IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2203.10774.html
   My bibliography  Save this paper

Fictitious Play with Maximin Initialization

Author

Listed:
  • Sam Ganzfried

Abstract

Fictitious play has recently emerged as the most accurate scalable algorithm for approximating Nash equilibrium strategies in multiplayer games. We show that the degree of equilibrium approximation error of fictitious play can be significantly reduced by carefully selecting the initial strategies. We present several new procedures for strategy initialization and compare them to the classic approach, which initializes all pure strategies to have equal probability. The best-performing approach, called maximin, solves a nonconvex quadratic program to compute initial strategies and results in a nearly 75% reduction in approximation error compared to the classic approach when 5 initializations are used.

Suggested Citation

  • Sam Ganzfried, 2022. "Fictitious Play with Maximin Initialization," Papers 2203.10774, arXiv.org, revised Nov 2022.
    • Handle: RePEc:arx:papers:2203.10774
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2203.10774
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Sam Ganzfried & Conner Laughlin & Charles Morefield, 2019. "Parallel Algorithm for Approximating Nash Equilibrium in Multiplayer Stochastic Games with Application to Naval Strategic Planning," Papers 1910.00193, arXiv.org, revised Mar 2020.
    2. Sam Ganzfried, 2020. "Empirical Analysis of Fictitious Play for Nash Equilibrium Computation in Multiplayer Games," Papers 2001.11165, arXiv.org, revised Dec 2023.
    Full references (including those not matched with items on IDEAS)

    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. Sam Ganzfried, 2021. "Algorithm for Computing Approximate Nash Equilibrium in Continuous Games with Application to Continuous Blotto," Games, MDPI, vol. 12(2), pages 1-11, June.
    2. Sam Ganzfried, 2020. "Fast Complete Algorithm for Multiplayer Nash Equilibrium," Papers 2002.04734, arXiv.org, revised Jan 2023.
    3. Sam Ganzfried, 2020. "Algorithm for Computing Approximate Nash Equilibrium in Continuous Games with Application to Continuous Blotto," Papers 2006.07443, arXiv.org, revised Jun 2021.

    More about this item

    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:arx:papers:2203.10774. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.