International Journal of Theoretical Physics

, Volume 55, Issue 10, pp 4310–4323 | Cite as

A Quantum Relativistic Prisoner’s Dilemma Cellular Automaton

  • Ramón Alonso-Sanz
  • Márcio Carvalho
  • Haozhen Situ


The effect of variable entangling on the dynamics of a spatial quantum relativistic formulation of the iterated prisoner’s dilemma game is studied in this work. The game is played in the cellular automata manner, i.e., with local and synchronous interaction. The game is assessed in fair and unfair contests.


Quantum games Entangling Unruh effect Cellular automata 


  1. 1.
    Alonso-Sanz, R.: A cellular automaton implementation of a quantum battle of the sexes game with imperfect information. Quantum Inf. Process 14(10), 3639–3659 (2015)ADSMathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Alonso-Sanz, R.: Variable entangling in a quantum prisoner’s dilemma cellular automaton. Quantum Inf. Process 14(1), 147–164 (2015)ADSMathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Alonso-Sanz, R.: A quantum prisoner’s dilemma cellular automaton. Proc. R. Soc. A 470, 20130793 (2014)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Alonso-Sanz, R.: On a three-parameter quantum battle of the sexes cellular automaton. Quantum Information Processing 12(5), 1835–1850 (2013)ADSMathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Alonso-Sanz, R.: A quantum battle of the sexes cellular automaton. Proc. R. Soc. A 468, 3370–3383 (2012)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Alonso-Sanz, R.: Dynamical Systems with Memory. World Scientific Pub (2011)Google Scholar
  7. 7.
    Alsing, P.M., Fuentes-Schuller, I., Mann, R.B., Tessier, T.E.: Phys. Rev. A 032326, 74 (2006)Google Scholar
  8. 8.
    Du, J.F., Xu, X.D., Li, H., Zhou, X., Han, R.: Entanglement playing a dominating role in quantum games. Phys. Lett. A 89(1–2), 9–15 (2001)ADSMathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Du, J.F., Li, H., Xu, X.D., Zhou, X., Han, R.: Phase-transition-like behaviour of quantum games. J. Phys. A Math. Gen. 36(23), 6551–6562 (2003)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Eisert, J., Wilkens, M., Lewenstein, M.: Quantum games and quantum strategies. Phys. Rev. Lett. 83(15), 3077–3080 (1999)ADSMathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Eisert, J., Wilkens, M.: Quantum Games. J. Mod. Opt. 47(14–15), 2543–2556 (2000)ADSMathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Flitney, A.P., Abbott, D.: Advantage of a quantum player over a classical one in 2x2 quantum games. Proc. R. Soc. Lond. A 459(2038), 2463–2474 (2003)ADSMathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Khan, S., Khan, M.K.: Noisy relativistic quantum games in noninertial frames. Quantum Inf. Process 12(2), 1351–1363 (2013)ADSCrossRefMATHGoogle Scholar
  14. 14.
    Khan, S., Khan, M.K.: Relativistic quantum games in noninertial frames. J. Phys. A: Math. Theor. 44, 355302 (2011)ADSCrossRefMATHGoogle Scholar
  15. 15.
    Marinatto, L., Weber, T.: A quantum approach to static games of complete information. Phys. Lett. A 272, 291–303 (2000)ADSMathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Nawaz, A., Toor, A.H.: Dilemma and quantum battle of sexes. J. Phys. A Math. Gen. 37(15), 4437–4443 (2004)ADSMathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Nawaz, A., Toor, A.H.: Generalized quantization scheme for two-person non-zero sum games. J. Phys. A Math. Gen. 37(42), 365305 (2004)MathSciNetMATHGoogle Scholar
  18. 18.
    Owen, G.: Game Theory. (Academic Press) (1995)Google Scholar
  19. 19.
    Schiff, J.L.: Cellular automata : A discrete view of the world. Wiley (2008)Google Scholar
  20. 20.
    Situ, H.Z., Huang, Z.M.: Relativistic Quantum Bayesian Game Under Decoherence. Int. J. Theor. Phys. 55, 2354–2363 (2016). doi:10.1007/s10773-015-2873-y
  21. 21.
    Situ, H.Z.: A quantum approach to play asymmetric coordination games. Quantum Inf. Process 13, 591–599 (2014)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Situ, H.Z.: Quantum Bayesian game with symmetric and asymmetric information. Quantum Inf. Process 14, 1827–1840 (2015)ADSMathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Situ, H.Z.: Two-player conflicting interest Bayesian games and Bell nonlocality. Quantum Inf. Process 15, 137–145 (2016)ADSMathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Situ, H.Z., Zhang, C., Yu, F.: Quantum advice enhances social optimality in three-party conflicting interest games 15, 558–596 (2016). arXiv:hep-th/1510.06918
  25. 25.
    Takagi, S.: Prog. Theor. Phys. Suppl. 88, 1 (1986)ADSCrossRefGoogle Scholar
  26. 26.
    Weng, G., Yu, Y.: A quantum battle of the sexes in noninertial frame. J. Mod. Phys. 5, 9 (2014). doi:10.4236/jmp.2014.59094 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Ramón Alonso-Sanz
    • 1
  • Márcio Carvalho
    • 1
  • Haozhen Situ
    • 2
  1. 1.Technical University of Madrid,ETSIA (Estadística, GSC). C.UniversitariaMadridSpain
  2. 2.College of Mathematics and InformaticsSouth China Agricultural UniversityGuangzhouChina

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