Learning Market Equilibria Using Performative Prediction: Balancing Efficiency and Privacy
Abstract
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 is introduced,
which aims to learn the EUs’ private information. The EUs
might have incentives to report biased and noisy readings to
preserve their privacy, which creates shifts in their strategies.
Relying on performative prediction, we define a decision-dependent
game G^stoch to couple the network game with a
data market. Two variants of the Repeated Stochastic Gradient
Method (RSGM) are proposed to compute the Performatively
Stable Equilibrium solution of G^stoch, that outperform RSGM
with respect to efficiency gap minimization, privacy preservation,
and convergence rates in numerical simulations.
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