A Differentially Private Energy Trading Mechanism Approaching Social Optimum

This paper proposes a differentially private energy trading mechanism for prosumers in peer-to-peer (P2P) markets, offering provable privacy guarantees while approaching the Nash equilibrium with nearly socially optimal efficiency. We first model the P2P energy trading as a (generalized) Nash game and prove the vulnerability of traditional distributed algorithms to privacy attacks through an adversarial inference model. To address this challenge, we develop a privacy-preserving Nash equilibrium seeking algorithm incorporating carefully calibrated Laplacian noise. We prove that the proposed algorithm achieves $\epsilon$-differential privacy while converging in expectation to the Nash equilibrium with a suitable stepsize. Numerical experiments are conducted to evaluate the algorithm's robustness against privacy attacks, convergence behavior, and optimality compared to the non-private solution. Results demonstrate that our mechanism effectively protects prosumers' sensitive information while maintaining near-optimal market outcomes, offering a practical approach for privacy-preserving coordination in P2P markets.