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 ...