IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1409.1786.html
   My bibliography  Save this paper

Zero-determinant strategies in iterated multi-strategy games

Author

Listed:
  • Jin-Li Guo

Abstract

Self-serving, rational agents sometimes cooperate to their mutual benefit. The two-player iterated prisoner's dilemma game is a model for including the emergence of cooperation. It is generally believed that there is no simple ultimatum strategy which a player can control the return of the other participants. The recent discovery of the powerful class of zero-determinant strategies in the iterated prisoner's dilemma dramatically expands our understanding of the classic game by uncovering strategies that provide a unilateral advantage to sentient players pitted against unwitting opponents. However, strategies in the prisoner's dilemma game are only two strategies. Are there these results for general multi-strategy games? To address this question, the paper develops a theory for zero-determinant strategies for multi-strategy games, with any number of strategies. The analytical results exhibit a similar yet different scenario to the case of two-strategy games. Zero-determinant strategies in iterated prisoner's dilemma can be seen as degenerate case of our results. The results are also applied to the snowdrift game, the hawk-dove game and the chicken game.

Suggested Citation

  • Jin-Li Guo, 2014. "Zero-determinant strategies in iterated multi-strategy games," Papers 1409.1786, arXiv.org, revised Sep 2014.
    • Handle: RePEc:arx:papers:1409.1786
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1409.1786
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Christian Hilbe & Torsten Röhl & Manfred Milinski, 2014. "Extortion subdues human players but is finally punished in the prisoner’s dilemma," Nature Communications, Nature, vol. 5(1), pages 1-6, September.
    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. 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.
    2. Masahiko Ueda, 2022. "Controlling Conditional Expectations by Zero-Determinant Strategies," SN Operations Research Forum, Springer, vol. 3(3), pages 1-22, September.
    3. 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).
    4. Taha, Mohammad A. & Ghoneim, Ayman, 2021. "Zero-determinant strategies in infinitely repeated three-player prisoner's dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

    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. Kang, Kai & Tian, Jinyan & Zhang, Boyu, 2024. "Cooperation and control in asymmetric repeated games," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    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. 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.
    4. 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.
    5. Xiang Wei & Peng Xu & Shuiting Du & Guanghui Yan & Huayan Pei, 2021. "Reputational preference-based payoff punishment promotes cooperation in spatial social dilemmas," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(10), pages 1-7, October.
    6. Jun Qian & Tongda Zhang & Xiao Sun & Yueting Chai, 2023. "The coordination of collective and individual solutions in risk-resistant scenarios," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(2), pages 1-15, February.
    7. 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.
    8. 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.
    9. 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.
    10. 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).
    11. Pan, Qiuhui & Wang, Linpeng & He, Mingfeng, 2020. "Social dilemma based on reputation and successive behavior," Applied Mathematics and Computation, Elsevier, vol. 384(C).
    12. Wang, Chaoqian & Huang, Chaochao & Pan, Qiuhui & He, Mingfeng, 2022. "Modeling the social dilemma of involution on a square lattice," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    13. Feng, Tian-Jiao & Fan, Song-Jia & Li, Cong & Tao, Yi & Zheng, Xiu-Deng, 2023. "Noise-induced sustainability of cooperation in Prisoner's Dilemma game," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    14. 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.
    15. Masahiko Ueda, 2022. "Controlling Conditional Expectations by Zero-Determinant Strategies," SN Operations Research Forum, Springer, vol. 3(3), pages 1-22, September.
    16. 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.
    17. 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.
    18. Feng, Sinan & Liu, Xuesong, 2024. "Effects of three-faced strategy on the evolution of cooperation in social dilemma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 639(C).
    19. Taha, Mohammad A. & Ghoneim, Ayman, 2020. "Zero-determinant strategies in repeated asymmetric games," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    20. 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.

    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:1409.1786. 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.