IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v390y2011i4p579-586.html
   My bibliography  Save this article

Quantum game interpretation for a special case of Parrondo’s paradox

Author

Listed:
  • Zhu, Yong-fei
  • Xie, Neng-gang
  • Ye, Ye
  • Peng, Fa-rui

Abstract

By using the discrete Markov chain method, Parrondo’s paradox is studied by means of theoretical analysis and computer simulation, built on the case of game AB played in alternation with modulus M=4. We find that such a case does not have a definite stationary probability distribution and that payoffs of the game depend on the parity of the initial capital. Besides, this paper reveals the phenomenon that “processing in order produces non-deterministic results, while a random process produces deterministic results”. The quantum game method is used in a further study. The results show that the explanation of the game corresponding to a stationary probability distribution is that the probability of the initial capital has reached parity.

Suggested Citation

  • Zhu, Yong-fei & Xie, Neng-gang & Ye, Ye & Peng, Fa-rui, 2011. "Quantum game interpretation for a special case of Parrondo’s paradox," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(4), pages 579-586.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:4:p:579-586
    DOI: 10.1016/j.physa.2010.10.039
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437110009180
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2010.10.039?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. N. Masuda & N. Konno, 2004. "Subcritical behavior in the alternating supercritical Domany-Kinzel dynamics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 40(3), pages 313-319, August.
    2. Flitney, A.P. & Abbott, D., 2003. "Quantum models of Parrondo's games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 152-156.
    3. Flitney, A.P. & Ng, J. & Abbott, D., 2002. "Quantum Parrondo's games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 35-42.
    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. Zhang, Cuihua & Xing, Peng, 2015. "A research on service quality decision-making of Chinese communications industry based on quantum game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 9-15.
    2. Wang, Lu & Zhu, Yong-fei & Ye, Ye & Meng, Rui & Xie, Neng-gang, 2012. "The coupling effect of the process sequence and the parity of the initial capital on Parrondo’s games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(21), pages 5197-5207.
    3. Wang, Lu & Xie, Neng-gang & Zhu, Yong-fei & Ye, Ye & Meng, Rui, 2011. "Parity effect of the initial capital based on Parrondo’s games and the quantum interpretation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4535-4542.

    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. Soo, Wayne Wah Ming & Cheong, Kang Hao, 2013. "Parrondo’s paradox and complementary Parrondo processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 17-26.
    2. 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).
    3. Cheong, Kang Hao & Soo, Wayne Wah Ming, 2013. "Construction of novel stochastic matrices for analysis of Parrondo’s paradox," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4727-4738.
    4. Wang, Lu & Xie, Neng-gang & Zhu, Yong-fei & Ye, Ye & Meng, Rui, 2011. "Parity effect of the initial capital based on Parrondo’s games and the quantum interpretation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4535-4542.
    5. Ejlali, Nasim & Pezeshk, Hamid & Chaubey, Yogendra P. & Sadeghi, Mehdi & Ebrahimi, Ali & Nowzari-Dalini, Abbas, 2020. "Parrondo’s paradox for games with three players and its potential application in combination therapy for type II diabetes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    6. Soo, Wayne Wah Ming & Cheong, Kang Hao, 2014. "Occurrence of complementary processes in Parrondo’s paradox," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 412(C), pages 180-185.
    7. Ho Fai Ma & Ka Wai Cheung & Ga Ching Lui & Degang Wu & Kwok Yip Szeto, 2019. "Effect of Information Exchange in a Social Network on Investment," Computational Economics, Springer;Society for Computational Economics, vol. 54(4), pages 1491-1503, December.
    8. Fotoohinasab, Atiyeh & Fatemizadeh, Emad & Pezeshk, Hamid & Sadeghi, Mehdi, 2018. "Denoising of genetic switches based on Parrondo’s paradox," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 410-420.
    9. Edward W. Piotrowski & Jan Sladkowski, "undated". "The Next Stage: Quantum Game Theory," Departmental Working Papers 18, University of Bialtystok, Department of Theoretical Physics.
    10. Piotrowski, Edward W. & Sładkowski, Jan, 2008. "Quantum auctions: Facts and myths," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3949-3953.
    11. Xie, Neng-gang & Chen, Yun & Ye, Ye & Xu, Gang & Wang, Lin-gang & Wang, Chao, 2011. "Theoretical analysis and numerical simulation of Parrondo’s paradox game in space," Chaos, Solitons & Fractals, Elsevier, vol. 44(6), pages 401-414.
    12. Edward W. Piotrowski & Jan Sladkowski, "undated". "Quantum Games and Programmable Quantum Systems," Departmental Working Papers 22, University of Bialtystok, Department of Theoretical Physics.
    13. Edward W. Piotrowski & Jan Sladkowski, "undated". "An Invitation to Quantum Game Theory," Departmental Working Papers 15, University of Bialtystok, Department of Theoretical Physics.
    14. Breuer, Sandro & Mielke, Andreas, 2023. "Multi player Parrondo games with rigid coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).
    15. Ye, Ye & Zhang, Xin-shi & Liu, Lin & Xie, Neng-Gang, 2021. "Effects of group interactions on the network Parrondo’s games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    16. Wang, Lu & Zhu, Yong-fei & Ye, Ye & Meng, Rui & Xie, Neng-gang, 2012. "The coupling effect of the process sequence and the parity of the initial capital on Parrondo’s games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(21), pages 5197-5207.

    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:phsmap:v:390:y:2011:i:4:p:579-586. 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: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.