Differentially Private Distributed Algorithms for Aggregative Games With Directed Communication Graphs

Due to the transmission of information during seeking the Nash equilibrium and the possible leaking of sensitive information deduced from the transmitted information, it is urgent to propose privacy-preserving seeking algorithms for aggregative games. This article proposes two $\epsilon$-differentially private distributed Nash equilibrium seeking algorithms for aggregative games under directed communication graphs with row- and column-stochastic adjacency matrices, respectively. By utilizing the diameters of players' strategy sets, Laplacian noise free from the uniformly upper bound information of gradients is proposed to achieve $\epsilon$-differential privacy and guarantee the algorithms being fully distributed. To avoid the noise accumulating in the estimate of the aggregate strategy, a noise deduction mechanism is employed to ensure the accuracy of the algorithms. The tradeoff between accuracy and privacy level is investigated. Simulation examples and comparisons with existing result are carried out to verify the effectiveness of our algorithms and theorems.