IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v104y2017icp1-5.html
   My bibliography  Save this article

Historical payoff promotes cooperation in the prisoner's dilemma game

Author

Listed:
  • Deng, Zhenghong
  • Ma, Chunmiao
  • Mao, Xudong
  • Wang, Shenglan
  • Niu, Zhenxi
  • Gao, Li

Abstract

Understanding the evolution of cooperation among selfish individuals remains a large challenge. Network reciprocity has been proved to be an efficient way that can promote cooperation and has spawned many studies focused on network. Traditional evolutionary games on graph assumes players updating their strategies based on their current payoff, however, historical payoff may also play an indispensable role in agent's decision making processes. Another unavoidable fact in real word is that not all players can know exactly their historical payoff. Based on these considerations, in this paper, we introduce historical payoff and use a tunable parameter u to control the agent's fitness between her current payoff and historical payoff. When u equals to zero, it goes back to the traditional version; while positive u incorporates historical payoff. Besides, considering the limited knowledge of individuals, the structured population is divided into two types. Players of type A, whose proportion is v, calculate their fitness using historical and current payoff. And for players of type B, whose proportion is1−v, their fitness is merely determined by their current payoff due to the limited knowledge. Besides, the proportion of these types keeps unchanged during the simulations. Through numerous simulations, we find that historical payoff can promote cooperation. When the contribution of historical payoff to the fitness is larger, the facilitating effect becomes more striking. Moreover, the larger the proportion of players of type A, the more obvious this promoting effect seems.

Suggested Citation

  • Deng, Zhenghong & Ma, Chunmiao & Mao, Xudong & Wang, Shenglan & Niu, Zhenxi & Gao, Li, 2017. "Historical payoff promotes cooperation in the prisoner's dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 1-5.
    • Handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:1-5
    DOI: 10.1016/j.chaos.2017.07.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077917303144
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2017.07.024?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. Keke Huang & Tao Wang & Yuan Cheng & Xiaoping Zheng, 2015. "Effect of Heterogeneous Investments on the Evolution of Cooperation in Spatial Public Goods Game," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-10, March.
    2. 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.
    3. Anna Dreber & David G. Rand & Drew Fudenberg & Martin A. Nowak, 2008. "Winners don’t punish," Nature, Nature, vol. 452(7185), pages 348-351, March.
    4. Huang, Keke & Zheng, Xiaoping & Su, Yunpeng, 2015. "Effect of heterogeneous sub-populations on the evolution of cooperation," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 681-687.
    5. Azevedo, Alcino & Paxson, Dean, 2014. "Developing real option game models," European Journal of Operational Research, Elsevier, vol. 237(3), pages 909-920.
    6. Chen, Xiaojie & Fu, Feng & Wang, Long, 2008. "Promoting cooperation by local contribution under stochastic win-stay-lose-shift mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5609-5615.
    7. Imhof, Lorens & Nowak, Martin & Fudenberg, Drew, 2007. "Tit-for-Tat or Win-Stay, Lose-Shift?," Scholarly Articles 3200671, Harvard University Department of Economics.
    8. Shen, Chen & Lu, Jun & Shi, Lei, 2016. "Does coevolution setup promote cooperation in spatial prisoner's dilemma game?," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 201-207.
    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. Xu, Liang & Cao, Xianbin & Du, Wenbo & Li, Yumeng, 2018. "Effects of taxation on the evolution of cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 63-68.
    2. Takahara, Akihiro & Sakiyama, Tomoko, 2023. "Twisted strategy may enhance the evolution of cooperation in spatial prisoner’s dilemma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 629(C).

    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. Chang, Shuhua & Zhang, Zhipeng & Wu, Yu’e & Xie, Yunya, 2018. "Cooperation is enhanced by inhomogeneous inertia in spatial prisoner’s dilemma game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 419-425.
    2. Guo, Tian & Du, Chunpeng & Shi, Lei, 2024. "Evolution of cooperation on interdependent networks: The impact of asymmetric punishment," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    3. Chang, Shuhua & Wang, Xinyu & Wang, Zheng, 2016. "Modelling and computing the peaks of carbon emission with balanced growth," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 452-460.
    4. Lee, Hsuan-Wei & Cleveland, Colin & Szolnoki, Attila, 2021. "Small fraction of selective cooperators can elevate general wellbeing significantly," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    5. Deng, Zheng-Hong & Huang, Yi-Jie & Gu, Zhi-Yang & Li-Gao,, 2018. "Multigames with social punishment and the evolution of cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 164-170.
    6. Wang, Tao & Chen, Zhigang & Li, Kenli & Deng, Xiaoheng & Li, Deng, 2014. "Memory does not necessarily promote cooperation in dilemma games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 218-227.
    7. Sun, Chengbin & Luo, Chao & Li, Junqiu, 2020. "Aspiration-based co-evolution of cooperation with resource allocation on interdependent networks," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    8. 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.
    9. Liu, Jinzhuo & Meng, Haoran & Wang, Wei & Li, Tong & Yu, Yong, 2018. "Synergy punishment promotes cooperation in spatial public good game," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 214-218.
    10. Jia, Danyang & Shen, Chen & Guo, Hao & Chu, Chen & Lu, Jun & Shi, Lei, 2018. "The impact of loners’ participation willingness on cooperation in voluntary prisoner's dilemma," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 218-223.
    11. Pedro Dal Bó & Guillaume R. Fréchette, 2019. "Strategy Choice in the Infinitely Repeated Prisoner's Dilemma," American Economic Review, American Economic Association, vol. 109(11), pages 3929-3952, November.
    12. Deng, Zheng-Hong & Wang, Zi-Ren & Wang, Huan-Bo & Huang, Yijie, 2021. "Impact of informers on the evolution of cooperation in prisoner's dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).
    13. Jinzhuo Liu & Mao Peng & Yunchen Peng & Yong Li & Chen Chu & Xiaoyu Li & Qing Liu, 2021. "Effects of inequality on a spatial evolutionary public goods game," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(8), pages 1-7, August.
    14. Quan, Ji & Yang, Xiukang & Wang, Xianjia, 2018. "Spatial public goods game with continuous contributions based on Particle Swarm Optimization learning and the evolution of cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 973-983.
    15. Quan, Ji & Liu, Wei & Chu, Yuqing & Wang, Xianjia, 2018. "Stochastic dynamics and stable equilibrium of evolutionary optional public goods game in finite populations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 123-134.
    16. Chang, Shuhua & Li, Yue & Gao, Fanglu, 2016. "The impact of delaying an investment decision on R&D projects in real option game," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 182-189.
    17. Wang, Xu-Wen & Nie, Sen & Jiang, Luo-Luo & Wang, Bing-Hong & Chen, Shi-Ming, 2017. "Role of delay-based reward in the spatial cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 153-158.
    18. Elsadany, A.A., 2017. "Dynamics of a Cournot duopoly game with bounded rationality based on relative profit maximization," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 253-263.
    19. Balter, Anne G. & Huisman, Kuno J.M. & Kort, Peter M., 2022. "Effects of creative destruction on the size and timing of an investment," International Journal of Production Economics, Elsevier, vol. 252(C).
    20. Deng, Zhenghong & Wang, Shengnan & Gu, Zhiyang & Xu, Juwei & Song, Qun, 2017. "Heterogeneous preference selection promotes cooperation in spatial prisoners’ dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 20-23.

    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:chsofr:v:104:y:2017:i:c:p:1-5. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.