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Cyclic Game Dynamics Driven by Iterated Reasoning

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  • 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
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    References listed on IDEAS

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    1. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
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    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. repec:cup:judgdm:v:13:y:2018:i:1:p:79-98 is not listed on IDEAS
    3. 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.
    4. 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.
    5. 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.
    6. Erik Brockbank & Edward Vul, 2021. "Formalizing Opponent Modeling with the Rock, Paper, Scissors Game," Games, MDPI, vol. 12(3), pages 1-20, September.
    7. 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.
    8. 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.
    9. 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.

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