IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2312.10695.html
   My bibliography  Save this paper

Nonparametric Strategy Test

Author

Listed:
  • Sam Ganzfried

Abstract

We present a nonparametric statistical test for determining whether an agent is following a given mixed strategy in a repeated strategic-form game given samples of the agent's play. This involves two components: determining whether the agent's frequencies of pure strategies are sufficiently close to the target frequencies, and determining whether the pure strategies selected are independent between different game iterations. Our integrated test involves applying a chi-squared goodness of fit test for the first component and a generalized Wald-Wolfowitz runs test for the second component. The results from both tests are combined using Bonferroni correction to produce a complete test for a given significance level $\alpha.$ We applied the test to publicly available data of human rock-paper-scissors play. The data consists of 50 iterations of play for 500 human players. We test with a null hypothesis that the players are following a uniform random strategy independently at each game iteration. Using a significance level of $\alpha = 0.05$, we conclude that 305 (61%) of the subjects are following the target strategy.

Suggested Citation

  • Sam Ganzfried, 2023. "Nonparametric Strategy Test," Papers 2312.10695, arXiv.org, revised Oct 2024.
  • Handle: RePEc:arx:papers:2312.10695
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2312.10695
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dimitris Batzilis & Sonia Jaffe & Steven Levitt & John A. List & Jeffrey Picel, 2019. "Behavior in Strategic Settings: Evidence from a Million Rock-Paper-Scissors Games," Games, MDPI, vol. 10(2), pages 1-34, April.
    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. Emara, Noha & Owens, David & Smith, John & Wilmer, Lisa, 2017. "Serial correlation in National Football League play calling and its effects on outcomes," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 69(C), pages 125-132.
    2. Jon Kleinberg & Annie Liang & Sendhil Mullainathan, 2017. "The Theory is Predictive, but is it Complete? An Application to Human Perception of Randomness," PIER Working Paper Archive 18-010, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 09 Aug 2017.
    3. Sean Duffy & J. J. Naddeo & David Owens & John Smith, 2024. "Cognitive Load and Mixed Strategies: On Brains and Minimax," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 26(03), pages 1-34, September.
    4. Hanshu Zhang & Frederic Moisan & Cleotilde Gonzalez, 2021. "Rock-Paper-Scissors Play: Beyond the Win-Stay/Lose-Change Strategy," Games, MDPI, vol. 12(3), pages 1-15, June.
    5. Jung S You, 2021. "Random Actions in Experimental Zero-Sum Games," Journal of Economics and Behavioral Studies, AMH International, vol. 13(1), pages 69-81.
    6. Jan C. van Ours, 2024. "Non-Transitive Patterns in Long-Term Football Rivalries," Tinbergen Institute Discussion Papers 24-031/V, Tinbergen Institute.
    7. Hanshu Zhang & Frederic Moisan & Cleotilde Gonzalez, 2021. "Rock-paper-scissors play: Beyond the win-stay/lose-change strategy," Post-Print hal-04325630, HAL.
    8. Drew Fudenberg & Jon Kleinberg & Annie Liang & Sendhil Mullainathan, 2019. "Measuring the Completeness of Theories," Papers 1910.07022, arXiv.org.
    9. Emara, Noha & Owens, David & Smith, John & Wilmer, Lisa, 2014. "Minimax on the gridiron: Serial correlation and its effects on outcomes in the National Football League," MPRA Paper 58907, University Library of Munich, Germany.

    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:2312.10695. 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.