Optimal control and zero-sum games for markov chains of mean-field type

Salah Eddine Choutri, Boualem Djehiche, Tembine Hamidou

    Research output: Contribution to journalArticle

    Abstract

    We establish existence of Markov chains of mean-field type with unbounded jump intensities by means of a fixed point argument using the total variation distance. We further show existence of nearly-optimal controls and, using a Markov chain backward SDE approach, we suggest conditions for existence of an optimal control and a saddle-point for respectively a control problem and a zero-sum differential game associated with payoff functionals of mean-field type, under dynamics driven by such Markov chains of mean-field type.

    Original languageEnglish (US)
    Pages (from-to)571-605
    Number of pages35
    JournalMathematical Control and Related Fields
    Volume9
    Issue number3
    DOIs
    StatePublished - Sep 1 2019

    Fingerprint

    Zero sum game
    Mean Field
    Markov processes
    Markov chain
    Optimal Control
    Total Variation Distance
    Differential Games
    Saddlepoint
    Control Problem
    Jump
    Fixed point

    Keywords

    • Backward SDEs
    • Mean-field
    • Nonlinear Markov chain
    • Optimal control
    • Saddle point
    • Stochastic maximum principle
    • Thinning
    • Zero-sum game

    ASJC Scopus subject areas

    • Control and Optimization
    • Applied Mathematics

    Cite this

    Optimal control and zero-sum games for markov chains of mean-field type. / Choutri, Salah Eddine; Djehiche, Boualem; Hamidou, Tembine.

    In: Mathematical Control and Related Fields, Vol. 9, No. 3, 01.09.2019, p. 571-605.

    Research output: Contribution to journalArticle

    Choutri, Salah Eddine ; Djehiche, Boualem ; Hamidou, Tembine. / Optimal control and zero-sum games for markov chains of mean-field type. In: Mathematical Control and Related Fields. 2019 ; Vol. 9, No. 3. pp. 571-605.
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