Equilibres de Nash dans les jeux concurrents : application aux jeux temporisés. (Nash equilibria in concurrent games : application to timed games)

Ces travaux portent sur l'etude des jeux concurrents et temporises. Ces deux types de jeux sont des modeles tres utilises en synthese de controleur. Dans des situations ou plusieurs agents interagissent, les notions de strategies gagnantes utilises jusqu'ici ne suffisent plus et il est necessaires de s'inspirer de notions issus de la theorie des jeux. Le principal concept etudie dans ce domaine est celui d'equilibre de Nash. Nous proposons une transformation qui permet de calculer les equilibres dans les jeux concurrents en se ramenant a un calcul de strategies gagnantes. Beaucoup de travaux ont deja porte sur les calculs des strategies gagnantes, et nous pouvons tirer parti des algorithmes a notre disposition. Pour le calcul des equilibres dans les jeux temporises, nous montrons qu'il est possible de se ramener au cas des jeux concurrents. Nous proposons des algorithmes pour le calcul des equilibres, d'abord avec des objectifs classiques, puis nous proposons un cadre plus general qui permet de decrire des preferences plus quantitatives. Nous etudions egalement la complexite theorique des problemes de decisions associes. Enfin, nous presentons un outil implementant l'un des algorithmes que nous avons developpe.

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