Stackelberg strategies in linear-quadratic stochastic differential games

Arunabha Bagchi, T. Basar

    Research output: Contribution to journalArticleAcademic

    20 Citations (Scopus)
    87 Downloads (Pure)

    Abstract

    This paper obtains the Stackelberg solution to a class of two-player stochastic differential games described by linear state dynamics and quadratic objective functionals. The information structure of the problem is such that the players make independent noisy measurements of the initial state and are permitted to utilize only this information in constructing their controls. Furthermore, by the very nature of the Stackelberg solution concept, one of the players is assumed to know, in advance, the strategy of the other player (the leader). For this class of problems, we first establish existence and uniqueness of the Stackelberg solution and then relate the derivation of the leader's Stackelberg solution to the optimal solution of a nonstandard stochastic control problem. This stochastic control problem is solved in a more general context, and its solution is utilized in constructing the Stackelberg strategy of the leader. For the special case Gaussian statistics, it is shown that this optimal strategy is affine in observation of the leader. The paper also discusses numerical aspects of the Stackelberg solution under general statistics and develops algorithms which converge to the unique Stackelberg solution.
    Original languageUndefined
    Pages (from-to)443-464
    JournalJournal of optimization theory and applications
    Volume35
    Issue number3
    DOIs
    Publication statusPublished - 1981

    Keywords

    • linear-quadratic games
    • Stochastic differential games
    • IR-85716
    • nonzero-sum games
    • Stackelberg solution

    Cite this

    @article{b97c7cd9ea2f4380a6579b3f4d2cf58b,
    title = "Stackelberg strategies in linear-quadratic stochastic differential games",
    abstract = "This paper obtains the Stackelberg solution to a class of two-player stochastic differential games described by linear state dynamics and quadratic objective functionals. The information structure of the problem is such that the players make independent noisy measurements of the initial state and are permitted to utilize only this information in constructing their controls. Furthermore, by the very nature of the Stackelberg solution concept, one of the players is assumed to know, in advance, the strategy of the other player (the leader). For this class of problems, we first establish existence and uniqueness of the Stackelberg solution and then relate the derivation of the leader's Stackelberg solution to the optimal solution of a nonstandard stochastic control problem. This stochastic control problem is solved in a more general context, and its solution is utilized in constructing the Stackelberg strategy of the leader. For the special case Gaussian statistics, it is shown that this optimal strategy is affine in observation of the leader. The paper also discusses numerical aspects of the Stackelberg solution under general statistics and develops algorithms which converge to the unique Stackelberg solution.",
    keywords = "linear-quadratic games, Stochastic differential games, IR-85716, nonzero-sum games, Stackelberg solution",
    author = "Arunabha Bagchi and T. Basar",
    year = "1981",
    doi = "10.1007/BF00934911",
    language = "Undefined",
    volume = "35",
    pages = "443--464",
    journal = "Journal of optimization theory and applications",
    issn = "0022-3239",
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    Stackelberg strategies in linear-quadratic stochastic differential games. / Bagchi, Arunabha; Basar, T.

    In: Journal of optimization theory and applications, Vol. 35, No. 3, 1981, p. 443-464.

    Research output: Contribution to journalArticleAcademic

    TY - JOUR

    T1 - Stackelberg strategies in linear-quadratic stochastic differential games

    AU - Bagchi, Arunabha

    AU - Basar, T.

    PY - 1981

    Y1 - 1981

    N2 - This paper obtains the Stackelberg solution to a class of two-player stochastic differential games described by linear state dynamics and quadratic objective functionals. The information structure of the problem is such that the players make independent noisy measurements of the initial state and are permitted to utilize only this information in constructing their controls. Furthermore, by the very nature of the Stackelberg solution concept, one of the players is assumed to know, in advance, the strategy of the other player (the leader). For this class of problems, we first establish existence and uniqueness of the Stackelberg solution and then relate the derivation of the leader's Stackelberg solution to the optimal solution of a nonstandard stochastic control problem. This stochastic control problem is solved in a more general context, and its solution is utilized in constructing the Stackelberg strategy of the leader. For the special case Gaussian statistics, it is shown that this optimal strategy is affine in observation of the leader. The paper also discusses numerical aspects of the Stackelberg solution under general statistics and develops algorithms which converge to the unique Stackelberg solution.

    AB - This paper obtains the Stackelberg solution to a class of two-player stochastic differential games described by linear state dynamics and quadratic objective functionals. The information structure of the problem is such that the players make independent noisy measurements of the initial state and are permitted to utilize only this information in constructing their controls. Furthermore, by the very nature of the Stackelberg solution concept, one of the players is assumed to know, in advance, the strategy of the other player (the leader). For this class of problems, we first establish existence and uniqueness of the Stackelberg solution and then relate the derivation of the leader's Stackelberg solution to the optimal solution of a nonstandard stochastic control problem. This stochastic control problem is solved in a more general context, and its solution is utilized in constructing the Stackelberg strategy of the leader. For the special case Gaussian statistics, it is shown that this optimal strategy is affine in observation of the leader. The paper also discusses numerical aspects of the Stackelberg solution under general statistics and develops algorithms which converge to the unique Stackelberg solution.

    KW - linear-quadratic games

    KW - Stochastic differential games

    KW - IR-85716

    KW - nonzero-sum games

    KW - Stackelberg solution

    U2 - 10.1007/BF00934911

    DO - 10.1007/BF00934911

    M3 - Article

    VL - 35

    SP - 443

    EP - 464

    JO - Journal of optimization theory and applications

    JF - Journal of optimization theory and applications

    SN - 0022-3239

    IS - 3

    ER -