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Win-Stay-Lose-Learn Promotes Cooperation in the Spatial Prisoner's Dilemma Game

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  • Yongkui Liu
  • Xiaojie Chen
  • Lin Zhang
  • Long Wang
  • Matjaž Perc

Abstract

Holding on to one's strategy is natural and common if the later warrants success and satisfaction. This goes against widespread simulation practices of evolutionary games, where players frequently consider changing their strategy even though their payoffs may be marginally different than those of the other players. Inspired by this observation, we introduce an aspiration-based win-stay-lose-learn strategy updating rule into the spatial prisoner's dilemma game. The rule is simple and intuitive, foreseeing strategy changes only by dissatisfied players, who then attempt to adopt the strategy of one of their nearest neighbors, while the strategies of satisfied players are not subject to change. We find that the proposed win-stay-lose-learn rule promotes the evolution of cooperation, and it does so very robustly and independently of the initial conditions. In fact, we show that even a minute initial fraction of cooperators may be sufficient to eventually secure a highly cooperative final state. In addition to extensive simulation results that support our conclusions, we also present results obtained by means of the pair approximation of the studied game. Our findings continue the success story of related win-stay strategy updating rules, and by doing so reveal new ways of resolving the prisoner's dilemma.

Suggested Citation

  • Yongkui Liu & Xiaojie Chen & Lin Zhang & Long Wang & Matjaž Perc, 2012. "Win-Stay-Lose-Learn Promotes Cooperation in the Spatial Prisoner's Dilemma Game," PLOS ONE, Public Library of Science, vol. 7(2), pages 1-8, February.
    • Handle: RePEc:plo:pone00:0030689
    DOI: 10.1371/journal.pone.0030689
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    References listed on IDEAS

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    1. Hu, Mao-Bin & Jiang, Rui & Wu, Qing-Song & Wu, Yong-Hong, 2007. "Simulating the wealth distribution with a Richest-Following strategy on scale-free network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 467-472.
    2. Imhof, Lorens & Nowak, Martin & Fudenberg, Drew, 2007. "Tit-for-Tat or Win-Stay, Lose-Shift?," Scholarly Articles 3200671, Harvard University Department of Economics.
    3. Francisco C. Santos & Marta D. Santos & Jorge M. Pacheco, 2008. "Social diversity promotes the emergence of cooperation in public goods games," Nature, Nature, vol. 454(7201), pages 213-216, July.
    4. Cho, In-Koo & Matsui, Akihiko, 2005. "Learning aspiration in repeated games," Journal of Economic Theory, Elsevier, vol. 124(2), pages 171-201, October.
    5. Sergi Lozano & Alex Arenas & Angel Sánchez, 2008. "Mesoscopic Structure Conditions the Emergence of Cooperation on Social Networks," PLOS ONE, Public Library of Science, vol. 3(4), pages 1-9, April.
    6. Zhang, Haifeng & Small, Michael & Yang, Hanxin & Wang, Binghong, 2010. "Adjusting learning motivation to promote cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4734-4739.
    7. Szolnoki, Attila & Perc, Matjaž & Danku, Zsuzsa, 2008. "Towards effective payoffs in the prisoner’s dilemma game on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2075-2082.
    8. Marco Tomassini & Enea Pestelacci & Leslie Luthi, 2007. "Social Dilemmas And Cooperation In Complex Networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1173-1185.
    9. Jorge M Pacheco & Flávio L Pinheiro & Francisco C Santos, 2009. "Population Structure Induces a Symmetry Breaking Favoring the Emergence of Cooperation," PLOS Computational Biology, Public Library of Science, vol. 5(12), pages 1-7, December.
    10. 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.
    11. Jelena Grujić & Constanza Fosco & Lourdes Araujo & José A Cuesta & Angel Sánchez, 2010. "Social Experiments in the Mesoscale: Humans Playing a Spatial Prisoner's Dilemma," PLOS ONE, Public Library of Science, vol. 5(11), pages 1-9, November.
    12. Zhang, Jun & Fang, Yi-Ping & Du, Wen-Bo & Cao, Xian-Bin, 2011. "Promotion of cooperation in aspiration-based spatial prisoner’s dilemma game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2258-2266.
    13. Wu, Zhi-Xi & Guan, Jian-Yue & Xu, Xin-Jian & Wang, Ying-Hai, 2007. "Evolutionary prisoner's dilemma game on Barabási–Albert scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 672-680.
    14. M. Droz & J. Szwabiński & G. Szabó, 2009. "Motion of influential players can support cooperation in Prisoner’s Dilemma," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 71(4), pages 579-585, October.
    15. Julia Poncela & Jesús Gómez-Gardeñes & Luis M Floría & Angel Sánchez & Yamir Moreno, 2008. "Complex Cooperative Networks from Evolutionary Preferential Attachment," PLOS ONE, Public Library of Science, vol. 3(6), pages 1-6, June.
    16. Liu, Yongkui & Li, Zhi & Chen, Xiaojie & Wang, Long, 2010. "Memory-based prisoner’s dilemma on square lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(12), pages 2390-2396.
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