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Multistability and bifurcation analysis for a three-strategy game system with public goods feedback and discrete delays

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  • Cheng, Haihui
  • Meng, Xinzhu
  • Hayat, Tasawar
  • Hobiny, Aatef

Abstract

The interaction between evolution and public goods exists in social and biological systems. Exploring mathematical models that combine evolution and public goods facilitates insights and discoveries about the evolution of cooperation. We propose a third strategy called the encouragement strategy, which can reward and punish, and bear the related costs, in addition to the classical cooperation and defection strategies. We incorporate strategy and public goods dynamics to formulate a high-dimensional and high-order three-strategy evolutionary game system with public goods feedback. For this non-delayed system, we evaluate the existence of equilibria and the conditions for the occurrence of transcritical and Hopf bifurcations. Interestingly, the non-delayed system exhibits multiple multistability due to different payoffs and initial conditions. The results suggest that the environment with rich public goods is suitable for cooperators to survive. Surprisingly, raising reward does not always promote the survival of cooperators. Cooperators prevail in environments with moderate reward and severe punishment. Further, we develop a delayed system by considering information delay and production delay. For the delayed system, we investigate the properties of Hopf bifurcation, including existence, direction and stability. We find that small delays do not affect the evolutionary outcome of the strategies. However, delays larger than the critical value lead to periodic oscillations of the strategies, in which case the cooperators still have a dominant advantage. Unfortunately, larger delays can cause the disappearance of cooperators. Theoretical and numerical results show that public goods feedback, reward, punishment, payoffs, initial conditions, and delays are all significant factors in determining the outcome of strategic evolution.

Suggested Citation

  • Cheng, Haihui & Meng, Xinzhu & Hayat, Tasawar & Hobiny, Aatef, 2023. "Multistability and bifurcation analysis for a three-strategy game system with public goods feedback and discrete delays," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
  • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923009128
    DOI: 10.1016/j.chaos.2023.114011
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    1. Dixit, Avinash & Olson, Mancur, 2000. "Does voluntary participation undermine the Coase Theorem?," Journal of Public Economics, Elsevier, vol. 76(3), pages 309-335, June.
    2. Larry Samuelson, 2016. "Game Theory in Economics and Beyond," Journal of Economic Perspectives, American Economic Association, vol. 30(4), pages 107-130, Fall.
    3. R. Craig MacLean & Ivana Gudelj, 2006. "Resource competition and social conflict in experimental populations of yeast," Nature, Nature, vol. 441(7092), pages 498-501, May.
    4. Krawiec, Adam & Szydłowski, Marek, 2017. "Economic growth cycles driven by investment delay," Economic Modelling, Elsevier, vol. 67(C), pages 175-183.
    5. Stefan Meyer & Paulo Santos & Fue Yang, 2021. "Economic games can be used to promote cooperation in the field," Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, vol. 118(47), pages 2026046118-, November.
    6. Rabin, Matthew, 1993. "Incorporating Fairness into Game Theory and Economics," American Economic Review, American Economic Association, vol. 83(5), pages 1281-1302, December.
    7. D. Joseph Sexton & Martin Schuster, 2017. "Nutrient limitation determines the fitness of cheaters in bacterial siderophore cooperation," Nature Communications, Nature, vol. 8(1), pages 1-8, December.
    8. Hommes, Cars H. & Ochea, Marius I., 2012. "Multiple equilibria and limit cycles in evolutionary games with Logit Dynamics," Games and Economic Behavior, Elsevier, vol. 74(1), pages 434-441.
    9. Andrew R. Tilman & Joshua B. Plotkin & Erol Akçay, 2020. "Evolutionary games with environmental feedbacks," Nature Communications, Nature, vol. 11(1), pages 1-11, December.
    10. Zhenhua Pei & Baokui Wang & Jinming Du, 2016. "Effects of income redistribution on the evolution of cooperation in spatial public goods games," Papers 1611.01531, arXiv.org.
    11. Duan, Daifeng & Niu, Ben & Wei, Junjie, 2019. "Hopf-Hopf bifurcation and chaotic attractors in a delayed diffusive predator-prey model with fear effect," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 206-216.
    12. Chen, Qin & Pan, Qiuhui & He, Mingfeng, 2022. "The influence of quasi-cooperative strategy on social dilemma evolution," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
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    Cited by:

    1. Wang, Yifei & Meng, Xinzhu & Alzahrani, Abdullah Khames, 2024. "Stability, period and chaos of the evolutionary game strategy induced by time-delay and mutation feedback," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. Tianjun Su & Linhai Wu & Jingxiang Zhang, 2024. "Evolutionary Game and Simulation Analysis of Food Safety Regulation under Time Delay Effect," Mathematics, MDPI, vol. 12(8), pages 1-23, April.

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