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Dissatisfaction-driven replicator dynamics of the evolutionary snowdrift game in structured populations

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  • Ke, Jianhong
  • Li, Ping-Ping
  • Lin, Zhenquan

Abstract

We study the evolutionary snowdrift game with an update rule of dissatisfaction-driven replicator on regular lattices, in which there exists a threshold value K of dissatisfaction dividing the update rule into unconditional imitation and probability replication. It is found that under the random initial state with fc0=0.5, the equilibrium cooperation frequency fc against the cost-to-benefit ratio r has a step-like piecewise structure when K is small and then neighboring plateaus gradually connect together as K increases, and finally fc will take the typical continuous form observed in the game system with the conventional replicator. By analyzing the stability and microscopic evolution of local strategy configurations, we interpret qualitatively both the emergence and disappearance of discontinuous transitions at several critical values of r. And we also enumerate some snapshots of spatial patterns of strategy distribution to exhibit how the competitive system evolves from one dynamical behavior to another. Numerical simulations show that the system can evolve to a mixed state with cooperators and defectors coexisting in the case of r<2/3, while it can certainly end up in a pure phase only with D agents in the case of r>3/4. We further investigate the dynamics of our model by the master equation approach and then calculate the numerical computation results of fc, in perfect accord with those obtained by numerical simulations.

Suggested Citation

  • Ke, Jianhong & Li, Ping-Ping & Lin, Zhenquan, 2022. "Dissatisfaction-driven replicator dynamics of the evolutionary snowdrift game in structured populations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    • Handle: RePEc:eee:phsmap:v:587:y:2022:i:c:s0378437121007512
    DOI: 10.1016/j.physa.2021.126478
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    References listed on IDEAS

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    1. Schlag, Karl H., 1999. "Which one should I imitate?," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 493-522, May.
    2. Hu, Xiang & Liu, Xingwen, 2021. "Unfixed-neighbor-mechanism promotes cooperation in evolutionary snowdrift game on lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    3. Xu, C. & Hui, P.M. & Zheng, Da-Fang, 2007. "Networking effects on evolutionary snowdrift game in networks with fixed degrees," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 773-780.
    4. Bin Wu & Da Zhou & Feng Fu & Qingjun Luo & Long Wang & Arne Traulsen, 2010. "Evolution of Cooperation on Stochastic Dynamical Networks," PLOS ONE, Public Library of Science, vol. 5(6), pages 1-7, June.
    5. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
    6. Swami Iyer & Timothy Killingback, 2016. "Evolution of Cooperation in Social Dilemmas on Complex Networks," PLOS Computational Biology, Public Library of Science, vol. 12(2), pages 1-25, February.
    7. Helbing, Dirk, 1992. "Interrelations between stochastic equations for systems with pair interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 181(1), pages 29-52.
    8. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 1999. "Mean-field theory for scale-free random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(1), pages 173-187.
    9. Ernst Fehr & Urs Fischbacher, 2003. "The nature of human altruism," Nature, Nature, vol. 425(6960), pages 785-791, October.
    10. Y.-C. Ni & H. P. Yin & C. Xu & P. M. Hui, 2011. "Analyzing phase diagrams and phase transitions in networked competing populations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 80(2), pages 233-241, March.
    11. Christoph Hauert & Michael Doebeli, 2004. "Spatial structure often inhibits the evolution of cooperation in the snowdrift game," Nature, Nature, vol. 428(6983), pages 643-646, April.
    12. Zhu, Jiabao & Liu, Xingwen, 2021. "The number of strategy changes can be used to promote cooperation in spatial snowdrift game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 575(C).
    13. M. Sysi-Aho & J. Saramäki & J. Kertész & K. Kaski, 2005. "Spatial snowdrift game with myopic agents," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 44(1), pages 129-135, March.
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