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Efficient Estimation of Equilibria in Large Aggregative Games with Coupling Constraints

Paulin Jacquot 1 Cheng Wan 2 Olivier Beaude 2 Nadia Oudjane 2
1 TROPICAL - TROPICAL
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : Aggregative games have many industrial applications, and computing an equilibrium in those games is challenging when the number of players is large. In the framework of atomic aggregative games with coupling constraints, we show that variational Nash equilibria of a large aggregative game can be approximated by a Wardrop equilibrium of an auxiliary population game of smaller dimension. Each population of this auxiliary game corresponds to a group of atomic players of the initial large game. This approach enables an efficient computation of an approximated equilibrium, as the variational inequality characterizing the Wardrop equilibrium is of smaller dimension than the initial one. This is illustrated on an example in the smart grid context.
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https://hal.archives-ouvertes.fr/hal-01904546
Contributor : Paulin Jacquot <>
Submitted on : Thursday, March 26, 2020 - 5:33:24 PM
Last modification on : Saturday, March 28, 2020 - 2:04:13 AM

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  • HAL Id : hal-01904546, version 3
  • ARXIV : 1911.10571

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Paulin Jacquot, Cheng Wan, Olivier Beaude, Nadia Oudjane. Efficient Estimation of Equilibria in Large Aggregative Games with Coupling Constraints. 2020. ⟨hal-01904546v3⟩

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