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How Individuals Learn To Take Turns: Emergence Of Alternating Cooperation In A Congestion Game And The Prisoner'S Dilemma

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  • DIRK HELBING

    (Institute for Transport & Economics, Dresden University of Technology, Andreas-Schubert-Str. 23, 01062 Dresden, Germany)

  • MARTIN SCHÖNHOF

    (Institute for Transport & Economics, Dresden University of Technology, Andreas-Schubert-Str. 23, 01062 Dresden, Germany)

  • HANS-ULRICH STARK

    (Institute for Transport & Economics, Dresden University of Technology, Andreas-Schubert-Str. 23, 01062 Dresden, Germany)

  • JANUSZ A. HOŁYST

    (Faculty of Physics and Center of Excellence for Complex Systems Research, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland)

Abstract

In many social dilemmas, individuals tend to generate a situation with low payoffs instead of a system optimum ("tragedy of the commons"). Is the routing of traffic a similar problem? In order to address this question, we present experimental results on humans playing a route choice game in a computer laboratory, which allow one to study decision behavior in repeated games beyond the Prisoner's Dilemma. We will focus on whether individuals manage to find a cooperative and fair solution compatible with the system-optimal road usage. We find that individuals tend towards a user equilibrium with equal travel times in the beginning. However, after many iterations, they often establish a coherent oscillatory behavior, as taking turns performs better than applying pure or mixed strategies. The resulting behavior is fair and compatible with system-optimal road usage. In spite of the complex dynamics leading to coordinated oscillations, we have identified mathematical relationships quantifying the observed transition process. Our main experimental discoveries for 2- and 4-person games can be explained with a novel reinforcement learning model for an arbitrary number of persons, which is based on past experience and trial-and-error behavior. Gains in the average payoff seem to be an important driving force for the innovation of time-dependent response patterns, i.e. the evolution of more complex strategies. Our findings are relevant for decision support systems and routing in traffic or data networks.

Suggested Citation

  • Dirk Helbing & Martin Schönhof & Hans-Ulrich Stark & Janusz A. Hołyst, 2005. "How Individuals Learn To Take Turns: Emergence Of Alternating Cooperation In A Congestion Game And The Prisoner'S Dilemma," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 87-116.
    • Handle: RePEc:wsi:acsxxx:v:08:y:2005:i:01:n:s0219525905000361
    DOI: 10.1142/S0219525905000361
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    References listed on IDEAS

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    1. Giulio Bottazzi & Giovanna Devetag, 2002. "Coordination and self-organization in minority games: experimental evidence," CEEL Working Papers 0215, Cognitive and Experimental Economics Laboratory, Department of Economics, University of Trento, Italia.
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    Cited by:

    1. Levy, Nadav & Klein, Ido & Ben-Elia, Eran, 2018. "Emergence of cooperation and a fair system optimum in road networks: A game-theoretic and agent-based modelling approach," Research in Transportation Economics, Elsevier, vol. 68(C), pages 46-55.
    2. Collins, Mor & Etzioni, Shelly & Ben-Elia, Eran, 2024. "Travel behavior and system dynamics in a simple gamified automated multimodal network," Transportation Research Part A: Policy and Practice, Elsevier, vol. 183(C).
    3. Oliveira, Fernando S., 2023. "The emergence of social inequality: A Co-Evolutionary analysis," Journal of Economic Behavior & Organization, Elsevier, vol. 215(C), pages 192-206.
    4. Richmond, Peter, 2007. "A roof over your head; house price peaks in the UK and Ireland," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 281-287.
    5. Zhao, Shuchen, 2021. "Taking turns in continuous time," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 257-279.
    6. Todd R. Kaplan & Bradley J. Ruffle, 2012. "Which Way to Cooperate," Economic Journal, Royal Economic Society, vol. 122(563), pages 1042-1068, September.
    7. Kloosterman, Andrew & Mago, Shakun, 2023. "The infinitely repeated volunteer's dilemma: An experimental study," Games and Economic Behavior, Elsevier, vol. 142(C), pages 812-832.
    8. Jean-Philippe Chancelier & Michel De Lara & André de Palma, 2007. "Risk Aversion, Road Choice, and the One-Armed Bandit Problem," Transportation Science, INFORMS, vol. 41(1), pages 1-14, February.
    9. Doğan, Gönül, 2018. "Collusion in a buyer–seller network formation game," Journal of Economic Behavior & Organization, Elsevier, vol. 155(C), pages 445-457.
    10. Riyanto, Yohanes E. & Roy, Nilanjan, 2019. "Path of intertemporal cooperation and limits to turn-taking behavior," Journal of Economic Behavior & Organization, Elsevier, vol. 165(C), pages 21-36.
    11. Hadzibeganovic, Tarik & Liu, Chao & Li, Rong, 2021. "Effects of reproductive skew on the evolution of ethnocentrism in structured populations with variable size," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 568(C).
    12. Kaplan, Todd R. & Ruffle, Bradley J. & Shtudiner, Zeev, 2018. "Cooperation through coordination in two stages," Journal of Economic Behavior & Organization, Elsevier, vol. 154(C), pages 206-219.
    13. Anton M Unakafov & Thomas Schultze & Alexander Gail & Sebastian Moeller & Igor Kagan & Stephan Eule & Fred Wolf, 2020. "Emergence and suppression of cooperation by action visibility in transparent games," PLOS Computational Biology, Public Library of Science, vol. 16(1), pages 1-32, January.
    14. Stathopoulos, Amanda & Cirillo, Cinzia & Cherchi, Elisabetta & Ben-Elia, Eran & Li, Yeun-Touh & Schmöcker, Jan-Dirk, 2017. "Innovation adoption modeling in transportation: New models and data," Journal of choice modelling, Elsevier, vol. 25(C), pages 61-68.
    15. Meneguzzer, Claudio, 2022. "Day-to-day dynamics in a simple traffic network with mixed direct and contrarian route choice behaviors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    16. Riyanto, Yohanes E. & Roy, Nilanjan, 2017. "It's your turn: experiments with three-player public good games," MPRA Paper 76565, University Library of Munich, Germany.
    17. Carina Goldbach & Deniz Kayar & Thomas Pitz & Jörn Sickmann, 2022. "Driving, Fast and Slow: An Experimental Investigation of Speed Choice and Information," SAGE Open, , vol. 12(2), pages 21582440221, April.
    18. Michael E Roberts & Robert L Goldstone, 2011. "Adaptive Group Coordination and Role Differentiation," PLOS ONE, Public Library of Science, vol. 6(7), pages 1-8, July.
    19. He, Simin & Zou, Xinlu, 2024. "Public goods provision in a network formation game," Journal of Economic Behavior & Organization, Elsevier, vol. 218(C), pages 104-131.
    20. Koller, Florian, 2021. "What determines the acceptance of socially optimal traffic coordination?: A scenario-based examination in Germany," Transportation Research Part A: Policy and Practice, Elsevier, vol. 149(C), pages 62-75.

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