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Preprints, Working Papers, ... Year : 2023

Learning Market Equilibria Preserving Statistical Privacy Using Performative Prediction

Abstract

We consider a peer-to-peer electricity market modeled as a private network game, where End Users (EUs) 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 the EUs. Thus, to update their strategy, EUs rely on readings from the other EUs. However, to preserve their privacy, the EUs might report randomized readings. A Data Aggregator (DA) is introduced, which aims to learn the EUs’ private information, while remunerating them depending on the quality of their readings. Using performative prediction, we define a decision-dependent game Gstoch, to explicitly take into account the distribution shift caused by the EUs’ hidden ability. We focus on three solution concepts: (⋆) Nash Equilibrium (NE), (⋆) Performatively Stable Equilibrium (PSE), and (⋆) Stackelberg Equilibrium (SE). Relying on the strong monotonicity of the game, we prove that there exist unique NE and PSE solutions of Gstoch. Both PSE and SE account for the feedback-loop effect of the EUs’ hidden ability. The related market robustness can be evaluated by comparing the market efficiency in the PSE and SE with respect to the social optimum. We show that under mild assumptions, the PSE 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 SE. Finally, we formulate the DA’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.
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Dates and versions

hal-04343535 , version 1 (13-12-2023)
hal-04343535 , version 2 (18-05-2024)

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  • HAL Id : hal-04343535 , version 2

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Hélène Le Cadre, Mandar Datar, Mathis Guckert, Eitan Altman. Learning Market Equilibria Preserving Statistical Privacy Using Performative Prediction. 2023. ⟨hal-04343535v2⟩
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