Learning Market Equilibria Preserving Statistical Privacy Using Performative Prediction

We consider a peer-to-peer electricity market modeled as a private network game, where end users minimize their cost by computing their demand and controllable generation. Their nominal demand constitutes sensitive information that they might want to keep private. We prove that the private network game admits a unique variational equilibrium, which depends on the private information of all end users. Thus, to update their strategy, end users rely on randomized readings. A data aggregator is introduced, which aims to learn the end users' private information, while remunerating them depending on the quality of their readings. Using performative prediction, we define a decision-dependent game explicitly taking into account the distribution shift caused by the end users' hidden ability. The decision-dependent game coincides with a Stackelberg game when the end users' hidden abilities are best responses. Further, the market robustness can be quantified by evaluating the efficiency loss as the difference between the social cost in the performatively stable equilibrium and the optimum. We show that under mild assumptions, the performatively stable equilibrium can be found by distributed and sequential variants of the repeated stochastic gradient method while we propose a two-timescale stochastic approximation method to learn Stackelberg equilibrium. Finally, we formulate the data aggregator's optimal contract design as a bilevel optimization problem that we cast as a more tractable nonlinear nonconvex optimization problem which can be solved using simulated annealing. Simulations on small and large scale problem instances illustrate the results.