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The second-order probabilistic pool punishment proportional to the payoff difference can solve the punishment problem of previous studies

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  • Ohdaira, Tetsushi

Abstract

The public goods game is one of the models utilized in theoretical studies of social dilemmas where the pursuit of individual interests does not benefit society as a whole. In the context of the public goods game, the optimal response of participants is defecting (not investing in the public goods). Therefore, the evolution of cooperation in the public goods game generally requires punishment or reward. Out of these two elements, this study deals with punishment. There are two types of punishment: peer punishment and pool punishment. The problem of peer punishment is the high cost of punishment, and the problem of pool punishment is that the cost of punishment is always incurred. Here, extending the previously proposed probabilistic pool punishment, we consider the punishment on cooperators (second-order free riders) as well as defectors. Comparing the pool punishment of this study with pool and peer punishment of existing studies, especially in terms of the average payoff, it is superior to those previous punishment mechanisms. In addition, the various programming techniques in the construction of the simulator in this study are expected to be utilized as teaching materials for specialized education at Kanagawa Institute of Technology.

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  • Ohdaira, Tetsushi, 2025. "The second-order probabilistic pool punishment proportional to the payoff difference can solve the punishment problem of previous studies," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:chsofr:v:194:y:2025:i:c:s0960077925002681
    DOI: 10.1016/j.chaos.2025.116255
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    References listed on IDEAS

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    1. Ohdaira, Tetsushi, 2024. "The universal probabilistic reward based on the difference of payoff realizes the evolution of cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    2. Rand, David Gertler & Dreber, Anna & Fudenberg, Drew & Ellingson, Tore & Nowak, Martin A., 2009. "Positive Interactions Promote Public Cooperation," Scholarly Articles 3804483, Harvard University Department of Economics.
    3. Tetsushi Ohdaira, 2021. "Cooperation evolves by the payoff-difference-based probabilistic reward," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(11), pages 1-8, November.
    4. Lee, Hsuan-Wei & Cleveland, Colin & Szolnoki, Attila, 2024. "Supporting punishment via taxation in a structured population," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    5. David G. Rand & Martin A. Nowak, 2011. "The evolution of antisocial punishment in optional public goods games," Nature Communications, Nature, vol. 2(1), pages 1-7, September.
    6. Hisashi Ohtsuki & Yoh Iwasa & Martin A. Nowak, 2009. "Indirect reciprocity provides only a narrow margin of efficiency for costly punishment," Nature, Nature, vol. 457(7225), pages 79-82, January.
    7. Dirk Helbing & Attila Szolnoki & Matjaž Perc & György Szabó, 2010. "Evolutionary Establishment of Moral and Double Moral Standards through Spatial Interactions," PLOS Computational Biology, Public Library of Science, vol. 6(4), pages 1-9, April.
    8. Ohdaira, Tetsushi, 2017. "Characteristics of the evolution of cooperation by the probabilistic peer-punishment based on the difference of payoff," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 77-83.
    9. Karl Sigmund & Hannelore De Silva & Arne Traulsen & Christoph Hauert, 2010. "Social learning promotes institutions for governing the commons," Nature, Nature, vol. 466(7308), pages 861-863, August.
    10. Lee, Hsuan-Wei & Cleveland, Colin & Szolnoki, Attila, 2022. "Mercenary punishment in structured populations," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    11. Xiaojie Chen & Attila Szolnoki, 2018. "Punishment and inspection for governing the commons in a feedback-evolving game," PLOS Computational Biology, Public Library of Science, vol. 14(7), pages 1-15, July.
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