Skip to main content

Advertisement

Springer Nature Link
Log in

Influence of initial conditions in \(2\times 2\) symmetric games

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

It is known that quantum game is characterized by the payoff matrix as well as initial states of the quantum objects used as carriers of information in a game. Further, the initial conditions of the quantum states influence the strategies adopted by the quantum players. In this paper, we identify the necessary condition on the initial states of quantum objects for converting symmetric games into potential games, in which the players acquire the same payoff matrix. The necessary condition to preserve the symmetric type and potential type of the game is found to be the same. The present work emphasizes the influence of the initial states in the quantization of games.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

References

  1. Meyer, D.A.: Quantum strategies. Phys. Rev. Lett. 82, 1052–1055 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Guo, Hong, Zhang, Juheng, Koehler, G.J.: A survey of quantum games. Decis. Supp. Syst. 46, 318–332 (2008)

    Article  Google Scholar 

  3. Eisert, J., Wilkens, M., Lewenstein, M.: Quantum games and quantum strategies. Phys. Rev. Lett. 83, 3077–3080 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. Marinatto, L., Weber, T.: A quantum approach to static games of complete information. Phys. Letts. A. 272, 291–303 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Nawaz, A., Toor, A.H.: Generalized quantization scheme for two-person non-zero sum games. J. Phys. A 37, 11457–11464 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Benjamin, S.C.: Comment on “A quantum approach to static games of complete information”. Phys. Lett. A 277, 180–182 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. van Enk, S.J.: Quantum and classical game strategies. Phys. Rev. Lett. 84, 789 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. Bleiler, S.A.: A formalism for quantum games and an application. preprint arxiv:0808.1389v1[quantph]

  9. Khan, F.S., Phoenix, S.J.D.: Gaming the quantum. Quantum Inf. Comput. 13(3 & 4), 231–244 (2013)

    MathSciNet  Google Scholar 

  10. Khan, F.S., Phoenix, S.J.D.: Mini-maximizing two qubit quantum computations. Quantum Inf. Process. 12, 3807–3819 (2013)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. Pykacz, Jarosław, Frackiewicz, Piotr: Arbiter as the third man in classical and quantum games. Int. J. Theor. Phys. 49(12), 3243–3249 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. van Enk, S.J., Pike, R.: Classical rules in quantum games. Phys. Rev. A 66, 024306 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  13. Balakrishnan, S., Sankaranarayanan, R.: Classical rules and quantum strategies in penny flip game. Quantum Inf. Process. 12, 1261–1268 (2013)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. Szabó, G., Fáth, G.: Evolutionary games on graphs. Phys. Rep. 446, 97–216 (2007)

    Article  MathSciNet  ADS  Google Scholar 

Download references

Acknowledgments

Author acknowledges the anonymous reviewer for critical suggestions which brought this work to the present form.

Author information

Authors and Affiliations

  1. Materials Physics Division, School of Advanced Sciences, VIT University, Vellore, 632014, India

    S. Balakrishnan

Authors
  1. S. Balakrishnan
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to S. Balakrishnan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Balakrishnan, S. Influence of initial conditions in \(2\times 2\) symmetric games. Quantum Inf Process 13, 2645–2651 (2014). https://doi.org/10.1007/s11128-014-0820-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-014-0820-0

Keywords