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Tactical cooperation of defectors in a multi-stage public goods game

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  • Szolnoki, Attila
  • Chen, Xiaojie

Abstract

The basic social dilemma is frequently captured by a public goods game where participants decide simultaneously whether to support a common pool or not and after the enhanced contributions are distributed uniformly among all competitors. What if the result of common efforts is not distributed immediately, but it is reinvested and added to the pool for a next round? This extension may not only result in an enhanced benefit for group members but also opens new strategies for involved players because they may act in distinct rounds differently. In this work we focus on the simplest case when two rounds are considered, but the applied multiplication factors dedicated to a certain round can be different. We show that in structured populations the winning strategy may depend sensitively on the ratio of these factors and the last round has a special importance to reach a fully cooperative state. We also observe that it may pay for defectors to support the first round and after enjoy the extra benefit of accumulated contributions. Full cooperator strategy is only viable if the second round ensures a premium benefit of investments.

Suggested Citation

  • Szolnoki, Attila & Chen, Xiaojie, 2022. "Tactical cooperation of defectors in a multi-stage public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s096007792101050x
    DOI: 10.1016/j.chaos.2021.111696
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    4. Li, Wen-Jing & Chen, Zhi & Jin, Ke-Zhong & Wang, Jun & Yuan, Lin & Gu, Changgui & Jiang, Luo-Luo & Perc, Matjaž, 2022. "Options for mobility and network reciprocity to jointly yield robust cooperation in social dilemmas," Applied Mathematics and Computation, Elsevier, vol. 435(C).
    5. Wang, Chaoqian & Szolnoki, Attila, 2022. "Involution game with spatio-temporal heterogeneity of social resources," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    6. 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.
    7. Lee, Hsuan-Wei & Cleveland, Colin & Szolnoki, Attila, 2023. "Restoring spatial cooperation with myopic agents in a three-strategy social dilemma," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    8. Li, Dandan & Zhou, Kai & Sun, Mei & Han, Dun, 2023. "Investigating the effectiveness of individuals’ historical memory for the evolution of the prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    9. 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).
    10. Wang, Jianwei & Xu, Wenshu & Yu, Fengyuan & He, Jialu & Chen, Wei & Dai, Wenhui, 2024. "Evolution of cooperation under corrupt institutions," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
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