Differentially Private Nash Equilibrium Seeking in Quadratic Network Games

In this article, we develop distributed computation algorithms for Nash equilibriums of linear–quadratic network games with proven differential privacy guarantees. In a network game with each player's payoff being a quadratic function, the dependencies of the decisions in the payoff function naturally encode a network structure governing the players' interpersonal influences. Such social influence structure and the individual marginal payoffs of the players indicate economic spillovers and individual preferences, and thus, they are subject to privacy concerns. For distributed computing of the Nash equilibrium, the players are interconnected by a public communication graph, over which dynamical states are shared among neighboring nodes. When the players' marginal payoffs are considered to be private knowledge, we propose a distributed randomized gradient descent algorithm, in which each player adds a Laplacian random noise to her marginal payoff in the recursive updates. It is proven that the algorithm can guarantee differential privacy and convergence in expectation to the Nash equilibrium of the network game at each player's state. Moreover, the mean-square error between the players' states and the Nash equilibrium is shown to be bounded by a constant related to the differential privacy level. Next, when both the players' marginal payoffs and the influence graph are private information, we propose two distributed algorithms by randomized communication and randomized projection, respectively, for privacy preservation. The differential privacy and convergence guarantees are also established for such algorithms.