IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v369y2020ics0096300319308549.html
   My bibliography  Save this article

Zero-determinant strategies in repeated asymmetric games

Author

Listed:
  • Taha, Mohammad A.
  • Ghoneim, Ayman

Abstract

Zero-determinant (ZD) strategies are conditional strategies which allow players adopting them to establish a relation between their expected payoffs and those of their opponents. The ZD strategies were investigated in different models including finite and infinite repeated two players’ games, multiplayer games, continuous action spaces and alternating move games. However, all previous studies considered only symmetric games between players, i.e., players have the same strategies and the same associated payoffs, thus the players’ identities are interchangeable without affecting the game's dynamics. In this study, we analytically model and derive the ZD strategies for asymmetric two players’ games, focusing on one-memory strategies and infinite repeated encounters. We derive the analytical bounds of equalizer and extortionate ZD strategies in 2 × 2 asymmetric games, which differ from the symmetric games case. Furthermore, we derive under what conditions a player using an extortionate ZD strategy will get a higher expected payoff than his/her opponent. Finally using a numerical example, we investigate ZD strategies in 2 × 2 asymmetric prisoner's dilemma game.

Suggested Citation

  • Taha, Mohammad A. & Ghoneim, Ayman, 2020. "Zero-determinant strategies in repeated asymmetric games," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    • Handle: RePEc:eee:apmaco:v:369:y:2020:i:c:s0096300319308549
    DOI: 10.1016/j.amc.2019.124862
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319308549
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.124862?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. repec:cla:levarc:786969000000001297 is not listed on IDEAS
    3. EL-Seidy, Essam & Elshobaky, Entisarat.M. & Soliman, Karim.M., 2016. "Two population three-player prisoner’s dilemma game," Applied Mathematics and Computation, Elsevier, vol. 277(C), pages 44-53.
    4. Zhijian Wang & Yanran Zhou & Jaimie W. Lien & Jie Zheng & Bin Xu, 2016. "Extortion Can Outperform Generosity in the Iterated Prisoners' Dilemma," Levine's Bibliography 786969000000001297, UCLA Department of Economics.
    5. McAvoy, Alex & Hauert, Christoph, 2017. "Autocratic strategies for alternating games," Theoretical Population Biology, Elsevier, vol. 113(C), pages 13-22.
    6. Guth, Werner & Schmittberger, Rolf & Schwarze, Bernd, 1982. "An experimental analysis of ultimatum bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 367-388, December.
    7. El-Seidy, Essam & Taha, Mohammad A., 2016. "The payoff matrix of repeated asymmetric 2×2 gamesAuthor-Name: Elshobaky, Entisarat M," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 393-402.
    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. 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).
    2. Kang, Kai & Tian, Jinyan & Zhang, Boyu, 2024. "Cooperation and control in asymmetric repeated games," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    3. Jiali Wang & Changbing Tang & Jianquan Lu & Guanrong Chen, 2023. "Toward Zero-Determinant Strategies for Optimal Decision Making in Crowdsourcing Systems," Mathematics, MDPI, vol. 11(5), pages 1-21, February.
    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. 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).
    3. 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.
    4. Christian Hilbe & Kristin Hagel & Manfred Milinski, 2016. "Asymmetric Power Boosts Extortion in an Economic Experiment," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-14, October.
    5. 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).
    6. Ding, Hong & Zhang, Geng-shun & Wang, Shi-hao & Li, Juan & Wang, Zhen, 2019. "Q-learning boosts the evolution of cooperation in structured population by involving extortion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    7. 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.
    8. Masahiko Ueda, 2022. "Controlling Conditional Expectations by Zero-Determinant Strategies," SN Operations Research Forum, Springer, vol. 3(3), pages 1-22, September.
    9. Zhang, Yifan & Shu, Gang & Li, Ya, 2017. "Strategy-updating depending on local environment enhances cooperation in prisoner’s dilemma game," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 224-232.
    10. McAvoy, Alex & Hauert, Christoph, 2017. "Autocratic strategies for alternating games," Theoretical Population Biology, Elsevier, vol. 113(C), pages 13-22.
    11. Michael Seiler, 2014. "The Effect of Perceived Lender Characteristics and Market Conditions on Strategic Mortgage Defaults," The Journal of Real Estate Finance and Economics, Springer, vol. 48(2), pages 256-270, February.
    12. Giuseppe Attanasi & Aurora García-Gallego & Nikolaos Georgantzís & Aldo Montesano, 2015. "Bargaining over Strategies of Non-Cooperative Games," Games, MDPI, vol. 6(3), pages 1-26, August.
    13. Robison, Lindon J. & Hanson, Steven D., 1995. "Social Capital and Economic Cooperation," Journal of Agricultural and Applied Economics, Cambridge University Press, vol. 27(1), pages 43-58, July.
    14. Anne Corcos & Yorgos Rizopoulos, 2011. "Is prosocial behavior egocentric? The “invisible hand” of emotions," Post-Print halshs-01968213, HAL.
    15. Burks, Stephen V. & Carpenter, Jeffrey P. & Verhoogen, Eric, 2003. "Playing both roles in the trust game," Journal of Economic Behavior & Organization, Elsevier, vol. 51(2), pages 195-216, June.
    16. Seema Kacker & Tin Aung & Dominic Montagu & David Bishai, 2021. "Providers preferences towards greater patient health benefit is associated with higher quality of care," International Journal of Health Economics and Management, Springer, vol. 21(3), pages 271-294, September.
    17. Mazen Hassan & Sarah Mansour & Stefan Voigt & May Gadallah, 2022. "When Syria was in Egypt’s land: Egyptians cooperate with Syrians, but less with each other," Public Choice, Springer, vol. 191(3), pages 337-362, June.
    18. Thomas Dohmen & Armin Falk & David Huffman & Uwe Sunde, 2009. "Homo Reciprocans: Survey Evidence on Behavioural Outcomes," Economic Journal, Royal Economic Society, vol. 119(536), pages 592-612, March.
    19. Sylvie Thoron, 2016. "Morality Beyond Social Preferences: Smithian Sympathy, Social Neuroscience and the Nature of Social Consciousness [La moralité au delà des préférences sociales. La sympathie Smithienne, les neurosc," Post-Print hal-01645043, HAL.
    20. Liqi Zhu & Gerd Gigerenzer & Gang Huangfu, 2013. "Psychological Traces of China's Socio-Economic Reforms in the Ultimatum and Dictator Games," PLOS ONE, Public Library of Science, vol. 8(8), pages 1-6, August.

    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:eee:apmaco:v:369:y:2020:i:c:s0096300319308549. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.