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Volunteering leads to rock–paper–scissors dynamics in a public goods game

Author

Listed:
  • Dirk Semmann

    (Max Planck Institute of Limnology)

  • Hans-Jürgen Krambeck

    (Max Planck Institute of Limnology)

  • Manfred Milinski

    (Max Planck Institute of Limnology)

Abstract

Collective efforts are a trademark of both insect and human societies1. They are achieved through relatedness in the former2 and unknown mechanisms in the latter. The problem of achieving cooperation among non-kin has been described as the ‘tragedy of the commons’, prophesying the inescapable collapse of many human enterprises3,4. In public goods experiments, initial cooperation usually drops quickly to almost zero5. It can be maintained by the opportunity to punish defectors6 or the need to maintain good reputation7. Both schemes require that defectors are identified. Theorists propose that a simple but effective mechanism operates under full anonymity. With optional participation in the public goods game, ‘loners’ (players who do not join the group), defectors and cooperators will coexist through rock–paper–scissors dynamics8,9. Here we show experimentally that volunteering generates these dynamics in public goods games and that manipulating initial conditions can produce each predicted direction. If, by manipulating displayed decisions, it is pretended that defectors have the highest frequency, loners soon become most frequent, as do cooperators after loners and defectors after cooperators. On average, cooperation is perpetuated at a substantial level.

Suggested Citation

  • Dirk Semmann & Hans-Jürgen Krambeck & Manfred Milinski, 2003. "Volunteering leads to rock–paper–scissors dynamics in a public goods game," Nature, Nature, vol. 425(6956), pages 390-393, September.
  • Handle: RePEc:nat:nature:v:425:y:2003:i:6956:d:10.1038_nature01986
    DOI: 10.1038/nature01986
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    Citations

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    Cited by:

    1. Wang, Xianjia & Ding, Rui & Zhao, Jinhua & Chen, Wenman & Gu, Cuiling, 2022. "Competition of punishment and reward among inequity-averse individuals in spatial public goods games," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    2. Chaoqian Wang & Matjaž Perc & Attila Szolnoki, 2024. "Evolutionary dynamics of any multiplayer game on regular graphs," Nature Communications, Nature, vol. 15(1), pages 1-15, December.
    3. Ma, Xiaojian & Quan, Ji & Wang, Xianjia, 2021. "Effect of reputation-based heterogeneous investment on cooperation in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. 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.
    5. Duiverman, Sytse, 2022. "Four essays on the quality of auditing: Causes and consequences," Other publications TiSEM 7d7be078-670f-4712-959b-f, Tilburg University, School of Economics and Management.
    6. Yang, Yimei & Sun, Hao & Yang, Guangjing & Sun, Yanru, 2024. "Bilateral negotiation facilitates stable coexistence of cooperation with defection in Prisoner's Dilemma game," Applied Mathematics and Computation, Elsevier, vol. 471(C).
    7. Ding, Rui & Wang, Xianjia & Zhao, Jinhua & Gu, Cuiling & Wang, Tao, 2023. "The evolution of cooperation in spatial public goods games under a risk-transfer mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    8. Quan, Ji & Zhang, Xiyue & Chen, Wenman & Tang, Caixia & Wang, Xianjia, 2024. "Reputation-dependent social learning on the evolution of cooperation in spatial public goods games," Applied Mathematics and Computation, Elsevier, vol. 475(C).
    9. Quan, Ji & Yu, Junyu & Li, Xia & Wang, Xianjia, 2023. "Conditional switching between social excluders and loners promotes cooperation in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    10. Marcus Dittrich & Bianka Mey, 2023. "Voluntary labour supply by birth cohort: empirical evidence from Germany," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 50(2), pages 389-410, May.
    11. José Pedro Gaivão & Telmo Peixe, 2021. "Periodic Attractor in the Discrete Time Best-Response Dynamics of the Rock-Paper-Scissors Game," Dynamic Games and Applications, Springer, vol. 11(3), pages 491-511, September.
    12. Wang, Xianjia & Ding, Rui & Zhao, Jinhua & Gu, Cuiling, 2022. "The rise and fall of cooperation in populations with multiple groups," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    13. Wang, Xianjia & Ding, Rui & Zhao, Jinhua & Chen, Wenman, 2021. "The rise and fall of donation behavior through reputation," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    14. Francesca Pancotto & Simone Righi & Károly Takács, 2023. "Voluntary play increases cooperation in the presence of punishment: a lab in the field experiment," Theory and Decision, Springer, vol. 95(3), pages 405-428, October.

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