IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v259y2015icp552-568.html
   My bibliography  Save this article

Spatial reciprocity for discrete, continuous and mixed strategy setups

Author

Listed:
  • Kokubo, Satoshi
  • Wang, Zhen
  • Tanimoto, Jun

Abstract

The existence of cooperation in the social dilemma has been extensively studied based on spatial structure populations, namely, the so-called spatial reciprocity. However, vast majority of existing works just simply presume that agents can offer the discrete choice: either the cooperative (C) or defective (D) strategy, which, to some extent, seems unrealistic in the empirical observations since actual options might be continuous, mixed rather than discrete. Here, we propose discrete, continuous and mixed strategy setups in the social dilemma games and further explore their performance on network populations. Interestingly, it is unveiled that there is actually considerable inconsistency in terms of equilibrium among different strategy games. Furthermore, we reveal how different cooperative arrangements among these three strategy setups can be established, depending on whether the presumed dilemma subclass is a boundary game between prisoner’s dilemma game and Chicken game or between prisoner’s dilemma game and Stag-Hunt game.

Suggested Citation

  • Kokubo, Satoshi & Wang, Zhen & Tanimoto, Jun, 2015. "Spatial reciprocity for discrete, continuous and mixed strategy setups," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 552-568.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:552-568
    DOI: 10.1016/j.amc.2015.03.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315003124
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.03.018?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. A. Szolnoki & M. Perc & G. Szabó, 2008. "Diversity of reproduction rate supports cooperation in the prisoner's dilemma game on complex networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 61(4), pages 505-509, February.
    3. 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.
    4. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, December.
    5. 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.
    6. 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.
    7. Tanimoto, Jun & Nakata, Makoto & Hagishima, Aya & Ikegaya, Naoki, 2012. "Spatially correlated heterogeneous aspirations to enhance network reciprocity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 680-685.
    8. repec:hhs:iuiwop:487 is not listed on IDEAS
    9. Gilbert Roberts & Thomas N. Sherratt, 1998. "Development of cooperative relationships through increasing investment," Nature, Nature, vol. 394(6689), pages 175-179, July.
    10. Shijun Wang & Máté S Szalay & Changshui Zhang & Peter Csermely, 2008. "Learning and Innovative Elements of Strategy Adoption Rules Expand Cooperative Network Topologies," PLOS ONE, Public Library of Science, vol. 3(4), pages 1-9, April.
    11. Cheng-Yi Xia & Sandro Meloni & Yamir Moreno, 2012. "Effects Of Environment Knowledge On Agglomeration And Cooperation In Spatial Public Goods Games," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 15(supp0), pages 1-17.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Askar, S.S., 2021. "On complex dynamics of Cournot-Bertrand game with asymmetric market information," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    2. Hu, Xiang & Liu, Xingwen & Zhou, Xiaobing, 2022. "A proportional-neighborhood-diversity evolution in snowdrift game on square lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    3. Alam, Muntasir & Nagashima, Keisuke & Tanimoto, Jun, 2018. "Various error settings bring different noise-driven effects on network reciprocity in spatial prisoner's dilemma," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 338-346.
    4. Wang, Xianjia & Lv, Shaojie, 2019. "The roles of particle swarm intelligence in the prisoner’s dilemma based on continuous and mixed strategy systems on scale-free networks," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 213-220.
    5. Askar, S.S. & Alnowibet, K., 2016. "Cooperation versus noncooperation: Cournot duopolistic game based on delay and time-dependent parameters," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 580-584.
    6. Yu, Xiaohui & He, Mingke & Sun, Hongxia & Zhou, Zhen, 2020. "Uncertain coalition structure game with payoff of belief structure," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    7. Lv, Shaojie & Wang, Xianjia, 2020. "The impact of heterogeneous investments on the evolution of cooperation in public goods game with exclusion," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    8. Tanimoto, Jun, 2017. "How does resolution of strategy affect network reciprocity in spatial prisoner's dilemma games?," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 36-42.
    9. Ye, Wenxing & Fan, Suohai, 2020. "Evolutionary traveler’s dilemma game based on particle swarm optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    10. Li, Cong & Xu, Hedong & Fan, Suohai, 2020. "Synergistic effects of self-optimization and imitation rules on the evolution of cooperation in the investor sharing game," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    11. Welburn, Jonathan W. & Hausken, Kjell, 2015. "A game theoretic model of economic crises," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 738-762.
    12. 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.
    13. 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.
    14. Shu, Gang & Du, Xia & Li, Ya, 2016. "Surrounding information consideration promotes cooperation in Prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 689-694.
    15. Tanimoto, Jun, 2017. "Coevolution of discrete, mixed, and continuous strategy systems boosts in the spatial prisoner's dilemma and chicken games," Applied Mathematics and Computation, Elsevier, vol. 304(C), pages 20-27.
    16. Askar, S.S., 2022. "On the dynamics of Cournot duopoly game with private firms: Investigations and analysis," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    17. Wang, Yadong & Wang, Delu & Shi, Xunpeng, 2021. "Exploring the dilemma of overcapacity governance in China's coal industry: A tripartite evolutionary game model," Resources Policy, Elsevier, vol. 71(C).
    18. Askar, S.S. & Alshamrani, Ahmad M. & Alnowibet, K., 2016. "The arising of cooperation in Cournot duopoly games," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 535-542.
    19. Ahsan Habib, Md. & Tanaka, Masaki & Tanimoto, Jun, 2020. "How does conformity promote the enhancement of cooperation in the network reciprocity in spatial prisoner's dilemma games?," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    20. Zheng, Liping & Xu, Hedong & Tian, Cunzhi & Fan, Suohai, 2021. "Evolutionary dynamics of information in the market: Transmission and trust," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    21. Shu, Feng & Liu, Xingwen & Fang, Kai & Chen, Hao, 2018. "Memory-based snowdrift game on a square lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 15-26.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Yanlong Zhang, 2015. "Partially and Wholly Overlapping Networks: The Evolutionary Dynamics of Social Dilemmas on Social Networks," Computational Economics, Springer;Society for Computational Economics, vol. 46(1), pages 1-14, June.
    3. Liang, Rizhou & Zhang, Jiqiang & Zheng, Guozhong & Chen, Li, 2021. "Social hierarchy promotes the cooperation prevalence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    4. Huang, Shasha & Luo, Dang, 2015. "Impact of separation of interaction and replacement neighborhoods on spatial reciprocity," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 318-323.
    5. Zhang, Jun & Hu, Bin & Huang, Yi Jie & Deng, Zheng Hong & Wu, Tao, 2020. "The evolution of cooperation affected by aspiration-driven updating rule in multi-games with voluntary participation," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    6. Du, Faqi & Fu, Feng, 2013. "Quantifying the impact of noise on macroscopic organization of cooperation in spatial games," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 35-44.
    7. Li, Yan & Ye, Hang, 2015. "Effect of migration based on strategy and cost on the evolution of cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 156-165.
    8. Jorge Peña & Yannick Rochat, 2012. "Bipartite Graphs as Models of Population Structures in Evolutionary Multiplayer Games," PLOS ONE, Public Library of Science, vol. 7(9), pages 1-13, September.
    9. Lv, Shaojie & Wang, Xianjia, 2020. "The impact of heterogeneous investments on the evolution of cooperation in public goods game with exclusion," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    10. Deng, Zheng-Hong & Huang, Yi-Jie & Gu, Zhi-Yang & Liu, Dan & Gao, Li, 2018. "Multi-games on interdependent networks and the evolution of cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 83-90.
    11. Rong-Hua Li & Jeffrey Xu Yu & Jiyuan Lin, 2013. "Evolution of Cooperation in Spatial Traveler's Dilemma Game," PLOS ONE, Public Library of Science, vol. 8(3), pages 1-11, March.
    12. Yu, Fengyuan & Wang, Jianwei & He, Jialu, 2022. "Inequal dependence on members stabilizes cooperation in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    13. Wang, Zhen & Chen, Tong & Wang, Yongjie, 2017. "Leadership by example promotes the emergence of cooperation in public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 100-105.
    14. 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.
    15. Flávio L Pinheiro & Jorge M Pacheco & Francisco C Santos, 2012. "From Local to Global Dilemmas in Social Networks," PLOS ONE, Public Library of Science, vol. 7(2), pages 1-6, February.
    16. Ye, Ye & Hang, Xiao Rong & Koh, Jin Ming & Miszczak, Jarosław Adam & Cheong, Kang Hao & Xie, Neng-gang, 2020. "Passive network evolution promotes group welfare in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    17. Deng, Zheng-Hong & Huang, Yi-Jie & Gu, Zhi-Yang & Liu, Dan & Gao, Li, 2018. "Multigames with voluntary participation on interdependent networks and the evolution of cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 151-157.
    18. Matjaž Perc & Zhen Wang, 2010. "Heterogeneous Aspirations Promote Cooperation in the Prisoner's Dilemma Game," PLOS ONE, Public Library of Science, vol. 5(12), pages 1-8, December.
    19. Li, Pei & Duan, Haibin, 2015. "Evolution of cooperation driven by incremental learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 14-22.
    20. Wes Maciejewski & Feng Fu & Christoph Hauert, 2014. "Evolutionary Game Dynamics in Populations with Heterogenous Structures," PLOS Computational Biology, Public Library of Science, vol. 10(4), pages 1-16, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:552-568. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.