  This paper explores distributed aggregative games in multi-agent systems.
Current methods for finding distributed Nash equilibrium require players to
send original messages to their neighbors, leading to communication burden and
privacy issues. To jointly address these issues, we propose an algorithm that
uses stochastic compression to save communication resources and conceal
information through random errors induced by compression. Our theoretical
analysis shows that the algorithm guarantees convergence accuracy, even with
aggressive compression errors used to protect privacy. We prove that the
algorithm achieves differential privacy through a stochastic quantization
scheme. Simulation results for energy consumption games support the
effectiveness of our approach.
