, Le théorème 2.1 donne une condition suffisante sur les dérivées des fonctions prix (correspondant aux fonctions de latence dans un jeu de congestion) pour l'unicité d'un équilibre. Ce résultat repose sur la condition standard de stricte monotonie [Ros65], explicitée en utilisant un résultat d'algèbre linéaire (perturbation de spectre matriciel). Dans le même chapitre, le théorème 2.2 établit une borne supérieure sur le prix de l'anarchie (défini en Section B.2) pour cette classe de jeu, fractionnable (dénoté mécanisme Hourly Proportional

, Ce chapitre se focalise sur les aspects algorithmiques des jeux de congestion. Tout d'abord, le théorème 3.2 étend le résultat [ORS93] d'unicité d'un NE à un contexte plus général. Nous donnons différents résultats sur la convergence de l'algorithme de meilleure réponse

. Enfin and . Dans-ce-chapitre, en commande prédictive [Wu+11présence de contraintes couplantes, nous définissons la notion d'équilibre de Wardrop Variationnel (VWE) pour un jeu nonatomique avec une infinité de types (Definition 6.4), caractérisé par une inégalité variationnelle de dimension infinie. Le théorème 6.5 prouve le résultat d'approximation suivant : un VWE dans un jeu nonatomique peut être approximé par un équilibre de Wardrop d'un jeu avec un nombre fini de populations homogènes, ce dernier équilibre étant symétrique au sens que les joueurs au sein d'une même population jouent la même action. Ce résultat présente également un fort intérêt numériquement

, Nous introduisons un modèle original d'échanges d'énergie pair-à-pair (peerto-peer) au sein d'une communauté de consommateurs-producteurs d'électricité (prosumers)

. Le, puisque les contraintes de réciprocité des échanges définissent des contraintes couplantes entre chaque consommateur et ses voisins. Ce modèle de jeu permet de prendre en compte le caractère stratégique des interactions entre consommateurs, contrairement aux approches de décomposition et optimisation distribuée qui ont été considérées pour ce problème, vol.18

, Nous étudions numériquement l'efficacité des équilibres, à travers le PoA, en calculant les équilibres généralisés du jeu sur différents cas tests, et nous comparons les flux d'énergie obtenus aux équilibres avec les flux obtenus lors de la solution centralisée

, Chacun des sept chapitres présentés dans cette thèse est basé soit sur un article accepté et présenté à une conférence avec comité de lecture, soit sur un article de journal

, ? le chapitre 2 est basé sur l'article, IEEE Conference on Innovative Smart Grid Technologies

. Le-chapitre, 3 est basé sur l'article de journal

, ? le chapitre 4 est basé sur l'article

. Le-chapitre, European Journal of Operational Research

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, List of publications, proceedings and preprints

P. Jacquot, O. Beaude, S. Gaubert, and N. Oudjane, Demand Response in the Smart Grid: the Impact of Consumers Temporal Preferences, IEEE International Conference on Smart Grid Communications, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01651263

P. Jacquot, O. Beaude, S. Gaubert, and N. Oudjane, Demand Side Management in the Smart Grid: an Efficiency and Fairness Tradeoff, IEEE/PES 8thInnovative Smart Grid Technologies Europe (ISGT). IEEE. 2017
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P. Jacquot, C. Wan, O. Beaude, and N. Oudjane, Efficient Estimation of Equilibria of Large Congestion Games with Heterogeneous Players, 2018.

P. Jacquot, N. Oudjane, O. Beaude, P. Benchimol, and S. Gaubert, Procédé de gestion décentralisée de consommation électrique nonintrusif, French Patent FR1872553. EDF and Inria. 2018. filed to INPI on 7 Dec, 2018.

P. Jacquot, O. Beaude, P. Benchimol, S. Gaubert, and N. Oudjane, A Privacy-preserving Disaggregation Algorithm for Non-intrusive Management of Flexible Energy, IEEE 58th Conference on Decision and Control (CDC). IEEE. 2019
URL : https://hal.archives-ouvertes.fr/hal-02150209

P. Jacquot, O. Beaude, P. Benchimol, S. Gaubert, and N. Oudjane, A Privacy-preserving Method to optimize distributed resource allocation, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02262271

P. Jacquot, O. Beaude, S. Gaubert, and N. Oudjane, Analysis and Implementation of an Hourly Billing Mechanism for Demand Response Management, IEEE Transactions on Smart Grid, vol.10, issue.4, pp.1949-3053, 2019.

P. Jacquot and C. Wan, Nonsmooth Aggregative Games with Coupling Constraints and Infinitely Many Classes of Players". In: arXiv preprint, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01904527

P. Jacquot and C. Wan, Routing Game on Parallel Networks: the Convergence of Atomic to Nonatomic, IEEE 57th Conference on Decision and Control (CDC), 2018.
URL : https://hal.archives-ouvertes.fr/hal-01762547

P. Jacquot and C. Wan, Nonatomic Aggregative Games with Infinitely Many Types". In: arXiv preprint, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02146294

P. Hélène-le-cadre, C. Jacquot, C. Wan, and . Alasseur, Peerto-Peer Electricity Market Analysis: From Variational to Generalized Nash Equilibrium, European Journal of Operational Research, 2019.

, En pratique un opérateur peut faire face à un très grand nombre de joueurs, et calculer les équilibres d'un jeu de congestion dans ce cas est difficile. Afin de traiter ce problème, nous établissons des résultats sur l'approximation d'un équilibre dans les jeux de congestion et jeux agrégatifs avec un très grand nombre de joueurs et en présence de contraintes couplantes. Ces résultats, obtenus dans le cadre des inégalités variationnelles et sous certaines hypothèses de monotonie, peuvent être utilisés pour calculer un équilibre approché comme solution d'un problème de petite dimension. Toujours dans la perspective de modéliser un très grand nombre d'agents, nous considérons des jeux de congestion nonatomiques avec contraintes couplantes et avec une infinité de joueurs hétérogènes : ce type de jeux apparaît lorsque les caractéristiques d'une population sont décrites par une fonction de distribution paramétrique. Sous certaines hypothèses de monotonie, nous prouvons que les équilibres de Wardrop de ces jeux, définis comme solutions d'une inégalité variationnelle de dimension infinie, peuvent être approchés par des équilibres de Wardrop symétriques de jeux annexes, solutions d'inégalités variationnelles de petite dimension. Enfin, nous considérons un modèle de jeu pour l'étude d'échanges d'électricité pair-à-pair au sein d'une communauté de consommateurs possédant des actifs de production électrique renouvelable, Titre : Méthodes de Théorie des jeux et d'Optimisation appliquées aux Systèmes Électriques Décentralisés Mots clés : jeux de congestion, optimisation décentralisée, smart grid, gestion de flexibilités Résumé : Dans le contexte de transition vers un système électrique décentralisé et intelligent, nous abordons le problème de la gestion des flexibilités de consommation électriques. Nous développons différentes méthodes basées sur l'optimisation distribuée et la théorie des jeux