IDEAS home Printed from https://ideas.repec.org/a/sae/jocore/v53y2009i5p774-793.html
   My bibliography  Save this article

Same Game, New Tricks

Author

Listed:
  • Andrzej Pelc

    (Département d'informatique Université du Québec en Outaouais, Gatineau, Québec)

  • Krzysztof J. Pelc

    (Department of Government Georgetown University, Washington, D.C.)

Abstract

The aim of this article is to distinguish between strategies in the Iterated Prisoner’s Dilemma on the basis of their relative performance in a given population set. We first define a natural order on such strategies that disregards isolated disturbances, by using the limit of time-average payoffs. This order allows us to consider one strategy as strictly better than another in some population of strategies. We then determine a strategy σ to be ‘‘robust,’’ if in any population consisting of copies of two types of strategies, σ itself and some other strategy τ, the strategy σ is never worse than τ. We present a large class of such robust strategies. Strikingly, robustness can accommodate an arbitrary level of generosity, conditional on the strength of subsequent retaliation; and it does not require symmetric retaliation. Taken together, these findings allow us to design strategies that significantly lessen the problem of noise, without forsaking performance. Finally, we show that no strategy exhibits robustness in all population sets of three or more strategy types.

Suggested Citation

  • Andrzej Pelc & Krzysztof J. Pelc, 2009. "Same Game, New Tricks," Journal of Conflict Resolution, Peace Science Society (International), vol. 53(5), pages 774-793, October.
    • Handle: RePEc:sae:jocore:v:53:y:2009:i:5:p:774-793
    DOI: 10.1177/0022002709339045
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/0022002709339045
    Download Restriction: no
    File URL: https://libkey.io/10.1177/0022002709339045?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
    ---><---

    References listed on IDEAS

    as
    1. Martin A. Nowak & Akira Sasaki & Christine Taylor & Drew Fudenberg, 2004. "Emergence of cooperation and evolutionary stability in finite populations," Nature, Nature, vol. 428(6983), pages 646-650, April.
    2. Fudenberg, Drew & Maskin, Eric, 1990. "Evolution and Cooperation in Noisy Repeated Games," American Economic Review, American Economic Association, vol. 80(2), pages 274-279, May.
    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. John T. Scholz & Cheng‐Lung Wang, 2009. "Learning to Cooperate: Learning Networks and the Problem of Altruism," American Journal of Political Science, John Wiley & Sons, vol. 53(3), pages 572-587, July.
    2. Zhang, Huanren, 2018. "Errors can increase cooperation in finite populations," Games and Economic Behavior, Elsevier, vol. 107(C), pages 203-219.
    3. Matthijs van Veelen & Benjamin Allen & Moshe Hoffman & Burton Simon & Carl Veller, 2016. "Inclusive Fitness," Tinbergen Institute Discussion Papers 16-055/I, Tinbergen Institute.
    4. Benjamin M Zagorsky & Johannes G Reiter & Krishnendu Chatterjee & Martin A Nowak, 2013. "Forgiver Triumphs in Alternating Prisoner's Dilemma," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-8, December.
    5. Hilbe, Christian & Traulsen, Arne & Sigmund, Karl, 2015. "Partners or rivals? Strategies for the iterated prisoner's dilemma," Games and Economic Behavior, Elsevier, vol. 92(C), pages 41-52.
    6. Fudenberg, Drew & Imhof, Lorens A., 2008. "Monotone imitation dynamics in large populations," Journal of Economic Theory, Elsevier, vol. 140(1), pages 229-245, May.
    7. Christopher Graser & Matthijs van Veelen, 2024. "Repeated prisoner’s dilemmas with errors: how much subgame-perfection, how much forgiveness, and how much cooperation?," Tinbergen Institute Discussion Papers 24-022/I, Tinbergen Institute.
    8. Flávio L Pinheiro & Vítor V Vasconcelos & Francisco C Santos & Jorge M Pacheco, 2014. "Evolution of All-or-None Strategies in Repeated Public Goods Dilemmas," PLOS Computational Biology, Public Library of Science, vol. 10(11), pages 1-5, November.
    9. Zeng, Weijun & Ai, Hongfeng & Zhao, Man, 2019. "Asymmetrical expectations of future interaction and cooperation in the iterated prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 148-164.
    10. Julián García & Arne Traulsen, 2012. "The Structure of Mutations and the Evolution of Cooperation," PLOS ONE, Public Library of Science, vol. 7(4), pages 1-9, April.
    11. Dai, Darong, 2012. "On the Existence and Stability of Pareto Optimal Endogenous Matching with Fairness," MPRA Paper 40560, University Library of Munich, Germany.
    12. Bhaskar V., 1996. "On the neutral stability of mixed strategies in asymmetric contests," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 56-57, February.
    13. Takuya Sekiguchi, 2023. "Fixation Probabilities of Strategies for Trimatrix Games and Their Applications to Triadic Conflict," Dynamic Games and Applications, Springer, vol. 13(3), pages 1005-1033, September.
    14. Konrad, Kai A. & Morath, Florian, 2020. "The Volunteer’s Dilemma in Finite Populations," CEPR Discussion Papers 15536, C.E.P.R. Discussion Papers.
    15. M. Kleshnina & K. Kaveh & K. Chatterjee, 2020. "The role of behavioural plasticity in finite vs infinite populations," Papers 2009.13160, arXiv.org.
    16. Bhaskar, V., 1993. "Neutral Stability in Assymetric Evolutionary Games," Papers 9358, Tilburg - Center for Economic Research.
    17. Martina Testori & Hedwig Eisenbarth & Rebecca B Hoyle, 2022. "Selfish risk-seeking can provide an evolutionary advantage in a conditional public goods game," PLOS ONE, Public Library of Science, vol. 17(1), pages 1-18, January.
    18. Huang, Keke & Liu, Yishun & Zhang, Yichi & Yang, Chunhua & Wang, Zhen, 2018. "Understanding cooperative behavior of agents with heterogeneous perceptions in dynamic networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 234-240.
    19. Qinghu Liao & Wenwen Dong & Boxin Zhao, 2023. "A New Strategy to Solve “the Tragedy of the Commons” in Sustainable Grassland Ecological Compensation: Experience from Inner Mongolia, China," Sustainability, MDPI, vol. 15(12), pages 1-24, June.
    20. Chaitanya S. Gokhale & Joseph Bulbulia & Marcus Frean, 2022. "Collective narratives catalyse cooperation," Palgrave Communications, Palgrave Macmillan, vol. 9(1), pages 1-9, December.

    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:sae:jocore:v:53:y:2009:i:5:p:774-793. 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: SAGE Publications (email available below). General contact details of provider: http://pss.la.psu.edu/ .

    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.