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Ergodic control of a heterogeneous population and application to electricity pricing

Quentin Jacquet 1, 2 Wim van Ackooij 1 Clémence Alasseur 1 Stéphane Gaubert 2 
2 TROPICAL - TROPICAL
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : We consider a control problem for a heterogeneous population composed of customers able to switch at any time between different contracts, depending not only on the tariff conditions but also on the characteristics of each individual. A provider aims to maximize an average gain per time unit, supposing that the population is of infinite size. This leads to an ergodic control problem for a "mean-field" MDP in which the state space is a product of simplices, and the population evolves according to a controlled linear dynamics. By exploiting contraction properties of the dynamics in Hilbert's projective metric, we show that the ergodic eigenproblem admits a solution. This allows us to obtain optimal strategies, and to quantify the gap between steady-state strategies and optimal ones. We illustrate this approach on examples from electricity pricing, and show in particular that the optimal policies may be cyclic-alternating between discount and profit taking stages.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03629189
Contributor : Quentin Jacquet Connect in order to contact the contributor
Submitted on : Thursday, October 6, 2022 - 9:33:21 AM
Last modification on : Thursday, October 27, 2022 - 3:37:10 AM

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  • HAL Id : hal-03629189, version 2

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Quentin Jacquet, Wim van Ackooij, Clémence Alasseur, Stéphane Gaubert. Ergodic control of a heterogeneous population and application to electricity pricing. 2022. ⟨hal-03629189v2⟩

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