We consider a peer-to-peer electricity market modeled as a network game, where End Users (EUs) minimize their cost by computing their demand and generation while satisfying a set of local and coupling constraints. Their nominal demand constitutes sensitive information, that they might want to keep private. We prove that the network game admits a unique Variational Equilibrium, which depends on the private information of all the EUs. A data aggregator (DA) is introduced, which aims to learn the EUs' private information, while remunerating them depending on the quality of the readings they report to the DA. The EUs might have incentives to report biased and noisy readings to preserve their privacy. Relying on performative prediction, we define a decision-dependent game G stoch , to explicitly take into account the shift caused by the EUs' strategic information on their strategies and market equilibria. To compute market equilibria solutions of G stoch , two variants of the Repeated Stochastic Gradient Method (RSGM) and a two-timescale stochastic approximation algorithm are proposed. We prove the convergence of each algorithm. Finally, the algorithms performance is assessed on a numerical example, by comparing the achieved efficiency loss, privacy preservation capabilities, convergence rates, and EUs' utility functions at equilibrium. The results highlight the benefits for the EUs to model performative effects.