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Spatial snowdrift game with myopic agents

Author

Listed:
  • M. Sysi-Aho

  • J. Saramäki
  • J. Kertész
  • K. Kaski

Abstract

We have studied a spatially extended snowdrift game, in which the players are located on the sites of two-dimensional square lattices and repeatedly have to choose one of the two strategies, either cooperation (C) or defection (D). A player interacts with its nearest neighbors only, and aims at playing a strategy which maximizes its instant pay-off, assuming that the neighboring agents retain their strategies. If a player is not content with its current strategy, it will change it to the opposite one with probability p next round. Here we show through simulations and analytical approach that these rules result in cooperation levels, which differ to large extent from those obtained using the replicator dynamics. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005

Suggested Citation

  • 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.
    • Handle: RePEc:spr:eurphb:v:44:y:2005:i:1:p:129-135
    DOI: 10.1140/epjb/e2005-00108-5
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    References listed on IDEAS

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    Cited by:

    1. Xiaoyu Li & Le Cheng & Xiaotong Niu & Siying Li & Chen Liu & Peican Zhu, 2021. "Highly cooperative individuals’ clustering property in myopic strategy groups," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(6), pages 1-7, June.
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    4. Lee, Hsuan-Wei & Cleveland, Colin & Szolnoki, Attila, 2023. "Restoring spatial cooperation with myopic agents in a three-strategy social dilemma," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    5. Mobin Zarreh & Paul T. Grogan, 2025. "Strategic Engineering Design in Water Infrastructure: A Game-Theoretic Approach and Network Topology for Flood Irrigation Systems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 39(13), pages 7263-7281, October.
    6. Szabó, György & Hódsági, Kristóf, 2016. "The role of mixed strategies in spatial evolutionary games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 198-206.
    7. Mathew, Ann Mary & Sasidevan, V., 2025. "Modeling competition for space: Emergent inefficiency and inequality due to spatial self-organization among a group of crowd-avoiding agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 660(C).
    8. Zhong, Shiquan & Jia, Ning & Ma, Shoufeng, 2014. "Iterated snowdrift game among mobile agents with myopic expected-reward based decision rule: Numerical and analytical research," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 6-18.
    9. Kohei Miyaji & Jun Tanimoto & Zhen Wang & Aya Hagishima & Naoki Ikegaya, 2013. "Direct Reciprocity in Spatial Populations Enhances R -Reciprocity As Well As ST -Reciprocity," PLOS ONE, Public Library of Science, vol. 8(8), pages 1-8, August.
    10. Xia, Chengyi & Miao, Qin & Zhang, Juanjuan, 2013. "Impact of neighborhood separation on the spatial reciprocity in the prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 51(C), pages 22-30.
    11. 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).
    12. Zhang, Liming & Huang, Changwei & Li, Haihong & Dai, Qionglin & Yang, Junzhong, 2021. "Cooperation guided by imitation, aspiration and conformity-driven dynamics in evolutionary games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    13. Xia, Chengyi & Wang, Juan & Wang, Li & Sun, Shiwen & Sun, Junqing & Wang, Jinsong, 2012. "Role of update dynamics in the collective cooperation on the spatial snowdrift games: Beyond unconditional imitation and replicator dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1239-1245.
    14. Cheng-Yi Xia & Xiao-Kun Meng & Zhen Wang, 2015. "Heterogeneous Coupling between Interdependent Lattices Promotes the Cooperation in the Prisoner’s Dilemma Game," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-13, June.
    15. Wang, Zhen & Wu, Bin & Li, Ya-peng & Gao, Hang-xian & Li, Ming-chu, 2013. "Does coveting the performance of neighbors of thy neighbor enhance spatial reciprocity?," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 28-34.
    16. Sanz Nogales, Jose M. & Zazo, S., 2020. "Replicator based on imitation for finite and arbitrary networked communities," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    17. Su, Qi & Li, Aming & Wang, Long, 2017. "Spatial structure favors cooperative behavior in the snowdrift game with multiple interactive dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 299-306.
    18. Ye, Wenxing & Fan, Suohai, 2017. "Evolutionary snowdrift game with rational selection based on radical evaluation," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 310-317.
    19. Jin, Jiahua & Shen, Chen & Chu, Chen & Shi, Lei, 2017. "Incorporating dominant environment into individual fitness promotes cooperation in the spatial prisoners' dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 70-75.
    20. Zhang, Lan & Huang, Changwei, 2023. "Preferential selection to promote cooperation on degree–degree correlation networks in spatial snowdrift games," Applied Mathematics and Computation, Elsevier, vol. 454(C).
    21. Shi, Juan & Liu, Xucheng & Li, Jiqin & Shu, Youqi & Wang, Zhen & Liu, Jinzhuo, 2023. "The role of Far-Sighted agents on the evolution of cooperation in social dilemma," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    22. Chen, Mei-huan & Wang, Li & Wang, Juan & Sun, Shi-wen & Xia, Cheng-yi, 2015. "Impact of individual response strategy on the spatial public goods game within mobile agents," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 192-202.
    23. Jin, Jiahua & Chu, Chen & Shen, Chen & Guo, Hao & Geng, Yini & Jia, Danyang & Shi, Lei, 2018. "Heterogeneous fitness promotes cooperation in the spatial prisoner's dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 141-146.

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