Quantum Information Processing

, Volume 13, Issue 12, pp 2645–2651 | Cite as

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

  • S. Balakrishnan


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.


Quantum game Symmetric games Potential games  Quantum strategy 



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


  1. 1.
    Meyer, D.A.: Quantum strategies. Phys. Rev. Lett. 82, 1052–1055 (1999)MathSciNetCrossRefADSMATHGoogle Scholar
  2. 2.
    Guo, Hong, Zhang, Juheng, Koehler, G.J.: A survey of quantum games. Decis. Supp. Syst. 46, 318–332 (2008)CrossRefGoogle Scholar
  3. 3.
    Eisert, J., Wilkens, M., Lewenstein, M.: Quantum games and quantum strategies. Phys. Rev. Lett. 83, 3077–3080 (1999)MathSciNetCrossRefADSMATHGoogle Scholar
  4. 4.
    Marinatto, L., Weber, T.: A quantum approach to static games of complete information. Phys. Letts. A. 272, 291–303 (2000)MathSciNetCrossRefADSMATHGoogle Scholar
  5. 5.
    Nawaz, A., Toor, A.H.: Generalized quantization scheme for two-person non-zero sum games. J. Phys. A 37, 11457–11464 (2004)MathSciNetCrossRefADSMATHGoogle Scholar
  6. 6.
    Benjamin, S.C.: Comment on “A quantum approach to static games of complete information”. Phys. Lett. A 277, 180–182 (2000)MathSciNetCrossRefADSMATHGoogle Scholar
  7. 7.
    van Enk, S.J.: Quantum and classical game strategies. Phys. Rev. Lett. 84, 789 (2000)MathSciNetCrossRefADSMATHGoogle Scholar
  8. 8.
    Bleiler, S.A.: A formalism for quantum games and an application. preprint arxiv:0808.1389v1[quantph]
  9. 9.
    Khan, F.S., Phoenix, S.J.D.: Gaming the quantum. Quantum Inf. Comput. 13(3 & 4), 231–244 (2013)MathSciNetGoogle Scholar
  10. 10.
    Khan, F.S., Phoenix, S.J.D.: Mini-maximizing two qubit quantum computations. Quantum Inf. Process. 12, 3807–3819 (2013)MathSciNetCrossRefADSMATHGoogle Scholar
  11. 11.
    Pykacz, Jarosław, Frackiewicz, Piotr: Arbiter as the third man in classical and quantum games. Int. J. Theor. Phys. 49(12), 3243–3249 (2010)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    van Enk, S.J., Pike, R.: Classical rules in quantum games. Phys. Rev. A 66, 024306 (2002)MathSciNetCrossRefADSGoogle Scholar
  13. 13.
    Balakrishnan, S., Sankaranarayanan, R.: Classical rules and quantum strategies in penny flip game. Quantum Inf. Process. 12, 1261–1268 (2013)MathSciNetCrossRefADSMATHGoogle Scholar
  14. 14.
    Szabó, G., Fáth, G.: Evolutionary games on graphs. Phys. Rep. 446, 97–216 (2007)MathSciNetCrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Materials Physics Division, School of Advanced SciencesVIT UniversityVelloreIndia

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