IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0081855.html
   My bibliography  Save this article

Direct Sum Matrix Game with Prisoner's Dilemma and Snowdrift Game

Author

Listed:
  • Chengzhang Ma
  • Wei Cao
  • Wangheng Liu
  • Rong Gui
  • Ya Jia

Abstract

A direct sum form is proposed for constructing a composite game from two games, prisoner's dilemma and snowdrift game. This kind of direct sum form game is called a multiple roles game. The replicator dynamics of the multiple roles game with will-mixed populations is explored. The dynamical behaviors on square lattice are investigated by numerical simulation. It is found that the dynamical behaviors of population on square lattice depend on the mixing proportion of the two simple games. Mixing SD activities to pure PD population inhibits the proportion of cooperators in PD, and mixing PD activities to pure SD population stimulates the proportion of cooperators in SD. Besides spatial reciprocity, our results show that there are roles reciprocities between different types of individuals.

Suggested Citation

  • Chengzhang Ma & Wei Cao & Wangheng Liu & Rong Gui & Ya Jia, 2013. "Direct Sum Matrix Game with Prisoner's Dilemma and Snowdrift Game," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-7, December.
    • Handle: RePEc:plo:pone00:0081855
    DOI: 10.1371/journal.pone.0081855
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0081855
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0081855&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0081855?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
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Martin A. Nowak & Karl Sigmund, 1998. "Evolution of indirect reciprocity by image scoring," Nature, Nature, vol. 393(6685), pages 573-577, June.
    4. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
    5. M.A. Nowak & K. Sigmund, 1998. "Evolution of Indirect Reciprocity by Image Scoring/ The Dynamics of Indirect Reciprocity," Working Papers ir98040, International Institute for Applied Systems Analysis.
    6. Helbing, Dirk, 1992. "Interrelations between stochastic equations for systems with pair interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 181(1), pages 29-52.
    7. Martin A. Nowak & Karl Sigmund, 2005. "Evolution of indirect reciprocity," Nature, Nature, vol. 437(7063), pages 1291-1298, October.
    8. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
    9. 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.
    10. Xiaojie Chen & Yongkui Liu & Yonghui Zhou & Long Wang & Matjaž Perc, 2012. "Adaptive and Bounded Investment Returns Promote Cooperation in Spatial Public Goods Games," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-8, May.
    11. Arnon Lotem & Michael A. Fishman & Lewi Stone, 1999. "Evolution of cooperation between individuals," Nature, Nature, vol. 400(6741), pages 226-227, July.
    12. 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.
    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. Zhong, Li-Xin & Xu, Wen-Juan & He, Yun-Xin & Zhong, Chen-Yang & Chen, Rong-Da & Qiu, Tian & Shi, Yong-Dong & Ren, Fei, 2017. "A generalized public goods game with coupling of individual ability and project benefit," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 73-80.

    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. 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.
    2. Swami Iyer & Timothy Killingback, 2020. "Evolution of Cooperation in Social Dilemmas with Assortative Interactions," Games, MDPI, vol. 11(4), pages 1-31, September.
    3. Isamu Okada, 2020. "A Review of Theoretical Studies on Indirect Reciprocity," Games, MDPI, vol. 11(3), pages 1-17, July.
    4. Bandyopadhyay, Abhirup & Kar, Samarjit, 2018. "Coevolution of cooperation and network structure in social dilemmas in evolutionary dynamic complex network," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 710-730.
    5. Cao, Lixuan & Wu, Bin, 2021. "Eco-evolutionary dynamics with payoff-dependent environmental feedback," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    6. Yao Meng & Sean P. Cornelius & Yang-Yu Liu & Aming Li, 2024. "Dynamics of collective cooperation under personalised strategy updates," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    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. Hu, Menglong & Wang, Juan & Kong, Lingcong & An, Kang & Bi, Tao & Guo, Baohong & Dong, Enzeng, 2015. "Incorporating the information from direct and indirect neighbors into fitness evaluation enhances the cooperation in the social dilemmas," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 47-52.
    9. Quan, Ji & Zhou, Yawen & Wang, Xianjia & Yang, Jian-Bo, 2020. "Information fusion based on reputation and payoff promotes cooperation in spatial public goods game," Applied Mathematics and Computation, Elsevier, vol. 368(C).
    10. Jiang, Zhi-Qiang & Wang, Peng & Ma, Jun-Chao & Zhu, Peican & Han, Zhen & Podobnik, Boris & Stanley, H. Eugene & Zhou, Wei-Xing & Alfaro-Bittner, Karin & Boccaletti, Stefano, 2023. "Unraveling the effects of network, direct and indirect reciprocity in online societies," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    11. Tatsuya Sasaki & Hitoshi Yamamoto & Isamu Okada & Satoshi Uchida, 2017. "The Evolution of Reputation-Based Cooperation in Regular Networks," Games, MDPI, vol. 8(1), pages 1-16, January.
    12. Fabio Della Rossa & Fabio Dercole & Anna Di Meglio, 2020. "Direct Reciprocity and Model-Predictive Strategy Update Explain the Network Reciprocity Observed in Socioeconomic Networks," Games, MDPI, vol. 11(1), pages 1-28, March.
    13. Wang, Yi-Ling, 2013. "Asymmetric evaluation of fitness enhances spatial reciprocity in social dilemmas," Chaos, Solitons & Fractals, Elsevier, vol. 54(C), pages 76-81.
    14. Chen, Wei & Wu, Te & Li, Zhiwu & Wang, Long, 2016. "Friendship-based partner switching promotes cooperation in heterogeneous populations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 192-199.
    15. Mike Farjam & Wladislaw Mill & Marian Panganiban, 2016. "Ignorance Is Bliss, But for Whom? The Persistent Effect of Good Will on Cooperation," Games, MDPI, vol. 7(4), pages 1-19, October.
    16. Song, Sha & Pan, Qiuhui & Zhu, Wenqiang & He, Mingfeng, 2023. "Evolution of cooperation in games with dual attribute strategy," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    17. Heller, Yuval & Mohlin, Erik, 2018. "Social learning and the shadow of the past," Journal of Economic Theory, Elsevier, vol. 177(C), pages 426-460.
    18. Guan, Kaixuan & Chen, Yuyou & Zheng, Wanjun & Zeng, Lulu & Ye, Hang, 2022. "Costly signals can facilitate cooperation and punishment in the prisoner’s dilemma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    19. 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.
    20. Berger, Ulrich, 2011. "Learning to cooperate via indirect reciprocity," Games and Economic Behavior, Elsevier, vol. 72(1), pages 30-37, May.

    More about this item

    Statistics

    Access and download statistics

    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:plo:pone00:0081855. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.