Risk-sensitive mean-field-type games with Lp-norm drifts

Tembine Hamidou

    Research output: Contribution to journalArticle

    Abstract

    Abstract We study how risk-sensitive players act in situations where the outcome is influenced not only by the state-action profile but also by the distribution of it. In such interactive decision-making problems, the classical mean-field game framework does not apply. We depart from most of the mean-field games literature by presuming that a decision-maker may include its own-state distribution in its decision. This leads to the class of mean-field-type games. In mean-field-type situations, a single decision-maker may have a big impact on the mean-field terms for which new type of optimality equations are derived. We establish a finite dimensional stochastic maximum principle for mean-field-type games where the drift functions have a p-norm structure which weaken the classical Lipschitz and differentiability assumptions. Sufficient optimality equations are established via Dynamic Programming Principle but in infinite dimension. Using de Finetti-Hewitt-Savage theorem, we show that a propagation of chaos property with virtual particles holds for the non-linear McKean-Vlasov dynamics.

    Original languageEnglish (US)
    Article number6454
    Pages (from-to)224-237
    Number of pages14
    JournalAutomatica
    Volume59
    DOIs
    StatePublished - Jan 1 2015

    Fingerprint

    Maximum principle
    Dynamic programming
    Chaos theory
    Decision making

    Keywords

    • Game theory
    • Mean-field
    • Risk-sensitive

    ASJC Scopus subject areas

    • Control and Systems Engineering
    • Electrical and Electronic Engineering

    Cite this

    Risk-sensitive mean-field-type games with Lp-norm drifts. / Hamidou, Tembine.

    In: Automatica, Vol. 59, 6454, 01.01.2015, p. 224-237.

    Research output: Contribution to journalArticle

    Hamidou, Tembine. / Risk-sensitive mean-field-type games with Lp-norm drifts. In: Automatica. 2015 ; Vol. 59. pp. 224-237.
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