratic functions, and derive explicit
conditions on how the LLQFP mechanism ensures differential privacy with a given
privacy budget. Lastly, numerical examples are provided for the verification of
the advantages of the LLQFP mechanism.
