IDEAS home Printed from https://ideas.repec.org/a/nat/natcom/v4y2013i1d10.1038_ncomms3193.html
   My bibliography  Save this article

Evolutionary instability of zero-determinant strategies demonstrates that winning is not everything

Author

Listed:
  • Christoph Adami

    (Michigan State University
    Michigan State University
    BEACON Center for the Study of Evolution in Action, Michigan State University)

  • Arend Hintze

    (Michigan State University
    BEACON Center for the Study of Evolution in Action, Michigan State University)

Abstract

Zero-determinant strategies are a new class of probabilistic and conditional strategies that are able to unilaterally set the expected payoff of an opponent in iterated plays of the Prisoner’s Dilemma irrespective of the opponent’s strategy (coercive strategies), or else to set the ratio between the player’s and their opponent’s expected payoff (extortionate strategies). Here we show that zero-determinant strategies are at most weakly dominant, are not evolutionarily stable, and will instead evolve into less coercive strategies. We show that zero-determinant strategies with an informational advantage over other players that allows them to recognize each other can be evolutionarily stable (and able to exploit other players). However, such an advantage is bound to be short-lived as opposing strategies evolve to counteract the recognition.

Suggested Citation

  • Christoph Adami & Arend Hintze, 2013. "Evolutionary instability of zero-determinant strategies demonstrates that winning is not everything," Nature Communications, Nature, vol. 4(1), pages 1-8, October.
    • Handle: RePEc:nat:natcom:v:4:y:2013:i:1:d:10.1038_ncomms3193
    DOI: 10.1038/ncomms3193
    as

    Download full text from publisher

    File URL: https://www.nature.com/articles/ncomms3193
    File Function: Abstract
    Download Restriction: no
    File URL: https://libkey.io/10.1038/ncomms3193?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

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


    Cited by:

    1. Wang, JunFang & Guo, JinLi, 2019. "A synergy of punishment and extortion in cooperation dilemmas driven by the leader," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 263-268.
    2. Masahiko Ueda & Toshiyuki Tanaka, 2020. "Linear algebraic structure of zero-determinant strategies in repeated games," PLOS ONE, Public Library of Science, vol. 15(4), pages 1-13, April.
    3. Yali Dong & Cong Li & Yi Tao & Boyu Zhang, 2015. "Evolution of Conformity in Social Dilemmas," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-12, September.
    4. Christopher Graser & Takako Fujiwara-Greve & Julian García & Matthijs van Veelen, 2024. "Repeated games with partner choice," Tinbergen Institute Discussion Papers 24-038/I, Tinbergen Institute.
    5. McAvoy, Alex & Hauert, Christoph, 2017. "Autocratic strategies for alternating games," Theoretical Population Biology, Elsevier, vol. 113(C), pages 13-22.
    6. El-Salam, Salsabeel M. Abd & El-Seidy, Essam & Abdel-Malek, Amira R., 2023. "Evaluating zero-determinant strategies’ effects on cooperation and conflict resolution in repeated games," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    7. Kang, Kai & Tian, Jinyan & Zhang, Boyu, 2024. "Cooperation and control in asymmetric repeated games," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    8. Taha, Mohammad A. & Ghoneim, Ayman, 2020. "Zero-determinant strategies in repeated asymmetric games," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    9. He, Zhixue & Geng, Yini & Shen, Chen & Shi, Lei, 2020. "Evolution of cooperation in the spatial prisoner’s dilemma game with extortion strategy under win-stay-lose-move rule," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    10. Jie, Yingmo & Liu, Charles Zhechao & Choo, Kim-Kwang Raymond & Guo, Cheng, 2024. "An incentive compatible ZD strategy-based data sharing model for federated learning: A perspective of iterated prisoner's dilemma," European Journal of Operational Research, Elsevier, vol. 315(2), pages 764-776.
    11. Axel Gautier & Ashwin Ittoo & Pieter Cleynenbreugel, 2020. "AI algorithms, price discrimination and collusion: a technological, economic and legal perspective," European Journal of Law and Economics, Springer, vol. 50(3), pages 405-435, December.
    12. Yohsuke Murase & Seung Ki Baek, 2021. "Friendly-rivalry solution to the iterated n-person public-goods game," PLOS Computational Biology, Public Library of Science, vol. 17(1), pages 1-17, January.
    13. Marc Harper & Vincent Knight & Martin Jones & Georgios Koutsovoulos & Nikoleta E Glynatsi & Owen Campbell, 2017. "Reinforcement learning produces dominant strategies for the Iterated Prisoner’s Dilemma," PLOS ONE, Public Library of Science, vol. 12(12), pages 1-33, December.
    14. Christopher Lee & Marc Harper & Dashiell Fryer, 2015. "The Art of War: Beyond Memory-one Strategies in Population Games," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-16, March.
    15. Nikoleta E. Glynatsi & Vincent A. Knight, 2021. "A bibliometric study of research topics, collaboration, and centrality in the iterated prisoner’s dilemma," Palgrave Communications, Palgrave Macmillan, vol. 8(1), pages 1-12, December.
    16. Jin-Li Guo, 2014. "Zero-determinant strategies in iterated multi-strategy games," Papers 1409.1786, arXiv.org, revised Sep 2014.
    17. Christian Hilbe & Martin A Nowak & Arne Traulsen, 2013. "Adaptive Dynamics of Extortion and Compliance," PLOS ONE, Public Library of Science, vol. 8(11), pages 1-9, November.
    18. Vincent Knight & Marc Harper & Nikoleta E Glynatsi & Owen Campbell, 2018. "Evolution reinforces cooperation with the emergence of self-recognition mechanisms: An empirical study of strategies in the Moran process for the iterated prisoner’s dilemma," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-33, October.
    19. Amnon Rapoport & Darryl A Seale & Andrew M Colman, 2015. "Is Tit-for-Tat the Answer? On the Conclusions Drawn from Axelrod's Tournaments," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-11, July.

    More about this item

    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:nat:natcom:v:4:y:2013:i:1:d:10.1038_ncomms3193. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.nature.com .

    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.