IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0029015.html
   My bibliography  Save this article

Analysis of Two-Player Quantum Games in an EPR Setting Using Clifford's Geometric Algebra

Author

Listed:
  • James M Chappell
  • Azhar Iqbal
  • Derek Abbott

Abstract

The framework for playing quantum games in an Einstein-Podolsky-Rosen (EPR) type setting is investigated using the mathematical formalism of geometric algebra (GA). The main advantage of this framework is that the players' strategy sets remain identical to the ones in the classical mixed-strategy version of the game, and hence the quantum game becomes a proper extension of the classical game, avoiding a criticism of other quantum game frameworks. We produce a general solution for two-player games, and as examples, we analyze the games of Prisoners' Dilemma and Stag Hunt in the EPR setting. The use of GA allows a quantum-mechanical analysis without the use of complex numbers or the Dirac Bra-ket notation, and hence is more accessible to the non-physicist.

Suggested Citation

  • James M Chappell & Azhar Iqbal & Derek Abbott, 2012. "Analysis of Two-Player Quantum Games in an EPR Setting Using Clifford's Geometric Algebra," PLOS ONE, Public Library of Science, vol. 7(1), pages 1-8, January.
    • Handle: RePEc:plo:pone00:0029015
    DOI: 10.1371/journal.pone.0029015
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0029015
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0029015&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0029015?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. Piotrowski, E.W & Sładkowski, J, 2002. "Quantum market games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(1), pages 208-216.
    2. James M Chappell & Azhar Iqbal & Derek Abbott, 2011. "Analyzing Three-Player Quantum Games in an EPR Type Setup," PLOS ONE, Public Library of Science, vol. 6(7), pages 1-11, July.
    3. Binmore, Ken, 2007. "Game Theory: A Very Short Introduction," OUP Catalogue, Oxford University Press, number 9780199218462.
    4. Edward W. Piotrowski & Jan Sladkowski, "undated". "An Invitation to Quantum Game Theory," Departmental Working Papers 15, University of Bialtystok, Department of Theoretical Physics.
    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. James M Chappell & Azhar Iqbal & Derek Abbott, 2012. "N-Player Quantum Games in an EPR Setting," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-9, May.
    2. Iqbal, Azhar & Chappell, James M. & Abbott, Derek, 2015. "Social optimality in quantum Bayesian games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 798-805.

    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. Iqbal, Azhar & Chappell, James M. & Abbott, Derek, 2015. "Social optimality in quantum Bayesian games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 798-805.
    2. Emmanuel Haven, 2008. "Private Information and the ‘Information Function’: A Survey of Possible Uses," Theory and Decision, Springer, vol. 64(2), pages 193-228, March.
    3. Katarzyna Miakisz & Edward W. Piotrowski & Jan Sladkowski, "undated". "Quantization of Games: Towards Quantum Artificial Intelligence," Departmental Working Papers 21, University of Bialtystok, Department of Theoretical Physics.
    4. Edward W. Piotrowski, "undated". "Quantum Mind. A sketch (in Polish)," Departmental Working Papers 120pl, University of Bialtystok, Department of Theoretical Physics.
    5. 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.
    6. Edward W. Piotrowski & Jan Sladkowski, "undated". "Quantum Games and Programmable Quantum Systems," Departmental Working Papers 22, University of Bialtystok, Department of Theoretical Physics.
    7. F. Bagarello & E. Haven, 2014. "Towards a formalization of a two traders market with information exchange," Papers 1412.8725, arXiv.org.
    8. James M Chappell & Azhar Iqbal & Derek Abbott, 2012. "N-Player Quantum Games in an EPR Setting," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-9, May.
    9. Luca Lambertini, 2013. "John von Neumann between Physics and Economics: A methodological note," Review of Economic Analysis, Digital Initiatives at the University of Waterloo Library, vol. 5(2), pages 177-189, December.
    10. Arfi, Badredine, 2007. "Quantum social game theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 794-820.
    11. repec:cup:judgdm:v:8:y:2013:i:5:p:521-526 is not listed on IDEAS
    12. Will Hicks, 2018. "Nonlocal Diffusions and The Quantum Black-Scholes Equation: Modelling the Market Fear Factor," Papers 1806.07983, arXiv.org, revised Jun 2018.
    13. Guevara Hidalgo, Esteban, 2006. "Quantum Replicator Dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 393-407.
    14. Piotrowski, Edward W. & Sładkowski, Jan, 2005. "Quantum diffusion of prices and profits," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 345(1), pages 185-195.
    15. Alonso-Sanz, Ramón & Martin-Gutierrez, Samuel, 2020. "The free-rider in the quantum Stackelberg duopoly game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    16. Pakuła, Ireneusz & Piotrowski, Edward W. & Sładkowski, Jan, 2007. "Universality of measurements on quantum markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(1), pages 397-405.
    17. Brandon Almy & Joachim I. Krueger, 2013. "Game interrupted: The rationality of considering the future," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 8(5), pages 521-526, September.
    18. Edward Piotrowski & Jan Sładkowski, 2004. "Quantum games in finance," Quantitative Finance, Taylor & Francis Journals, vol. 4(6), pages 61-67.
    19. Edward W. Piotrowski & Jan Sladkowski, "undated". "Quantum solution to the Newcomb's paradox," Departmental Working Papers 10, University of Bialtystok, Department of Theoretical Physics.
    20. Thomas Boyer-Kassem & Sébastien Duchêne & Eric Guerci, 2016. "Quantum-like models cannot account for the conjunction fallacy," Theory and Decision, Springer, vol. 81(4), pages 479-510, November.
    21. Wang Yijia & Wang Zhijian, 2023. "Pulse in collapse: a game dynamics experiment," Papers 2302.09336, arXiv.org.

    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:pone00:0029015. 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.