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Evolutionary multiplayer games on graphs with edge diversity

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  • Qi Su
  • Lei Zhou
  • Long Wang

Abstract

Evolutionary game dynamics in structured populations has been extensively explored in past decades. However, most previous studies assume that payoffs of individuals are fully determined by the strategic behaviors of interacting parties, and social ties between them only serve as the indicator of the existence of interactions. This assumption neglects important information carried by inter-personal social ties such as genetic similarity, geographic proximity, and social closeness, which may crucially affect the outcome of interactions. To model these situations, we present a framework of evolutionary multiplayer games on graphs with edge diversity, where different types of edges describe diverse social ties. Strategic behaviors together with social ties determine the resulting payoffs of interactants. Under weak selection, we provide a general formula to predict the success of one behavior over the other. We apply this formula to various examples which cannot be dealt with using previous models, including the division of labor and relationship- or edge-dependent games. We find that labor division can promote collective cooperation markedly. The evolutionary process based on relationship-dependent games can be approximated by interactions under a transformed and unified game. Our work stresses the importance of social ties and provides effective methods to reduce the calculating complexity in analyzing the evolution of realistic systems.Author summary: The outcome of an interaction often relies on not only interactants’ strategic behaviors but also genetic and physical relationships between interactants, such as genetic similarity and geographic proximity. Thus when encountering different opponents who use the same strategy, an individual may derive different payoffs. Social ties, acting as carriers of such information, are crucial to biological interactions. However, most prior studies simplify social ties as binary states (i.e., either present or absent) and ignore the information carried. Here we study evolutionary multiplayer games on graphs and introduce different types of edges to describe diverse social ties. We derive a simple rule to predict when a strategic behavior is more successful than the other. Based on this rule, we find that the labor division in eusocial insects could promote prosocial behavior. In addition, when payoff structures in different interactions are relationship-dependent, the condition for the success of one behavior can be obtained by studying interactions described by a unified payoff structure. Our work not only extends established results on the evolution of cooperation on graphs, but also shows the possibility to simplify complex and diverse interactions in real-world systems as simple and unified interactions in theoretical calculations.

Suggested Citation

  • Qi Su & Lei Zhou & Long Wang, 2019. "Evolutionary multiplayer games on graphs with edge diversity," PLOS Computational Biology, Public Library of Science, vol. 15(4), pages 1-22, April.
    • Handle: RePEc:plo:pcbi00:1006947
    DOI: 10.1371/journal.pcbi.1006947
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    as
    1. Ashleigh S. Griffin & Stuart A. West & Angus Buckling, 2004. "Cooperation and competition in pathogenic bacteria," Nature, Nature, vol. 430(7003), pages 1024-1027, August.
    2. 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.
    3. Alex McAvoy & Christoph Hauert, 2015. "Asymmetric Evolutionary Games," PLOS Computational Biology, Public Library of Science, vol. 11(8), pages 1-26, August.
    4. Ádám Kun & Ulf Dieckmann, 2013. "Resource heterogeneity can facilitate cooperation," Nature Communications, Nature, vol. 4(1), pages 1-8, December.
    5. Wu, Te & Fu, Feng & Dou, Puxuan & Wang, Long, 2014. "Social influence promotes cooperation in the public goods game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 86-93.
    6. Bin Wu & Arne Traulsen & Chaitanya S. Gokhale, 2013. "Dynamic Properties of Evolutionary Multi-player Games in Finite Populations," Games, MDPI, vol. 4(2), pages 1-18, May.
    7. Hisashi Ohtsuki & Christoph Hauert & Erez Lieberman & Martin A. Nowak, 2006. "A simple rule for the evolution of cooperation on graphs and social networks," Nature, Nature, vol. 441(7092), pages 502-505, May.
    8. Charles G Nathanson & Corina E Tarnita & Martin A Nowak, 2009. "Calculating Evolutionary Dynamics in Structured Populations," PLOS Computational Biology, Public Library of Science, vol. 5(12), pages 1-7, December.
    9. Martin A. Nowak & Akira Sasaki & Christine Taylor & Drew Fudenberg, 2004. "Emergence of cooperation and evolutionary stability in finite populations," Nature, Nature, vol. 428(6983), pages 646-650, April.
    10. Benjamin Allen & Gabor Lippner & Yu-Ting Chen & Babak Fotouhi & Naghmeh Momeni & Shing-Tung Yau & Martin A. Nowak, 2017. "Evolutionary dynamics on any population structure," Nature, Nature, vol. 544(7649), pages 227-230, April.
    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. Paul B. Rainey & Katrina Rainey, 2003. "Evolution of cooperation and conflict in experimental bacterial populations," Nature, Nature, vol. 425(6953), pages 72-74, September.
    13. Jeff Gore & Hyun Youk & Alexander van Oudenaarden, 2009. "Snowdrift game dynamics and facultative cheating in yeast," Nature, Nature, vol. 459(7244), pages 253-256, May.
    14. Peter D. Taylor & Troy Day & Geoff Wild, 2007. "Evolution of cooperation in a finite homogeneous graph," Nature, Nature, vol. 447(7143), pages 469-472, May.
    15. Jorge Peña & Bin Wu & Jordi Arranz & Arne Traulsen, 2016. "Evolutionary Games of Multiplayer Cooperation on Graphs," PLOS Computational Biology, Public Library of Science, vol. 12(8), pages 1-15, August.
    16. F. Débarre & C. Hauert & M. Doebeli, 2014. "Social evolution in structured populations," Nature Communications, Nature, vol. 5(1), pages 1-7, May.
    17. Bin Wu & Lei Zhou, 2018. "Individualised aspiration dynamics: Calculation by proofs," PLOS Computational Biology, Public Library of Science, vol. 14(9), pages 1-15, September.
    18. Ross Cressman & Andrea Gaunersdorfer & Jean-François Wen, 2000. "Evolutionary And Dynamic Stability In Symmetric Evolutionary Games With Two Independent Decisions," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 2(01), pages 67-81.
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    Cited by:

    1. M. Kleshnina & K. Kaveh & K. Chatterjee, 2020. "The role of behavioural plasticity in finite vs infinite populations," Papers 2009.13160, arXiv.org.
    2. Han, Xu & Zhao, Xiaowei & Xia, Haoxiang, 2022. "Hybrid learning promotes cooperation in the spatial prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Li, Bin-Quan & Wu, Zhi-Xi & Guan, Jian-Yue, 2022. "Critical thresholds of benefit distribution in an extended snowdrift game model," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    4. Li, Xiaopeng & Hao, Gang & Zhang, Zhipeng & Xia, Chengyi, 2021. "Evolution of cooperation in heterogeneously stochastic interactions," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    5. Liu, Yandi & Wang, Hexin & Ding, Yi & Yang, Xuan & Dai, Yu, 2022. "Can weak diversity help in propagating cooperation? Invasion of cooperators at the conformity-conflict boundary," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    6. Zhong, Xiaowen & Fan, Ying & Di, Zengru, 2021. "The evolution of cooperation in public goods games on signed networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    7. Maria Kleshnina & Christian Hilbe & Štěpán Šimsa & Krishnendu Chatterjee & Martin A. Nowak, 2023. "The effect of environmental information on evolution of cooperation in stochastic games," Nature Communications, Nature, vol. 14(1), pages 1-11, December.
    8. Zhu, Xiaochen, 2023. "The dynamic edge environment under interactive diversity is a double-edged sword," Applied Mathematics and Computation, Elsevier, vol. 436(C).

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