IDEAS home Printed from https://ideas.repec.org/h/spr/lnechp/978-3-642-02956-1_19.html
   My bibliography  Save this book chapter

A Model-to-Model Analysis of the Repeated Prisoners’ Dilemma: Genetic Algorithms vs. Evolutionary Dynamics

In: Artificial Economics

Author

Listed:
  • Xavier Vilà

    (Universitat Autònoma de Barcelona)

Abstract

We study the properties of the well known Replicator Dynamics when applied to a finitely repeated version of the Prisoners’ Dilemma game. We characterize the behavior of such dynamics under strongly simplifying assumptions (i.e. only 3 strategies are available) and show that the basin of attraction of defection shrinks as the number of repetitions increases. After discussing the difficulties involved in trying to relax the “strongly simplifying assumptions” above, we approach the same model by means of simulations based on genetic algorithms. The resulting simulations describe a behavior of the system very close to the one predicted by the replicator dynamics without imposing any of the assumptions of the analytical model. Our main conclusion is that analytical and computational models are good complements for research in social sciences. Indeed, while on the one hand computational models are extremely useful to extend the scope of the analysis to complex scenarios hard to analyze mathematically, on the other hand formal models can be extremely useful to verify and to explain the outcomes of computational models.

Suggested Citation

  • Xavier Vilà, 2009. "A Model-to-Model Analysis of the Repeated Prisoners’ Dilemma: Genetic Algorithms vs. Evolutionary Dynamics," Lecture Notes in Economics and Mathematical Systems, in: Cesáreo Hernández & Marta Posada & Adolfo López-Paredes (ed.), Artificial Economics, chapter 0, pages 237-244, Springer.
    • Handle: RePEc:spr:lnechp:978-3-642-02956-1_19
    DOI: 10.1007/978-3-642-02956-1_19
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Binmore, Kenneth G. & Samuelson, Larry, 1992. "Evolutionary stability in repeated games played by finite automata," Journal of Economic Theory, Elsevier, vol. 57(2), pages 278-305, August.
    2. 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.
    3. Miller, John H., 1996. "The coevolution of automata in the repeated Prisoner's Dilemma," Journal of Economic Behavior & Organization, Elsevier, vol. 29(1), pages 87-112, January.
    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. Zhang, Huanren, 2018. "Errors can increase cooperation in finite populations," Games and Economic Behavior, Elsevier, vol. 107(C), pages 203-219.
    2. Fukutomi, Masao & Kurokawa, Shun, 2018. "How much cost should reciprocators pay in order to distinguish the opponent's cooperation from the opponent's defection?," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 301-314.
    3. 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.
    4. Xavier Vilà, 2008. "A Model-To-Model Analysis of Bertrand Competition," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 11(2), pages 1-11.
    5. Peng Liu & Haoxiang Xia, 2015. "Structure and evolution of co-authorship network in an interdisciplinary research field," Scientometrics, Springer;Akadémiai Kiadó, vol. 103(1), pages 101-134, April.
    6. García, Julián & van Veelen, Matthijs, 2016. "In and out of equilibrium I: Evolution of strategies in repeated games with discounting," Journal of Economic Theory, Elsevier, vol. 161(C), pages 161-189.
    7. Xavier Vilà, 2005. "Consumers' Behavior and the Bertrand Paradox: An ACE approach," UFAE and IAE Working Papers 654.05, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    8. Matthijs van Veelen & Benjamin Allen & Moshe Hoffman & Burton Simon & Carl Veller, 2016. "Inclusive Fitness," Tinbergen Institute Discussion Papers 16-055/I, Tinbergen Institute.
    9. Jasmina Arifovic & James B. Bullard & John Duffy, 1995. "Learning in a model of economic growth and development," Working Papers 1995-017, Federal Reserve Bank of St. Louis.
    10. repec:cla:levarc:786969000000001297 is not listed on IDEAS
    11. ENGLE-WARNICK, Jim & McCAUSLAND, William J. & MILLER, John H., 2004. "The Ghost in the Machine: Inferring Machine-Based Strategies from Observed Behavior," Cahiers de recherche 2004-11, Universite de Montreal, Departement de sciences economiques.
    12. Bullard, James & Duffy, John, 1998. "A model of learning and emulation with artificial adaptive agents," Journal of Economic Dynamics and Control, Elsevier, vol. 22(2), pages 179-207, February.
    13. Hanaki, Nobuyuki & Sethi, Rajiv & Erev, Ido & Peterhansl, Alexander, 2005. "Learning strategies," Journal of Economic Behavior & Organization, Elsevier, vol. 56(4), pages 523-542, April.
    14. 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.
    15. 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.
    16. Christos Ioannou, 2014. "Coevolution of finite automata with errors," Journal of Evolutionary Economics, Springer, vol. 24(3), pages 541-571, July.
    17. 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.
    18. 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.
    19. Kang, Hongwei & Li, Zhekang & Shen, Yong & Huang, Zhiyuan & Sun, Xingping & Chen, Qingyi, 2024. "From eligibility to suitability: Regulation and restriction of reputation-based access system on free-riding behavior in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    20. Arifovic, Jasmina & Bullard, James & Duffy, John, 1997. "The Transition from Stagnation to Growth: An Adaptive Learning Approach," Journal of Economic Growth, Springer, vol. 2(2), pages 185-209, July.
    21. Robert Hoffmann, 2001. "The Ecology of Cooperation," Theory and Decision, Springer, vol. 50(2), pages 101-118, March.

    More about this item

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

    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:spr:lnechp:978-3-642-02956-1_19. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.