IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0056416.html
   My bibliography  Save this article

Cyclic Game Dynamics Driven by Iterated Reasoning

Author

Listed:
  • Seth Frey
  • Robert L Goldstone

Abstract

Recent theories from complexity science argue that complex dynamics are ubiquitous in social and economic systems. These claims emerge from the analysis of individually simple agents whose collective behavior is surprisingly complicated. However, economists have argued that iterated reasoning–what you think I think you think–will suppress complex dynamics by stabilizing or accelerating convergence to Nash equilibrium. We report stable and efficient periodic behavior in human groups playing the Mod Game, a multi-player game similar to Rock-Paper-Scissors. The game rewards subjects for thinking exactly one step ahead of others in their group. Groups that play this game exhibit cycles that are inconsistent with any fixed-point solution concept. These cycles are driven by a “hopping” behavior that is consistent with other accounts of iterated reasoning: agents are constrained to about two steps of iterated reasoning and learn an additional one-half step with each session. If higher-order reasoning can be complicit in complex emergent dynamics, then cyclic and chaotic patterns may be endogenous features of real-world social and economic systems.

Suggested Citation

  • Seth Frey & Robert L Goldstone, 2013. "Cyclic Game Dynamics Driven by Iterated Reasoning," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-11, February.
    • Handle: RePEc:plo:pone00:0056416
    DOI: 10.1371/journal.pone.0056416
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0056416
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0056416&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0056416?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. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
    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. Ngo-Hoang, Dai-Long, 2019. "A research paper of Hossein Sabzian (2019), Theories and Practice of Agent based Modeling: Some practical Implications for Economic Planners, ArXiv, 54p," AgriXiv xutyz, Center for Open Science.
    2. Seth Frey & Robert L. Goldstone, 2018. "Cognitive mechanisms for human flocking dynamics," Journal of Computational Social Science, Springer, vol. 1(2), pages 349-375, September.
    3. Hanshu Zhang & Frederic Moisan & Cleotilde Gonzalez, 2021. "Rock-Paper-Scissors Play: Beyond the Win-Stay/Lose-Change Strategy," Games, MDPI, vol. 12(3), pages 1-15, June.
    4. repec:cup:judgdm:v:13:y:2018:i:1:p:79-98 is not listed on IDEAS
    5. repec:osf:agrixi:xutyz_v1 is not listed on IDEAS
    6. Rineke Verbrugge & Ben Meijering & Stefan Wierda & Hedderik van Rijn & Niels Taatgen, 2018. "Stepwise training supports strategic second-order theory of mind in turn-taking games," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 13(1), pages 79-98, January.
    7. Hossein Sabzian & Mohammad Ali Shafia & Mehdi Ghazanfari & Ali Bonyadi Naeini, 2020. "Modeling the Adoption and Diffusion of Mobile Telecommunications Technologies in Iran: A Computational Approach Based on Agent-Based Modeling and Social Network Theory," Sustainability, MDPI, vol. 12(7), pages 1-36, April.
    8. Hossein Sabzian & Mohammad Ali Shafia & Ali Maleki & Seyeed Mostapha Seyeed Hashemi & Ali Baghaei & Hossein Gharib, 2019. "Theories and Practice of Agent based Modeling: Some practical Implications for Economic Planners," Papers 1901.08932, arXiv.org.
    9. Erik Brockbank & Edward Vul, 2021. "Formalizing Opponent Modeling with the Rock, Paper, Scissors Game," Games, MDPI, vol. 12(3), pages 1-20, September.
    10. João Plínio Juchem Neto & Angelo Francisco Sirtoli Delamare, 2021. "The level of tolerance of individuals, individual thinking, and the formation of social norms," Journal of Computational Social Science, Springer, vol. 4(2), pages 721-759, November.

    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. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October.
    2. Anthonisen, Niels, 1997. "On the Convergence of Beliefs within Populations in Games with Learning," Journal of Economic Theory, Elsevier, vol. 76(1), pages 169-184, September.
    3. Ianni, A., 2002. "Reinforcement learning and the power law of practice: some analytical results," Discussion Paper Series In Economics And Econometrics 203, Economics Division, School of Social Sciences, University of Southampton.
    4. Benaïm, Michel & Hofbauer, Josef & Hopkins, Ed, 2009. "Learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1694-1709, July.
    5. Sandholm,W.H., 2003. "Excess payoff dynamics, potential dynamics, and stable games," Working papers 5, Wisconsin Madison - Social Systems.
    6. DeJong, D.V. & Blume, A. & Neumann, G., 1998. "Learning in Sender-Receiver Games," Other publications TiSEM 4a8b4f46-f30b-4ad2-bb0c-1, Tilburg University, School of Economics and Management.
    7. Oechssler, Jorg, 1997. "An Evolutionary Interpretation of Mixed-Strategy Equilibria," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 203-237, October.
    8. Antonio Cabrales & Giovanni Ponti, 2000. "Implementation, Elimination of Weakly Dominated Strategies and Evolutionary Dynamics," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(2), pages 247-282, April.
    9. Dai Zusai, 2023. "Evolutionary dynamics in heterogeneous populations: a general framework for an arbitrary type distribution," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(4), pages 1215-1260, December.
    10. Ellison, Glenn, 1997. "Learning from Personal Experience: One Rational Guy and the Justification of Myopia," Games and Economic Behavior, Elsevier, vol. 19(2), pages 180-210, May.
    11. Giovanni Ponti, 2000. "Splitting The Baby In Two: How To Solve Solomon'S Dilemma When Agents Are Boundedly Rational," Working Papers. Serie AD 2000-08, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    12. Michel BenaÔm & J–rgen W. Weibull, 2003. "Deterministic Approximation of Stochastic Evolution in Games," Econometrica, Econometric Society, vol. 71(3), pages 873-903, May.
    13. Fudenberg, Drew & Takahashi, Satoru, 2011. "Heterogeneous beliefs and local information in stochastic fictitious play," Games and Economic Behavior, Elsevier, vol. 71(1), pages 100-120, January.
    14. Hopkins, Ed, 1999. "Learning, Matching, and Aggregation," Games and Economic Behavior, Elsevier, vol. 26(1), pages 79-110, January.
    15. Blume, A. & DeJong, D.V. & Neumann, G. & Savin, N.E., 2000. "Learning and Communication in Sender-Reciever Games : An Economic Investigation," Other publications TiSEM 138dc36b-5269-421a-9e79-b, Tilburg University, School of Economics and Management.
    16. Zauner, Klaus G., 1999. "A Payoff Uncertainty Explanation of Results in Experimental Centipede Games," Games and Economic Behavior, Elsevier, vol. 26(1), pages 157-185, January.
    17. Sobel, Joel, 2000. "Economists' Models of Learning," Journal of Economic Theory, Elsevier, vol. 94(2), pages 241-261, October.
    18. Martino Banchio & Giacomo Mantegazza, 2022. "Artificial Intelligence and Spontaneous Collusion," Papers 2202.05946, arXiv.org, revised Sep 2023.
    19. Funai, Naoki, 2022. "Reinforcement learning with foregone payoff information in normal form games," Journal of Economic Behavior & Organization, Elsevier, vol. 200(C), pages 638-660.
    20. Fulin Guo, 2023. "Experience-weighted attraction learning in network coordination games," Papers 2310.18835, arXiv.org.

    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:plo:pone00:0056416. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.