Faure

Publications

Principes de grandes déviations autonormalisées pour des chaînes de MarkovSelf-normalized large deviations for Markov chainsJournal articleMathieu Faure, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, Volume 333, Issue 9, pp. 885-890, 2001

Nous prouvons un principe de grandes déviations autonormalisé pour la moyenne empirique de fonctionnelles additives non bornées d'une chaı̂ne de Markov. L'autonormalisation s'applique à des cas pour lesquels une hypothèse de domination serait nécessaire pour avoir un principe de grandes déviations traditionnel. Nous suivons ainsi la voie ouverte par Dembo et Shao [2] dans le cas de suites indépendantes et identiquement distribuées pour l'obtention de principes de grandes déviations partiels.

Learning with minimal information in continuous gamesJournal articleSebastian Bervoets, Mario Bravo et Mathieu Faure, Theoretical Economics, Forthcoming

While payoff-based learning models are almost exclusively devised for finite action games, where players can test every action, it is harder to design such learning processes for continuous games. We construct a stochastic learning rule, designed for games with continuous action sets, which requires no sophistication from the players and is simple to implement: players update their actions according to variations in own payoff between current and previous action. We then analyze its behavior in several classes of continuous games and show that convergence to a stable Nash equilibrium is guaranteed in all games with strategic complements as well as in concave games, while convergence to Nash occurs in all locally ordinal potential games as soon as Nash equilibria are isolated.