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Fractional Punishment of Free Riders to Improve Cooperation in Optional Public Good Games

Author

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  • Rocio Botta

    (Polytechnic School, National University of Asuncion, San Lorenzo 2111, Paraguay)

  • Gerardo Blanco

    (Polytechnic School, National University of Asuncion, San Lorenzo 2111, Paraguay)

  • Christian E. Schaerer

    (Polytechnic School, National University of Asuncion, San Lorenzo 2111, Paraguay)

Abstract

Improving and maintaining cooperation are fundamental issues for any project to be time-persistent, and sanctioning free riders may be the most applied method to achieve it. However, the application of sanctions differs from one group (project or institution) to another. We propose an optional, public good game model where a randomly selected set of the free riders is punished. To this end, we introduce a parameter that establishes the portion of free riders sanctioned with the purpose to control the population state evolution in the game. This parameter modifies the phase portrait of the system, and we show that, when the parameter surpasses a threshold, the full cooperation equilibrium point becomes a stable global attractor. Hence, we demonstrate that the fractional approach improves cooperation while reducing the sanctioning cost.

Suggested Citation

  • Rocio Botta & Gerardo Blanco & Christian E. Schaerer, 2021. "Fractional Punishment of Free Riders to Improve Cooperation in Optional Public Good Games," Games, MDPI, vol. 12(1), pages 1-21, February.
    • Handle: RePEc:gam:jgames:v:12:y:2021:i:1:p:17-:d:494393
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    References listed on IDEAS

    as
    1. Jianlei Zhang & Yuying Zhu & Qiaoyu Li & Zengqiang Chen, 2018. "Promoting cooperation by setting a ceiling payoff for defectors under three-strategy public good games," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(10), pages 2267-2286, July.
    2. 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.
    3. Ernst Fehr & Simon Gächter, 2002. "Altruistic punishment in humans," Nature, Nature, vol. 415(6868), pages 137-140, January.
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    5. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, December.
    6. repec:fth:iniesr:487 is not listed on IDEAS
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