IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/89612.html
   My bibliography  Save this paper

Stackelberg type dynamic zero-sum game with leader and follower

Author

Listed:
  • Tanaka, Yasuhito

Abstract

We consider a Stackelberg type dynamic two-players zero-sum game. One of two players is the leader and the other player is the follower. The game is a two-stages game. In the first stage the leader determines the value of its strategic variable. In the second stage the follower determines the value of its strategic variable given the value of the leader's strategic variable. On the other hand, in the static game two players simultaneously determine the values of their strategic variable. We will show that Sion's minimax theorem (Sion(1958)) implies that at the sub-game perfect equilibrium of the Stackelberg type dynamic zero-sum game with a leader and a follower the roles of leader and follower are irrelevant to the payoffs of players, and that the Stackelberg equilbria of the dynamic game are equivalent to the equilibrium of the static game.

Suggested Citation

  • Tanaka, Yasuhito, 2018. "Stackelberg type dynamic zero-sum game with leader and follower," MPRA Paper 89612, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:89612
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/89612/1/MPRA_paper_89612.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Tanaka, Yasuhito, 2014. "Relative profit maximization and irrelevance of leadership in Stackelberg model," MPRA Paper 55887, University Library of Munich, Germany.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tanaka, Yasuhito, 2019. "Analysis of dynamic symmetric three-players zero-sum game with a leader and two followers without differentiability of payoff functions," MPRA Paper 91919, University Library of Munich, Germany.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tanaka, Yasuhito, 2019. "On the equivalence of Stackelberg equilibrium and static equilibrium of symmetric multi-players zero-sum game," MPRA Paper 91897, University Library of Munich, Germany.
    2. Jumpei Hamamura & Vinay Ramani, 2023. "Social performance versus relative performance evaluation, asymmetric costs, and quantity competition under managerial delegation," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 44(3), pages 1706-1719, April.
    3. Tanaka, Yasuhito, 2019. "Analysis of dynamic symmetric three-players zero-sum game with a leader and two followers without differentiability of payoff functions," MPRA Paper 91919, University Library of Munich, Germany.
    4. Tanaka, Yasuhito, 2019. "Stackelberg equilibrium of dynamic symmetric multi-players zero-sum game with a leader and followers without differentiability of payoff functions," MPRA Paper 91898, University Library of Munich, Germany.
    5. Tanaka, Yasuhito, 2019. "Stackelberg type dynamic symmetric three-players zero-sum game with a leader and two followers," MPRA Paper 91934, University Library of Munich, Germany.
    6. Satoh, Atsuhiro & Tanaka, Yasuhito, 2015. "Relative profit maximization and the choice of strategic variables in duopoly," MPRA Paper 63000, University Library of Munich, Germany.
    7. Jumpei Hamamura, 2021. "What level do disadvantaged firms weight rivals' profits in relative performance evaluations under quantity competition?," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 42(2), pages 493-501, March.

    More about this item

    Keywords

    zero-sum game; Stackelberg; dynamic zero-sum game;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:89612. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.