Quantum Information Processing

, Volume 14, Issue 10, pp 3639–3659 | Cite as

A cellular automaton implementation of a quantum battle of the sexes game with imperfect information

  • Ramón Alonso-Sanz


The dynamics of a spatial quantum formulation of the iterated battle of the sexes game with imperfect information is studied in this work. The game is played with variable entangling in a cellular automata manner, i.e. with local and synchronous interaction. The effect of spatial structure is assessed in fair and unfair scenarios.


Quantum games Bayesian games Entangling Cellular automata 



This work was supported by the Spanish Grant M2012-39101-C02-01. Part of the computations were performed in the HPC machines EOLO and FISWULF, based on the International Campus of Excellence of Moncloa, funded by the Spanish Government and Feder funds.


  1. 1.
    Alonso-Sanz, R.: Variable entangling in a quantum prisoner’s dilemma cellular automaton. Quantum Inf. Process. 14(1), 147–164 (2015)MathSciNetCrossRefADSzbMATHGoogle Scholar
  2. 2.
    Alonso-Sanz, R.: A quantum prisoner’s dilemma cellular automaton. Proc. R. Soc. A 470, 20130793 (2014)MathSciNetCrossRefADSGoogle Scholar
  3. 3.
    Alonso-Sanz, R.: Variable entangling in a quantum battle of the sexes cellular automaton. LNCS 8751, pp. 125–135 (2014)Google Scholar
  4. 4.
    Alonso-Sanz, R.: On a three-parameter quantum battle of the sexes cellular automaton. Quantum Inf. Process. 12(5), 1835–1850 (2013)MathSciNetCrossRefADSzbMATHGoogle Scholar
  5. 5.
    Alonso-Sanz, R.: A quantum battle of the sexes cellular automaton. Proc. R. Soc. A 468, 3370–3383 (2012)MathSciNetCrossRefADSGoogle Scholar
  6. 6.
    Alonso-Sanz, R.: Dynamical Systems with Memory. World Scientific Pub, Singapore (2011)zbMATHGoogle Scholar
  7. 7.
    Benjamin, S.C., Hayden, P.M.: Comment on “Quantum games and quantum strategies”. Phys. Rev. Lett. 87(6), 069801 (2001)CrossRefADSGoogle Scholar
  8. 8.
    Bleiler, S.: A formalism for quantum games and an application. (2008)
  9. 9.
    Branderburger, A.: The relationship between quantum and classical correlation games. Games Econ. Behav. 89, 157–183 (2010)MathSciNetGoogle Scholar
  10. 10.
    Cheon, T., Iqbal, A.: Bayesian Nash equilibria and bell inequalities. J. Phys. Soc. Jpn. 77(2), 024801 (2008). doi: 10.1143/JPSJ.77.024801
  11. 11.
    Du, J., Ju, C., Li, H.: Quantum entanglement helps in improving economic efficiency. J. Phys. A Maths. Gen. 38, 1559–1565 (2005)MathSciNetCrossRefADSzbMATHGoogle Scholar
  12. 12.
    Du, J.F., Xu, X.D., Li, H., Zhou, X., Han, R., et al.: Entanglement playing a dominating role in quantum games. Phys. Lett. A 89(1–2), 9–15 (2001)MathSciNetCrossRefADSzbMATHGoogle Scholar
  13. 13.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Eisert, J., Wilkens, M., Lewenstein, M.: Quantum games and quantum strategies. Phys. Rev. Lett. 83(15), 3077–3080 (1999)MathSciNetCrossRefADSzbMATHGoogle Scholar
  15. 15.
    Flitney, A.P., Abbott, D.: Advantage of a quantum player over a classical one in \(2\times 2\) quantum games. Proc. R. Soc. Lond. A 459(2038), 2463–2474 (2003)MathSciNetCrossRefADSzbMATHGoogle Scholar
  16. 16.
    Flitney. A.P., Abbott, D.: An Introduction to quantum game theory. Fluct. Noise Lett. 02, R175. (2002)
  17. 17.
    Frackiewicz, P.: A new quantum scheme for normal-form games. Process. Quantum Inf. (2015). doi: 10.1007/s11128-015-0979-z
  18. 18.
    Iqbal, A., Chappell, J.M., Li, Q., Pearce, C.E.M., Abbott, D.: A probabilistic approach to quantum Bayesian games of incomplete information. Quantum Inf. Process. 13(12), 2783–2800 (2014)MathSciNetCrossRefADSzbMATHGoogle Scholar
  19. 19.
    Khan, F.S.: Dominant Strategies in Two Qubit Quantum Computations. (2014)
  20. 20.
    Khan, F.S., Phoenix, S.J.D.: Mini-maximizing two qubit quantum computations. Quantum Inf. Process. 12(12), 3807–3819 (2013)MathSciNetCrossRefADSzbMATHGoogle Scholar
  21. 21.
    Khan, F.S., Phoenix, S.J.D.: Gaming the quantum. Quantum Inf. Comput. 13(3–4), 231–244 (2013)MathSciNetGoogle Scholar
  22. 22.
    Landsburg, S.E.: Quantum game theory. To appear in the The Wiley Encyclopedia of Operations Research and Management Science. (2011)
  23. 23.
    Landsburg, S.E.: Quantum game theory. Notices of the AMS. (2004)
  24. 24.
    Levine, D.K.: Quantum games have no news for economists. (2005)
  25. 25.
    Marinatto, L., Weber, T.: A quantum approach to static games of complete information. Phys. Lett. A 272, 291–303 (2000)MathSciNetCrossRefADSzbMATHGoogle Scholar
  26. 26.
    Meyer, D.A.: Quantum strategies. Phys. Rev. Lett. 82, 1052–1055 (1999)MathSciNetCrossRefADSzbMATHGoogle Scholar
  27. 27.
    Miszczak, J.A., Pawela, L., Sladkowski, J.: General model for an entanglement-enhanced composed quantum game on a two-dimensional lattice. Fluct. Noise Lett. 13(2) 1450012 (2014)
  28. 28.
    Nawaz, A., Toor, A.H.: Dilemma and quantum battle of sexes. J. Phys. A Math. Gen. 37(15), 4437 (2004)MathSciNetCrossRefADSzbMATHGoogle Scholar
  29. 29.
    Nawaz, A., Toor, A.H.: Generalized quantization scheme for two-person non-zero sum games. J. Phys. A Math. Gen. 37(47), 11457 (2004)MathSciNetCrossRefADSzbMATHGoogle Scholar
  30. 30.
    Osborne, M.J., Rubinstein, A.: A Course in Game Theory. MIT Press, Cambridge (1994)zbMATHGoogle Scholar
  31. 31.
    Owen, G.: Game Theory. Academic Press, New York (1995)zbMATHGoogle Scholar
  32. 32.
    Pappa, A., Kumar, N., Lawson, T., Santha, M., Zhang, S., Diamanti, E., Kerenidis, I.: Nonlocality and conflicting interest games. Phys. Rev. Lett. 114, 020401 (2015)CrossRefADSGoogle Scholar
  33. 33.
    Phoenix, S.J.D., Khan, F.S.: The role of correlations in classical and quantum games. Fluct. Noise Lett. 12(3), 1350011 (2013)CrossRefGoogle Scholar
  34. 34.
    Piotrowski, E.W., Sladkowski, J.: An invitation to quantum game theory. Int. J. Theor. Phys. 42(5), 1089–1099 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Situ, H.: A quantum approach to play asymmetric coordination games. Quantum Inf. Process. 13(3), 591–599 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Situ, H.: Quantum Bayesian game with symmetric and asymmetric information. Quantum Inf. Process. 14(6), 1827–1840 (2015)Google Scholar
  37. 37.
    Wiesner, K.: Quantum cellular automata. Encycl. Complex. Syst. Sci. 7154–7164. (2009)

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Technical University of MadridETSIA (Estadística, GSC). C. UniversitariaMadridSpain

Personalised recommendations