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Ecological public goods games: Cooperation and bifurcation

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  • Hauert, Christoph
  • Wakano, Joe Yuichiro
  • Doebeli, Michael

Abstract

The Public Goods Game is one of the most popular models for studying the origin and maintenance of cooperation. In its simplest form, this evolutionary game has two regimes: defection goes to fixation if the multiplication factor r is smaller than the interaction group size N, whereas cooperation goes to fixation if the multiplication factor r is larger than the interaction group size N. Hauert et al. [Hauert, C., Holmes, M., Doebeli, M., 2006a. Evolutionary games and population dynamics: Maintenance of cooperation in public goods games. Proc. R. Soc. Lond. B 273, 2565–2570] have introduced the Ecological Public Goods Game by viewing the payoffs from the evolutionary game as birth rates in a population dynamic model. This results in a feedback between ecological and evolutionary dynamics: if defectors are prevalent, birth rates are low and population densities decline, which leads to smaller interaction groups for the Public Goods game, and hence to dominance of cooperators, with a concomitant increase in birth rates and population densities. This feedback can lead to stable co-existence between cooperators and defectors. Here we provide a detailed analysis of the dynamics of the Ecological Public Goods Game, showing that the model exhibits various types of bifurcations, including supercritical Hopf bifurcations, which result in stable limit cycles, and hence in oscillatory co-existence of cooperators and defectors. These results show that including population dynamics in evolutionary games can have important consequences for the evolutionary dynamics of cooperation.

Suggested Citation

  • Hauert, Christoph & Wakano, Joe Yuichiro & Doebeli, Michael, 2008. "Ecological public goods games: Cooperation and bifurcation," Theoretical Population Biology, Elsevier, vol. 73(2), pages 257-263.
    • Handle: RePEc:eee:thpobi:v:73:y:2008:i:2:p:257-263
    DOI: 10.1016/j.tpb.2007.11.007
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    Citations

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    Cited by:

    1. Ivana Gudelj & Margie Kinnersley & Peter Rashkov & Karen Schmidt & Frank Rosenzweig, 2016. "Stability of Cross-Feeding Polymorphisms in Microbial Communities," PLOS Computational Biology, Public Library of Science, vol. 12(12), pages 1-17, December.
    2. Young, Glenn & Belmonte, Andrew, 2018. "Fast cheater migration stabilizes coexistence in a public goods dilemma on networks," Theoretical Population Biology, Elsevier, vol. 121(C), pages 12-25.
    3. Liu, Yuan & Cao, Lixuan & Wu, Bin, 2022. "General non-linear imitation leads to limit cycles in eco-evolutionary dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    4. Elhanati, Yuval & Schuster, Stefan & Brenner, Naama, 2011. "Dynamic modeling of cooperative protein secretion in microorganism populations," Theoretical Population Biology, Elsevier, vol. 80(1), pages 49-63.
    5. Felix Funk & Christoph Hauert, 2019. "Directed migration shapes cooperation in spatial ecological public goods games," PLOS Computational Biology, Public Library of Science, vol. 15(8), pages 1-14, August.
    6. Wakano, Joe Y. & Kawasaki, Kohkichi & Shigesada, Nanako & Aoki, Kenichi, 2011. "Coexistence of individual and social learners during range expansion," Theoretical Population Biology, Elsevier, vol. 80(2), pages 132-140.
    7. Feng Zhang & Cang Hui, 2011. "Eco-Evolutionary Feedback and the Invasion of Cooperation in Prisoner's Dilemma Games," PLOS ONE, Public Library of Science, vol. 6(11), pages 1-7, November.
    8. Faqi Du & Feng Fu, 2011. "Partner Selection Shapes the Strategic and Topological Evolution of Cooperation," Dynamic Games and Applications, Springer, vol. 1(3), pages 354-369, September.
    9. De Jaegher, Kris, 2017. "Harsh environments and the evolution of multi-player cooperation," Theoretical Population Biology, Elsevier, vol. 113(C), pages 1-12.
    10. Gokhale, Chaitanya S. & Hauert, Christoph, 2016. "Eco-evolutionary dynamics of social dilemmas," Theoretical Population Biology, Elsevier, vol. 111(C), pages 28-42.
    11. Behar, Hilla & Brenner, Naama & Louzoun, Yoram, 2014. "Coexistence of productive and non-productive populations by fluctuation-driven spatio-temporal patterns," Theoretical Population Biology, Elsevier, vol. 96(C), pages 20-29.

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